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| author | Thomas Stephen Lee | 2015-08-28 16:53:23 +0530 |
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| committer | Thomas Stephen Lee | 2015-08-28 16:53:23 +0530 |
| commit | db0855dbeb41ecb8a51dde8587d43e5d7e83620f (patch) | |
| tree | b95975d958cba9af36cb1680e3f77205354f6512 /Applied_Physics-I_by_I_A_Shaikh | |
| parent | 5a86a20b9de487553d4ef88719fb0fd76a5dd6a7 (diff) | |
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diff --git a/Applied_Physics-I_by_I_A_Shaikh/Chapter1.ipynb b/Applied_Physics-I_by_I_A_Shaikh/Chapter1.ipynb new file mode 100755 index 00000000..da15fd14 --- /dev/null +++ b/Applied_Physics-I_by_I_A_Shaikh/Chapter1.ipynb @@ -0,0 +1,2515 @@ +{ + "metadata": { + "celltoolbar": "Raw Cell Format", + "name": "", + "signature": "sha256:c884249c28dc1486b445f3d4013b1d4277c7f2f132398c648a2fa82d33db0def" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 1: Crystallography" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.3.1,Page number 1-14" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "A=26.98 #atomic weight of Al\n", + "N=6.023*10**26 #Avogadro's number\n", + "p=2700 #Density\n", + "n=4 #FCC structure\n", + "\n", + "a=(n*A/(N*p))**(1./3)\n", + "\n", + "print\"Unit cell dimension of Al=\",\"{0:.3e}\".format(a),\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Unit cell dimension of Al= 4.049e-10 m\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.3.2,Page number 1-15" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "As=28.1 #atomic weight of Si\n", + "Ag=69.7 #atomic weight of Ga\n", + "Aa=74.9 #atomic weight of As\n", + "a_s=5.43*10**-8 #lattice constant of Si\n", + "aga=5.65*10**-8 #lattice constant of GaAs\n", + "ns=8 #no of atoms/unit cell in Si\n", + "nga=4 #no of atoms/unit cell in GaAs\n", + "N=6.023*10**23 #Avogadro's number\n", + "\n", + "#p=(n*A)/(N*a**3) this is formula for density\n", + "\n", + "#for Si\n", + "\n", + "ps=(ns*As)/(N*a_s**3)\n", + "\n", + "print\"1) Density of Si=\",round(ps,4),\"gm/cm^3\"\n", + "\n", + "#for GaAs\n", + "\n", + "Aga=Ag+Aa #molecular wt of GaAs\n", + "\n", + "pga=(nga*Aga)/(N*aga**3)\n", + "\n", + "print\"2) Density of GaAs=\",round(pga,4),\"gm/cm^3\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Density of Si= 2.3312 gm/cm^3\n", + "2) Density of GaAs= 5.3244 gm/cm^3\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.3.3,Page number 1-16" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "A=63.5 #atomic weight of Cu\n", + "N=6.023*10**23 #Avogadro's number\n", + "n=4 #FCC structure\n", + "r=1.28*10**-8 #atomic radius of Cu\n", + "\n", + "#for FCC\n", + "\n", + "a=4*r/(sqrt(2)) #lattice constant\n", + "p=(n*A)/(N*a**3)\n", + "\n", + "print\"Density of Cu=\",round(p,4),\"gm/cm^3\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Density of Cu= 8.887 gm/cm^3\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.3.4,Page number 1-17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "A=50 #atomic weight of chromium\n", + "N=6.023*10**23 #Avogadro's number\n", + "p=5.96 #Density\n", + "n=2 #BCC structure\n", + "\n", + "#step 1 : claculation for lattice constant (a)\n", + "\n", + "a=(n*A/(N*p))**(1./3)\n", + "\n", + "#step 2 : radius of an atom in BCC\n", + "\n", + "r=sqrt(3)*a/4\n", + "\n", + "#step 3 : Atomic packing factor (APF)\n", + "\n", + "APF=n*((4./3)*math.pi*r**3)/a**3\n", + "\n", + "print\"Atomic packing factor (APF)=\",round(APF,4)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Atomic packing factor (APF)= 0.6802\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.3.5,Page number 1-17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "A=120 #atomic weight of chromium\n", + "N=6.023*10**23 #Avogadro's number\n", + "p=5.2 #Density\n", + "n=2 #BCC structure\n", + "m=20 #mass\n", + "\n", + "#step 1 : claculation for volume of unit cell(a**3)\n", + "\n", + "a=(n*A/(N*p))\n", + "\n", + "#step 2 : volume of 20 gm of the element\n", + "\n", + "v=m/p\n", + "\n", + "#step 3 :no of unit cell\n", + "\n", + "x=v/a\n", + "\n", + "print\"no of unit cell=\",\"{0:.3e}\".format(x)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "no of unit cell= 5.019e+22\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.3.6,Page number 1-18" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "A=132.91 #atomic weight of chromium\n", + "N=6.023*10**26 #Avogadro's number\n", + "p=1900 #Density\n", + "a=6.14*10**-10 #lattice constant\n", + "\n", + "#step 1 : type of structure\n", + "\n", + "n=(p*N*a**3)/A\n", + "\n", + "print\"n =\",round(n)\n", + "\n", + "print\"BCC structure\"\n", + "\n", + "#step 2: no of atoms/m**3\n", + "\n", + "x=n/a**3\n", + "\n", + "print\"no of atoms/m^3=\",\"{0:.3e}\".format(x)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "n = 2.0\n", + "BCC structure\n", + "no of atoms/m^3= 8.610e+27\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.3.7,Page number 1-18" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "a=0.4049*10**-9 #lattice constant\n", + "t=0.006*10**-2 #thickness of Al foil\n", + "A=50*10**-4 #Area of foil\n", + "\n", + "V1=a**3 #volume of unit cell\n", + "\n", + "V=A*t #volume of the foil\n", + "\n", + "N=V/V1 #no of unit cell in the foil\n", + "\n", + "print\"no of unit cell in the foil=\",\"{0:.3e}\".format(N)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "no of unit cell in the foil= 4.519e+21\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.5.1,Page number 1-29" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#refer diagram from textbook\n", + "\n", + "#on joining centre of 3 anions,an equilateral triangle is formed and on joining centres of any anion and cation a right angle triangle ABC os formed\n", + "\n", + "#where AC=rc+ra\n", + "\n", + "#and BC=ra\n", + "\n", + "#m(angle (ACB))=30 degree\n", + "\n", + "#therefore cos (30)=ra/(rc+ra)\n", + "\n", + "#assume rc/ra=r\n", + "\n", + "r=(1.0-math.cos(30.0*math.pi/180))/math.cos(math.pi*30/180) #by arrangimg terms we get value of r\n", + "\n", + "print\"critical radius ratio of ligancy 3=\",round(r,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "critical radius ratio of ligancy 3= 0.1547\n" + ] + } + ], + "prompt_number": 33 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.5.2,Page number 1-30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#refer diagram from textbook\n", + "\n", + "#in the said arrangement a cation is squeezed into 4 anions in a plane and 5th anion is in upper layer and 6th in bottom layer \n", + "\n", + "#join cation anion centres E and B and complete the triangle EBF\n", + "\n", + "#in triangle EBF m(angle F)=90 and EF=BF\n", + "\n", + "#m(angle B)=m(angle E)=45\n", + "\n", + "#and EB=rc+ra and BF=ra\n", + "\n", + "#cos(45)=ra/(rc+ra)\n", + "\n", + "#assume rc/ra=r\n", + "\n", + "r=(1-math.cos(45*math.pi/180))/math.cos(45*math.pi/180) #by arrangimg terms we get value of r\n", + "\n", + "print\"critical radius ratio for ligancy 6 =\",round(r,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.5.3,Page number 1-30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#refer diagram from textbook\n", + "\n", + "#since plane is square hence it is same as ligancy 6\n", + "\n", + "#in the said arrangement a cation is squeezed into 4 anions in a plane and 5th anion is in upper layer and 6th in bottom layer \n", + "\n", + "#join cation anion centres E and B and complete the triangle EBF\n", + "\n", + "#in triangle EBF m(angle F)=90 and EF=BF\n", + "\n", + "#m(angle B)=m(angle E)=45\n", + "\n", + "#and EB=rc+ra and BF=ra\n", + "\n", + "#cos(45)=ra/(rc+ra)\n", + "\n", + "#assume rc/ra=r\n", + "\n", + "r=(1-math.cos(45*math.pi/180))/math.cos(45*math.pi/180) #by arrangimg terms we get value of r\n", + "\n", + "print\"critical radius ratio for ligancy 8 =\",round(r,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "critical radius ratio for ligancy 8 = 0.4142\n" + ] + } + ], + "prompt_number": 38 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.5.4,Page number 1-31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#a tetrahedron CAEH can be considered with C as the apex of the tetrahedron.\n", + "\n", + "#the edges AE,AH and EH of the tetrahedron will then be the face of the cube faces ABEF,ADHF,EFHG resp.\n", + "\n", + "#from fig\n", + "\n", + "#AO=ra+rc and AJ=ra\n", + "\n", + "#AE=root(2)*a and AG=root(3)*a\n", + "\n", + "#AO/AJ=AG/AE=(ra+rc)/ra=root(3)*a/root(2)*a\n", + "\n", + "#assume rc/ra=r\n", + "r=(math.sqrt(3)-math.sqrt(2))/math.sqrt(2)\n", + "\n", + "print\"critical radius ratio for ligancy 4 = \",round(r,4)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "critical radius ratio for ligancy 4 = 0.2247\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.5.5,Page number 1-32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#ligancy 8 represents cubic arrangment .8 anions are at the corners and touch along cube edgs.Along the body diagonal the central cation and the corner anion are in contact.\n", + "\n", + "#cube edge=2*ra\n", + "\n", + "#refer diagram from textbook\n", + "\n", + "#and body diagonal=root(3)*cube edge=root(3)[2*(rc+ra)]\n", + "\n", + "#assume rc/ra=r\n", + "\n", + "r=math.sqrt(3)-1.0\n", + "\n", + "print\"critical radius ratio of ligancy 8=\",round(r,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "critical radius ratio of ligancy 8= 0.7321\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.5.6,Page number 1-32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#for an ionic crystal exibiting HCP structure the arrangment of ions refere from textbook\n", + "\n", + "#at centre we have a cation with radius rc=OA\n", + "\n", + "#it is an touch with 6 anions with radius ra=AB\n", + "\n", + "#OB=OC=ra+rc\n", + "\n", + "#intrangle ODB ,m(angle (OBC))=60 degree ,m(angle (ODB))=90 degree\n", + "\n", + "#therefore cos(60)=BD/OB=AB/(OA+OB)=ra/(rc+ra)\n", + "\n", + "#assume rc/ra=r\n", + "\n", + "r=(1.-math.cos(60*math.pi/180))/math.cos(60*math.pi/180) #by arrangimg terms we get value of r\n", + "\n", + "print\"critical radius ratio 0f HCP structure=\",round(r,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "critical radius ratio 0f HCP structure= 1.0\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.6.2,Page number 1-35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#intercept of planeare in proportion a,b/3,2*c\n", + "\n", + "#as a,b and c are basic vectors the proportin of intercepts 1:1/3:2\n", + "\n", + "#therefore reciprocal\n", + "\n", + "r1=1\n", + "\n", + "r2=3\n", + "\n", + "r3=1./2\n", + "\n", + "#taking LCM of 2 and 1 is 2\n", + "\n", + "l=2\n", + "\n", + "m1=(l*r1)\n", + "\n", + "m2=(l*r2)\n", + "\n", + "m3=(l*r3)\n", + "\n", + "print\"miler indices=\",m3,m2,m1\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "miler indices= 1.0 6 2\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.6.4,Page number 1-38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "r=1.414 #atomic radius in amstrong unit\n", + "\n", + "#for FCC structure\n", + "\n", + "a=4*r/math.sqrt(2)\n", + "\n", + "#part 1: plane(2,0,0)\n", + "\n", + "#the interplanar spacing of plane\n", + "\n", + "h1=2\n", + "k1=0\n", + "l1=0\n", + "\n", + "#we know that d=a/sqrt(h**2+k**2+l**2)\n", + "\n", + "d1=a/sqrt(h1**2+k1**2+l1**2)\n", + "\n", + "print\"1)interplanar spacing for (2,0,0) plane=\",round(d1,4),\"amstrong\"\n", + "\n", + "#part 2: plane(1,1,1)\n", + "\n", + "#the interplanar spacing of plane\n", + "\n", + "h2=1\n", + "k2=1\n", + "l2=1\n", + "\n", + "#we know that d=a/sqrt(h**2+k**2+l**2)\n", + "\n", + "d2=a/sqrt(h2**2+k2**2+l2**2)\n", + "\n", + "print\"2)interplanar spacing for(1,1,1) plane=\",round(d2,4),\"amstrong\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)interplanar spacing for (2,0,0) plane= 1.9997 amstrong\n", + "2)interplanar spacing for(1,1,1) plane= 2.3091 amstrong\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.1,Page number 1-58" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=4 #FCC structure\n", + "ro=2180 #density of NaCl\n", + "M=23+35.5 #molecular weight of NaCl\n", + "N=6.023*10**26 #Avogadro's number\n", + "\n", + "a=((n*M)/(N*ro))**(1.0/3)\n", + "\n", + "print\"Lattice constant=\",\"{0:.3e}\".format(a),\"m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Lattice constant= 5.627e-10 m\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.2,Page number 1-58" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=4 #FCC structure\n", + "ro=8.9 #density of Cu atom\n", + "A=63.55 #atomic weight of Cu atom\n", + "N=6.023*10**23 #Avogadro's number\n", + "\n", + "a=((n*A)/(N*ro))**(1./3)\n", + "\n", + "print\"1) Lattice constant=\",\"{0:.3e}\".format(a),\"cm\"\n", + "\n", + "r=math.sqrt(2)*a/4 #radius of Cu atom\n", + "\n", + "d=2*r #diameter of Cu atom\n", + "\n", + "print\"2) Diameter of Cu atom=\",\"{0:.3e}\".format(d),\"cm\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Lattice constant= 3.620e-08 cm\n", + "2) Diameter of Cu atom= 2.559e-08 cm\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.3,Page number 1-59" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=8 #diamond structure\n", + "A=12.01 #atomic wt\n", + "N=6.023*10**23 #Avogadro's number\n", + "a=3.75*10**-8 #lattice constant of diamond\n", + "\n", + "ro=(n*A)/(N*(a**3))\n", + "\n", + "print\"Density of diamond=\",round(ro,4),\"gm/cc\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Density of diamond= 3.025 gm/cc\n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.4,Page number 1-59" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#intercept of planeare in proportion 3a:4b:infinity (plane parallel to z axis)\n", + "\n", + "#as a,b and c are basic vectors the proportin of intercepts 3:4:infinity\n", + "\n", + "#therefore reciprocal\n", + "\n", + "r1=1./3\n", + "r2=1./4\n", + "r3=0\n", + "\n", + "#taking LCM of 3 and 4 i.e. 12\n", + "\n", + "l=12\n", + "\n", + "m1=(l*r1)\n", + "\n", + "m2=(l*r2)\n", + "\n", + "m3=(l*r3)\n", + "\n", + "print\"miler indices=\",(m3,m2,m1)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "miler indices= (0, 3.0, 4.0)\n" + ] + } + ], + "prompt_number": 29 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.5,Page number 1-59" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#intercept of planeare in proportion 3a:-2b:3/2c\n", + "\n", + "#as a,b and c are basic vectors the proportin of intercepts 3:-2:3/2\n", + "\n", + "#therefore reciprocal\n", + "\n", + "r1=1./3\n", + "r2=-1./2\n", + "r3=2./3\n", + "\n", + "#taking LCM of 3, 2 and 3/2 is 6\n", + "\n", + "l=6\n", + "\n", + "m1=(l*r1)\n", + "\n", + "m2=(l*r2)\n", + "\n", + "m3=(l*r3)\n", + "\n", + "print\"miler indices=\",(m3,m2,m1)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "miler indices= (4.0, -3.0, 2.0)\n" + ] + } + ], + "prompt_number": 31 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.6,Page number 1-59" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#if a plane cut at length m,n,p on the three crystal axes,then\n", + "\n", + "#m:n:p=xa:yb:zc\n", + "\n", + "#when primitive vectors of unit cell and numbers x,y,z,are related to miller indices (h,k,l)of the plane by relation\n", + "\n", + "#1/x:1/y:1/z=h:k:l\n", + "\n", + "#since a=b=c (crystal is simple cubic)\n", + "\n", + "#and (h,k,l)=(1,2,3)\n", + "\n", + "#therefore reciprocal\n", + "\n", + "r1=1./1\n", + "r2=1./2\n", + "r3=1./3\n", + "\n", + "#taking LCM of 1 ,2 and 3 is 6\n", + "\n", + "l=6\n", + "\n", + "m=(l*r1)\n", + "\n", + "n=(l*r2)\n", + "\n", + "p=(l*r3)\n", + "\n", + "print\"ratio of intercepts=\",(m,n,p)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "ratio of intercepts= (6.0, 3.0, 2.0)\n" + ] + } + ], + "prompt_number": 35 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.7,Page number 1-60" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#primitive vectors\n", + "\n", + "a=1.2 #in amstrong unit\n", + "b=1.8 #in amstrong unit\n", + "c=2 #in amstrong unit\n", + "\n", + "#miller indices of the plane\n", + "\n", + "h=2\n", + "k=3\n", + "l=1\n", + "\n", + "#therefore intercepts are a/h,b/k,c/l\n", + "\n", + "x=a/h\n", + "y=b/k\n", + "z=c/l\n", + "\n", + "#this gives intercepts along x axis as x amstrong but it is given tthat plane cut x axis at 1.2 amstrong .\n", + "\n", + "t=1.2/x\n", + "\n", + "#this shows that the plane under consideration is another plane which is parallel to it(to keep miller indices same)\n", + "\n", + "n=t*y #Y intercept\n", + "\n", + "p=t*z #Z intercept\n", + "\n", + "print\"1) Y intercept=\",n,\"amstrong\"\n", + "\n", + "print\"2)Z intercept=\",p,\"amstrong\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Y intercept= 1.2 amstrong\n", + "2)Z intercept= 4.0 amstrong\n" + ] + } + ], + "prompt_number": 37 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.8,Page number 1-61" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#the interplanar spacing of plane\n", + "\n", + "h=1\n", + "k=1\n", + "l=0\n", + "d=2 #interpanar spacing in amstrong unit\n", + "\n", + "#we know that d=a/sqrt(h**2+k**2+l**2) therefore\n", + "\n", + "a=d*math.sqrt(h**2+k**2+l**2)\n", + "\n", + "#for FCC structure\n", + "\n", + "r=math.sqrt(2)*a/4\n", + "\n", + "print\"radius r=\",(r),\"amstrong\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "radius r= 1.0 amstrong\n" + ] + } + ], + "prompt_number": 39 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.9,Page number 1-61" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=4 #for FCC structure\n", + "\n", + "#the interplanar spacing of plane\n", + "\n", + "h=1\n", + "k=1\n", + "l=1\n", + "d=2.08*10**-10 #distance\n", + "A=63.54 #atomic weight of Cu\n", + "N=6.023*10**26 #amstrong no\n", + "\n", + "#we know that d=a/sqrt(h**2+k**2+l**2) therefore\n", + "\n", + "a=d*math.sqrt(h**2+k**2+l**2)\n", + "\n", + "#also (a**3*q)=n*A/N\n", + "\n", + "q=n*A/(N*a**3)\n", + "\n", + "print\"1)density=\",round(q,4),\"kg/m^3\"\n", + "\n", + "#for FCC structure\n", + "\n", + "r=math.sqrt(2)*a/4\n", + "\n", + "d=r*2\n", + "\n", + "print\"2)radius r=\",\"{0:.3e}\".format(r),\"m\"\n", + "\n", + "print\"3)diameter d=\",\"{0:.3e}\".format(d),\"m\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)density= 9024.4855 kg/m^3\n", + "2)radius r= 1.274e-10 m\n", + "3)diameter d= 2.547e-10 m\n" + ] + } + ], + "prompt_number": 44 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.10,Page number 1-62" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "A=63.546 #atomic weight of Cu\n", + "N=6.023*10**26 #Avogadro's number\n", + "p=8930 #Density\n", + "n=1.23 #no.of electron per atom\n", + "\n", + "#density=mass/volume\n", + "\n", + "#therfore 1/volume=density/mass\n", + "\n", + "#since electron concentration is needed, let us find out no of atoms/volume(x)\n", + "\n", + "x=N*p/A\n", + "\n", + "#now one atom contribute n=1.23 electron\n", + "\n", + "#therefore x atoms contribute y no of free electron\n", + "\n", + "y=x*n\n", + "\n", + "print\"free electron concentration=\",\"{0:.3e}\".format(y),\"electron/m^3\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "free electron concentration= 1.041e+29 electron/m^3\n" + ] + } + ], + "prompt_number": 46 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.11,Page number 1-62" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#primitive vectors\n", + "\n", + "a=1.5 #in amstrong unit\n", + "b=2 #in amstrong unit\n", + "c=4. #in amstrong unit\n", + "\n", + "#miller indices of the plane\n", + "\n", + "h=3\n", + "k=2\n", + "l=6\n", + "\n", + "#therefore intercepts are a/h,b/k,c/l\n", + "\n", + "x=a/h\n", + "y=b/k\n", + "z=c/l\n", + "\n", + "#this gives intercepts along x axis as x amstrong but it is given that plane cut x axis at 1.2 amstrong .\n", + "\n", + "t=1.5/x\n", + "\n", + "#this shows that the plane under consideration is another plane which is parallel to it(to keep miller indices same)\n", + "\n", + "n=t*y #Y intercept\n", + "\n", + "p=t*z #Z intercept\n", + "\n", + "print\"1) Y intercept=\",(n),\"amstrong\"\n", + "\n", + "print\"2)Z intercept=\",(p),\"amstrong\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Y intercept= 3.0 amstrong\n", + "2)Z intercept= 2.0 amstrong\n" + ] + } + ], + "prompt_number": 48 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.12,Page number 1-63" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "ro=7.87 #density of metal\n", + "A=55.85 #atomic wt of metal\n", + "N=6.023*10**23 #Avogadro's number\n", + "a=2.9*10**-8 #lattice constant of metal\n", + "\n", + "n=(N*(a**3)*ro)/A\n", + "\n", + "print\"Number of atom per unit cell of a metal=\",round(n,0)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of atom per unit cell of a metal= 2.0\n" + ] + } + ], + "prompt_number": 52 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.13,Page number 1-63" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=2 #BCC structure\n", + "ro=9.6*10**2 #density of sodium crystal\n", + "A=23 #atomic weight of sodium crystal\n", + "N=6.023*10**26 #Avogadro's number\n", + "\n", + "a=((n*A)/(N*ro))**(1./3)\n", + "\n", + "print\"Lattice constant=\",\"{0:.3e}\".format(a),\"m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Lattice constant= 4.301e-10 m\n" + ] + } + ], + "prompt_number": 50 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.15,Page number 1-64" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "ro=2.7*10**3 #density of metal\n", + "A=27 #atomic wt of metal\n", + "N=6.023*10**26 #Avogadro's number\n", + "a=4.05*10**-10 #lattice constant of metal\n", + "\n", + "n=(N*(a**3)*ro)/A\n", + "\n", + "print\"1) Number of atom per unit cell of a metal=\",round(n,0)\n", + "\n", + "r=math.sqrt(2)*a/4 #radius of metal\n", + "\n", + "print\"2) atomic radius of a metal=\",\"{0:.3e}\".format(r),\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Number of atom per unit cell of a metal= 4.0\n", + "2) atomic radius of a metal= 1.432e-10 m\n" + ] + } + ], + "prompt_number": 56 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.16,Page number 1-64" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=2 #BCC structure\n", + "ro=5.98*10**3 #density of chromium\n", + "A=50 #atomic wt of chromium\n", + "N=6.023*10**26 #Avogadro's number\n", + "\n", + "a=((n*A)/(N*ro))**(1./3)\n", + "\n", + "print\"1) Lattice constant=\",\"{0:.3e}\".format(a),\"m\"\n", + "\n", + "#for BCC\n", + "\n", + "r=math.sqrt(3)*a/4 #radius of chromium\n", + "\n", + "APF=(n*(4./3)*math.pi*(r**3))/(a**3)\n", + "\n", + "print\"2) A.P.F. for chromium=\",round(APF,4)\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Lattice constant= 3.028e-10 m\n", + "2) A.P.F. for chromium= 0.6802\n" + ] + } + ], + "prompt_number": 60 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.17,Page number 1-65" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=4 #FCC structure\n", + "ro=6250 #density\n", + "M=60.2 #molecular weight\n", + "N=6.023*10**26 #Avogadro's number\n", + "\n", + "a=((n*M)/(N*ro))**(1./3)\n", + "\n", + "print\"Lattice constant=\",\"{0:.3e}\".format(a),\"m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Lattice constant= 3.999e-10 m\n" + ] + } + ], + "prompt_number": 62 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.19,Page number 1-66" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "a=2.82*10**-9 #lattice constant\n", + "n=2 #FCC crystal\n", + "t=17.167 #glancing angle in degree\n", + "q=math.pi/180*t #glancing angle in radians\n", + "\n", + "#assuming reflection in (1,0,0) plane\n", + "\n", + "h=1\n", + "k=0\n", + "l=0\n", + "\n", + "d=a/math.sqrt(h**2+k**2+l**2)\n", + "\n", + "#using Bragg's law , 2*d*sin(q)=n*la\n", + "\n", + "la=2*d*sin(q)/n\n", + "\n", + "print\"wavlength of X-ray=\",\"{0:.3e}\".format(la),\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "wavlength of X-ray= 8.323e-10 m\n" + ] + } + ], + "prompt_number": 64 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.20,Page number 1-66" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=8 #Diamond structure\n", + "ro=2.33*10**3 #density of diamond\n", + "M=28.9 #atomic weight of diamond\n", + "N=6.023*10**26 #Avogadro's number\n", + "\n", + "a=((n*M)/(N*ro))**(1./3)\n", + "\n", + "print\"1) Lattice constant=\",\"{0:.3e}\".format(a),\"m\"\n", + "\n", + "r=math.sqrt(3)*a/8 #radius of diamond structure\n", + "\n", + "print\"2) atomic radius of a metal=\",\"{0:.3e}\".format(r),\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Lattice constant= 5.482e-10 m\n", + "2) atomic radius of a metal= 1.187e-10 m\n" + ] + } + ], + "prompt_number": 66 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.21,Page number 1-66" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=2 #BCC structure\n", + "ro=8.57*10**3 #density of chromium\n", + "d=2.86*10**-10 #nearest atoms distance\n", + "\n", + "#d=sqrt(3)/2*a\n", + "\n", + "a=2*d/math.sqrt(3)\n", + "\n", + "#now use formulae a**3*ro=n*A/N\n", + "\n", + "#therefore a**3*ro/n=mass of unit cell/(no of atoms pre unit cell)=mass of one atom\n", + "\n", + "m=a**3*ro/n\n", + "\n", + "print\"mass of one atom=\",\"{0:.3e}\".format(m),\"kg\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "mass of one atom= 1.543e-25 kg\n" + ] + } + ], + "prompt_number": 68 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.1,Page number 1-68" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "d=4.255*10**-10 #interplaner spacing\n", + "l=1.549*10**-10 #wavelength of x ray\n", + "\n", + "#part 1: for smallest glancing angle(n=1)\n", + "\n", + "n1=1\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "q=math.degrees(math.asin(n1*l/(2*d)))\n", + "\n", + "print\"1)glancing angle=\",round(q,4),\"degree\"\n", + "\n", + "#part 2: for highst order\n", + "\n", + "#for highest order sin(q) not exceed one i.e maximum value is one\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "n2=2*d/l #since sin(q)is one\n", + "\n", + "print\"2)highest order possible =\",math.floor(n2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)glancing angle= 10.4875 degree\n", + "2)highest order possible = 5.0\n" + ] + } + ], + "prompt_number": 70 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.2,Page number 1-69" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "a=2.125*10**-10 #lattice constant\n", + "d=a/2 #interplaner spacing\n", + "n=2 #second order maximum\n", + "l=0.592*10**-10 #wavelength of rock salt crystal\n", + "\n", + "#using Bragg's law\n", + "\n", + "q=math.degrees(math.asin((n*l)/(2*d))) #glancing angle\n", + "\n", + "print\"glancing angle=\",round(q,4),\"degree\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "glancing angle= 33.8608 degree\n" + ] + } + ], + "prompt_number": 72 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.3,Page number 1-69" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n1=1 #for 1st order\n", + "n2=2 #for 2nd order\n", + "t=3.4 #angle where 1st order reflection done\n", + "t1=t*math.pi/180 #convert degree to radian\n", + "\n", + "m=math.sin(t1)\n", + "\n", + "#but from Bragg's law\n", + "\n", + "#n*l=2*d*sin(t)\n", + "\n", + "#for for constant distance(d) and wavelength(l) \n", + "\n", + "#order(n) is directly proportionl to sine of angle i.e (sin(t))\n", + "\n", + "#n1/n2=sin(t1)/sin(t2)\n", + "\n", + "#assume sin(t2)=a\n", + "\n", + "a=n2/n1*m\n", + "\n", + "t2=math.degrees(math.asin(a)) #taking sin inverese in degree\n", + "\n", + "print\"second order reflection take place at an angle=\",round(t2,4),\"degree\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "second order reflection take place at an angle= 6.812 degree\n" + ] + } + ], + "prompt_number": 75 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.4,Page number 1-70" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "V=50*10**3 #operating voltage of x-ray\n", + "M=74.6 #molecular weight\n", + "p=1.99*10**3 #density\n", + "n=4 #no of atoms per unit cell(for FCC structure)\n", + "h=6.63*10**-34 #plank's constant\n", + "c=3*10**8 #velocity \n", + "e=1.6*10**-19 #charge on electron\n", + "N=6.023*10**26 #Avogadro's number\n", + "\n", + "#step 1:clculating shortest wavelength\n", + "\n", + "l=h*c/(e*V)\n", + "\n", + "print\"1)shortest wavelength=\",(l),\"m\"\n", + "\n", + "#step:2 calculating distance(d)\n", + "\n", + "#now a**3*p=n*M/N therefore,\n", + "\n", + "a=(n*M/(N*p))**(1./3)\n", + "\n", + "#since KCl is ionic crystal herefore,\n", + "\n", + "d=a/2\n", + "\n", + "#step 3: calculaing glancing angle\n", + "\n", + "#using Bragg's law\n", + "\n", + "#n*l=2*d*sin(t)\n", + "\n", + "#assume sin(t)=a, wavelength is minimum i.e l and n=1\n", + "\n", + "n=1\n", + "\n", + "a=n*l/(2*d)\n", + "\n", + "t=math.degrees(math.asin(a)) #taking sin inverese in degree\n", + "\n", + "print\"2) glancing angle=\",round(t,4),\"degree\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)shortest wavelength= 2.48625e-11 m\n", + "2) glancing angle= 2.265 degree\n" + ] + } + ], + "prompt_number": 77 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.5,Page number 1-70" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=1.0 #first order maximum\n", + "l=0.82*10**-10 #wavelength of X ray\n", + "qd=7.0 #glancing angle in degree\n", + "qm=51./60 #glancing angle in minute\n", + "qs=48./3600 #glancing angle in second\n", + "\n", + "q=qd+qm+qs #total glancin angle in degree\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "d=n*l/(2*math.sin(q*math.pi/180))\n", + "\n", + "a=3*10**-10 #lattice constant\n", + "\n", + "#we know that d=a/root(h**2+k**2+l**2)\n", + "\n", + "#assume root(h**2+k**2+l**2) =m\n", + "\n", + "#arranging terms we get\n", + "\n", + "m=a/d\n", + "\n", + "print\"square root(h**2+k**2+l**2)=\",round(m,0)\n", + "\n", + "print\"hence possible solutions are (100),(010),(001)\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "square root(h**2+k**2+l**2)= 1.0\n", + "hence possible solutions are (100),(010),(001)\n" + ] + } + ], + "prompt_number": 90 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.6,Page number 1-71" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=1 #first order maximum\n", + "l=1j #wavelength of X ray\n", + "\n", + "#part 1:for(100)\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "q1=5.4 #glancing angle in degree\n", + "\n", + "dl1=n*l/(2*math.sin(q1*math.pi/180))\n", + "\n", + "#part 2:for(110)\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "q2=7.6 #glancing angle in degree\n", + "\n", + "dl2=n*l/(2*math.sin(q2*math.pi/180))\n", + "\n", + "#part 3:for(111)\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "q3=9.4 #glancing angle in degree\n", + "\n", + "dl3=n*l/(2*math.sin(q3*math.pi/180))\n", + "\n", + "#for taking ratio divide all dl by dl1\n", + "\n", + "d1=dl1/dl1\n", + "\n", + "d2=dl2/dl1\n", + "\n", + "d3=dl3/dl1\n", + "\n", + "print\"cubic lattice structure is=\",d1,d2,d3" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " cubic lattice structure is= (1+0j) (0.711559669333+0j) (0.576199350225+0j)\n" + ] + } + ], + "prompt_number": 94 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.7,Page number 1-71" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=1 #first order maximum\n", + "l=1.54*10**-10 #wavelength of rock salt crystal\n", + "q=21.7 #glancing angle in degree\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "d=n*l/(2*math.sin(q*math.pi/180))\n", + "\n", + "print\"lattice constant of crystal=\",\"{0:.3e}\".format(d),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "lattice constant of crystal= 2.083e-10 meter\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.8,Page number 1-72" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "a=2.814*10**-10 #lattice constant\n", + "\n", + "#the interplanar spacing of plane\n", + "\n", + "h=1\n", + "k=0\n", + "l=0\n", + "\n", + "d=a/math.sqrt(h**2+k**2+l**2)\n", + "\n", + "n=2 #first order maximum\n", + "\n", + "l=0.714*10**-10 #wavelength of X-ray crystal\n", + "\n", + "#using Bragg's law\n", + "\n", + "q=math.degrees(math.asin((n*l)/(2*d))) #glancing angle\n", + "\n", + "print\"glancing angle=\",round(q,4),\"degree\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "glancing angle= 14.6984 degree\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.9,Page number 1-72" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "d=2.82*10**-10 #interplaner spacing\n", + "t=10 #glancing angle\n", + "\n", + "#for part 1\n", + "\n", + "n=1 #first order maximum\n", + "\n", + "#using Bragg's law n*l=2*d*sin(t)\n", + "\n", + "l=2*d*math.sin(math.pi*t/180)/n\n", + "\n", + "print\"1)wavelength=\",\"{0:.3e}\".format(l),\"meter\"\n", + "\n", + "#for part 2\n", + "\n", + "n1=2\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "q=math.degrees(math.asin(n1*l/(2*d)))\n", + "\n", + "print\"2)glancing angle=\",round(q,4),\"degree\"\n", + "\n", + "#for part 3\n", + "\n", + "#for highest order sin(q) not exceed one i.e maximum value is one\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "n2=2*d/l #since sin(q)is one\n", + "\n", + "print\"3)highest order possible =\",(floor(n2))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)wavelength= 9.794e-11 meter\n", + "2)glancing angle= 20.322 degree\n", + "3)highest order possible = 5.0\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.10,Page number 1-73" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#for line -A\n", + "\n", + "n1=1 #1st order maximum\n", + "q1=30 #glancing angle in degree\n", + "\n", + "#using Bragg's law for line A n1*l1=2*d1*sin(q1)\n", + "\n", + "#d1=n1*l1/(2*sin(q1))\n", + "\n", + "#for line B\n", + "\n", + "l2=0.97 #wavelength in amstrong unit\n", + "n2=3 #1st order maximum\n", + "q2=60 #glancing angle in degree\n", + "\n", + "#using Bragg's law for line B n2*l2=2*d2*sin(q2)\n", + "\n", + "#since for both lines A and B we use same plane of same crystal,therefore\n", + "\n", + "#d1=d2\n", + "\n", + "#therefore equution became n2*l2=2*n1*l1/(2*sin(q1))*sin(q2)\n", + "\n", + "#by arranging terms we get\n", + "\n", + "\n", + "l1=n2*l2*2*math.sin(q1*math.pi/180)/(2*n1*math.sin(q2*math.pi/180))\n", + "\n", + "print\"wavelength of the line A=\",round(l1,4),\"amstrong\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "wavelength of the line A= 1.6801 amstrong\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.11,Page number 1-74" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=1.0 #first order minimum\n", + "d=5.5*10**-11 #atomic spacing\n", + "e=1.6*10**-19 #charge on one electron\n", + "Ee=10*10**3 #energy in eV\n", + "E=e*Ee #energy in Joule\n", + "m=9.1*10**-31 #mass of elelctron\n", + "h=6.63*10**-34 #plank's constant\n", + "\n", + "l=h/math.sqrt(2*m*E) #wavelength\n", + "\n", + "#using Bragg's law\n", + "\n", + "q=math.degrees(math.asin((n*l)/(2*d))) #glancing angle\n", + "\n", + "print\"glancing angle=\",round(q,4),\"degree\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "glancing angle= 6.4129 degree\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.12,Page number 1-74" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "a=2.814*10**-10 #lattice constant\n", + "\n", + "#for rock salt\n", + "\n", + "d=a/2 #interplaner spacing\n", + "\n", + "n=1 #first order maximum\n", + "\n", + "l=1.541*10**-10 #wavelength of rock salt crystal\n", + "\n", + "#using Bragg's law\n", + "\n", + "q=math.degrees(math.asin((n*l)/(2*d))) #glancing angl\n", + "\n", + "print\"glancing angle=\",round(q,4),\"degree\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "glancing angle= 33.2038 degree\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.16.1,Page number 1-75" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Ev=1.08 #average energy required to creaet a vacancy\n", + "k=1.38*10**-23 #boltzman constant in J/K\n", + "e=1.6*10**-19 #charge on 1 electron\n", + "\n", + "K=k/e #boltzman constant in eV/K\n", + "\n", + "#for a low concentration of vacancies a relation is\n", + "\n", + "#n=Nexp(-Ev/KT)\n", + "\n", + "#since total no atom is 1 hence N=1\n", + "\n", + "#at 1000k\n", + "\n", + "T1=1000 #temperature\n", + "\n", + "n1=math.exp(-Ev/(K*T1))\n", + "\n", + "#at 500k\n", + "\n", + "T2=500 #temperature\n", + "\n", + "n2=math.exp(-Ev/(K*T2))\n", + "\n", + "v=(n1)/(n2) #ratio of vacancies\n", + "\n", + "print\"ratio of vacancies=\",round(v,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "ratio of vacancies= 274234.5745\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.16.2,Page number 1-75" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Ev=1.95 #average energy required to creaet a vacancy\n", + "k=1.38*10**-23 #boltzman constant in J/K\n", + "e=1.6*10**-19 #charge on 1 electron\n", + "K=k/e #boltzman constant in eV/K\n", + "T=500 #temperature\n", + "\n", + "#for a low concentration of vacancies a relation is\n", + "\n", + "#n=Nexp(-Ev/KT)\n", + "\n", + "m=math.exp(-Ev/(K*T)) #ratio of no of vacancies to no of atoms n/N\n", + "\n", + "print\"ratio of no of vacancies to no of atoms=\",\"{0:.3e}\".format(m)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "ratio of no of vacancies to no of atoms= 2.303e-20\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.16.3,Page number 1-76" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Ev=1.8 #average energy required to creaet a vacancy\n", + "k=1.38*10**-23 #boltzman constant in J/K\n", + "e=1.6*10**-19 #charge on 1 electron\n", + "K=k/e #boltzman constant in eV/K\n", + "\n", + "#for a low concentration of vacancies a relation is\n", + "\n", + "#n=Nexp(-Ev/KT)\n", + "\n", + "#ratio of vacancy is n/N assume be r=exp(-Ev/KT)\n", + "\n", + "#since total no atom is 1 hence N=1\n", + "\n", + "#at 1000k\n", + "\n", + "t1=-119 #temperature in degree\n", + "T1=t1+273 #temperature in kelvine\n", + "r1=math.exp(-Ev/(K*T1))\n", + "\n", + "print\"1)ratio of vacancies at -119 degree=\",\"{0:.3e}\".format(r1)\n", + "\n", + "#at 500k\n", + "\n", + "t2=80 #temperature in degree\n", + "\n", + "T2=t2+273 #temperature in kelvine\n", + "\n", + "r2=exp(-Ev/(K*T2))\n", + "\n", + "v=(r1)/(r2) #ratio of vacancies\n", + "\n", + "print\"2)ratio of vacancies at 80 degree=\",\"{0:.3e}\".format(r2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)ratio of vacancies at -119 degree= 1.399e-59\n", + "2)ratio of vacancies at 80 degree= 2.110e-26\n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.16.4,Page number 1-76" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Ev=1.5 #energy of formaton of frankel defect\n", + "k=1.38*10**-23 #boltzman constant in J/K\n", + "e=1.6*10**-19 #charge on 1 electron\n", + "K=k/e #boltzman constant in eV/K\n", + "T=700 #temperature\n", + "N=6.023*10**26 #avogadro's no\n", + "\n", + "#for a low concentration of vacancies a relation is\n", + "\n", + "#n=Nexp(-Ev/KT)\n", + "\n", + "m=math.exp(-Ev/(2*K*T)) #ratio of no of vacancies to no of atoms n/N\n", + "\n", + "qs=5.56 #specific density\n", + "q=5.56*10**3 #real density ke/m**3\n", + "M=0.143 #molecular weight in kg/m**3\n", + "ma=M/N #mass of one molecule\n", + "v=ma/q #vol of one molecule\n", + "\n", + "#v volume containe 1 molecule\n", + "\n", + "#therefore 1 m**3 containe x molecule\n", + "\n", + "x=1./v\n", + "d=m*x #defect per m**3\n", + "dm=d*10**-9 #defect per mm**3\n", + "\n", + "print\"number of frankel defects per mm^3=\",\"{0:.3e}\".format(dm)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "number of frankel defects per mm^3= 9.432e+16\n" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Applied_Physics-I_by_I_A_Shaikh/Chapter2_.ipynb b/Applied_Physics-I_by_I_A_Shaikh/Chapter2_.ipynb new file mode 100755 index 00000000..cb41afc6 --- /dev/null +++ b/Applied_Physics-I_by_I_A_Shaikh/Chapter2_.ipynb @@ -0,0 +1,853 @@ +{ + "metadata": { + "celltoolbar": "Raw Cell Format", + "name": "", + "signature": "sha256:be03421cc765abd4c9572b7c61bb823243fbea415c12e649bb60ed73fc4375e6" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 2: Semiconductor Physics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21.1,Page number 2-47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "ro=1.72*10**-8 #resistivity of Cu\n", + "s=1/ro #conductivity of Cu\n", + "n=10.41*10**28 #no of electron per unit volume\n", + "e=1.6*10**-19 #charge on electron\n", + "\n", + "u=s/(n*e)\n", + "\n", + "print\"mobility of electron in Cu =\",\"{0:.3e}\".format(u),\"m^2/volt-sec\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "mobility of electron in Cu = 3.491e-03 m^2/volt-sec\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21.2,Page number 2-47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "m=63.5 #atomic weight\n", + "u=43.3 #mobility of electron\n", + "e=1.6*10**-19 #charge on electron\n", + "N=6.02*10**23 #Avogadro's number\n", + "d=8.96 #density\n", + "\n", + "Ad=N*d/m #Atomic density\n", + "\n", + "n=1*Ad\n", + "\n", + "ro=1/(n*e*u)\n", + "\n", + "print\"Resistivity of Cu =\",\"{0:.3e}\".format(ro),\"ohm-cm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Resistivity of Cu = 1.699e-06 ohm-cm\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21.3,Page number 2-47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "e=1.6*10**-19 #charge on electron\n", + "ne=2.5*10**19 #density of carriers\n", + "nh=ne #for intrinsic semiconductor\n", + "ue=0.39 #mobility of electron\n", + "uh=0.19 #mobility of hole\n", + "\n", + "s=ne*e*ue+nh*e*uh #conductivity of Ge\n", + "\n", + "ro=1.0/s #resistivity of Ge\n", + "\n", + "print\"Resistivity of Ge =\",round(ro,4),\"ohm-m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Resistivity of Ge = 0.431 ohm-m\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21.5,Page number 2-48" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Eg=1.2 #energy gap\n", + "T1=600 #temperature\n", + "T2=300 #temperature\n", + "\n", + "#since ue>>uh for intrinsic semiconductor\n", + "\n", + "#s=ni*e*ue\n", + "\n", + "K=8.62*10**-5 #Boltzman constant\n", + "\n", + "s=1l\n", + "\n", + "s1=s*exp((-Eg)/(2*K*T1))\n", + "\n", + "s2=s*exp((-Eg)/(2*K*T2))\n", + "\n", + "m=(s1/s2)\n", + "\n", + "print'Ratio between conductivity =',\"{0:.3e}\".format(m)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Ratio between conductivity = 1.092e+05\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21.6,Page number 2-49" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "c=5*10**28 #concentration of Si atoms\n", + "e=1.6*10**-19 #charge on electron\n", + "u=0.048 #mobility of hole\n", + "s=4.4*10**-4 #conductivity of Si\n", + "\n", + "#since millionth Si atom is replaced by an indium atom\n", + "\n", + "n=c*10**-6\n", + "\n", + "sp=u*e*n #conductivity of resultant\n", + "\n", + "print\"conductivity =\",(sp),\"mho/m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "conductivity = 384.0 mho/m\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21.7,Page number 2-49" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "m=28.1 #atomic weight of Si\n", + "e=1.6*10**-19 #charge on electron\n", + "N=6.02*10**26 #Avogadro's number\n", + "d=2.4*10**3 #density of Si\n", + "p=0.25 #resistivity\n", + "\n", + "#no. of Si atom/m**3\n", + "\n", + "Ad=N*d/m #Atomic density\n", + "\n", + "#impurity level is 0.01 ppm i.e. 1 atom in every 10**8 atoms of Si\n", + "\n", + "n=Ad/10**8 #no of impurity atoms\n", + "\n", + "#since each impurity produce 1 hole\n", + "\n", + "nh=n\n", + "\n", + "print\"1) hole concentration =\",round(n,4),\"holes/m^3\"\n", + "\n", + "up=1/(e*p*nh)\n", + "\n", + "print\"2) mobility =\",round(up,4),\"m^2/volt.sec\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) hole concentration = 5.14163701068e+20 holes/m^3\n", + "2) mobility = 0.0486 m^2/volt.sec\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.22.1,Page number 2-50" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "t=27 #temp in degree \n", + "T=t+273 #temp in kelvin\n", + "K=8.62*10**-5 #Boltzman constant in eV\n", + "Eg=1.12 #Energy band gap\n", + "\n", + "#For intrensic semiconductor (Ec-Ev)=Eg/2\n", + "\n", + "#let (Ec-Ev)=m\n", + "\n", + "m=Eg/2\n", + "\n", + "a=(m/(K*T))\n", + "\n", + "#probability f(Ec)=1/(1+exp((Ec-Ev)/(K*T))\n", + "\n", + "p=1/(1+exp(a))\n", + "\n", + "\n", + "print\"probability of an electron being thermally excited to conduction band=\",\"{0:.3e}\".format(p)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "probability of an electron being thermally excited to conduction band= 3.938e-10\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.22.2,Page number 2-50" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "T=300 #temp in kelvin\n", + "K=8.62*10**-5 #Boltzman constant in eV\n", + "m=0.012 #energy level(Ef-E)\n", + "\n", + "a=(m/(K*T))\n", + "\n", + "#probability f(Ec)=1/(1+exp((Ec-Ev)/(K*T))\n", + "\n", + "p=1.0/(1+exp(a))\n", + "\n", + "p1=1-p\n", + "\n", + "print\"probability of an energy level not being occupied by an electron=\",round(p1,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "probability of an energy level not being occupied by an electron= 0.614\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.22.3,Page number 2-51" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "t=20 #temp in degree \n", + "T=t+273 #temp in kelvin\n", + "K=8.62*10**-5 #Boltzman constant in eV\n", + "Eg=1.12 #Energy band gap\n", + "\n", + "#For intrensic semiconductor (Ec-Ev)=Eg/2\n", + "\n", + "#let (Ec-Ev)=m\n", + "\n", + "m=Eg/2\n", + "\n", + "a=(m/(K*T))\n", + "\n", + "#probability f(Ec)=1/(1+exp((Ec-Ev)/(K*T))\n", + "\n", + "p=1.0/(1+exp(a))\n", + "\n", + "\n", + "print\"probability of an electron being thermally excited to conduction band=\",\"{0:.3e}\".format(p)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "probability of an electron being thermally excited to conduction band= 2.348e-10\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.22.4,Page number 2-51" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "T=300 #temp in kelvin\n", + "K=8.62*10**-5 #Boltzman constant in eV\n", + "Eg=2.1 #Energy band gap\n", + "\n", + "#probability f(Ec)=1/(1+exp((Ec-Ev)/(K*T))\n", + "\n", + "m=K*T\n", + "\n", + "#for f(E)=0.99\n", + "\n", + "p1=0.99\n", + "\n", + "b=1.0-(1.0/p1)\n", + "\n", + "a=math.log(b) #a=(E-2.1)/m\n", + "\n", + "E=2.1+m*a\n", + "\n", + "print\"1) Energy for which probability is 0.99=\",(E),\"eV\"\n", + "\n", + "#for f(E)=0.01\n", + "\n", + "p2=0.01\n", + "\n", + "b2=1-1.0/p2\n", + "\n", + "a1=math.log(b2) #a=(E-2.1)/m\n", + "\n", + "E1=2.1+m*a1\n", + "\n", + "print\"2)Energy for which probability is 0.01=\",(E1),\"eV\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "ename": "ValueError", + "evalue": "math domain error", + "output_type": "pyerr", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m<ipython-input-4-0fb7e85ec399>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m 17\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1.0\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1.0\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mp1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 18\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 19\u001b[1;33m \u001b[0ma\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mmath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mb\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;31m#a=(E-2.1)/m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 20\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 21\u001b[0m \u001b[0mE\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m2.1\u001b[0m\u001b[1;33m+\u001b[0m\u001b[0mm\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mValueError\u001b[0m: math domain error" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.1,Page number 2-52" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "ni=2.4*10**19 #density of intrensic semiconductor\n", + "n=4.4*10**28 #no atom in Ge crystal\n", + "Nd=n/10**6 #density\n", + "Na=Nd\n", + "e=1.6*10**-19 #charge on electron\n", + "T=300 #temerature at N.T.P.\n", + "K=1.38*10**-23 #Boltzman constant\n", + "\n", + "Vo=(K*T/e)*log(Na*Nd/(ni**2))\n", + "\n", + "print\"Potential barrier for Ge =\",round(Vo,4),\"Volts\"\n", + "\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Potential barrier for Ge = 0.3888 Volts\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.2,Page number 2-52" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "B=0.6 #magnetic field\n", + "d=5*10**-3 #distancebetween surface\n", + "J=500 #current density\n", + "Nd=10**21 #density\n", + "e=1.6*10**-19 #charge on electron\n", + "\n", + "Vh=(B*J*d)/(Nd*e) #due to Hall effect\n", + "\n", + "print\"Hall voltage =\",\"{0:.3e}\".format(Vh),\"Volts\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Hall voltage = 9.375e-03 Volts\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.3,Page number 2-53" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Rh=6*10**-7 #Hall coefficient\n", + "B=1.5 #magnetic field\n", + "I=200 #current in strip\n", + "W=1*10**-3 #thickness of strip\n", + "\n", + "Vh=Rh*(B*I)/W #due to Hall effect\n", + "\n", + "print\"Hall voltage =\",(Vh),\"Volt\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Hall voltage = 0.18 Volt\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.4,Page number 2-53" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Rh=2.25*10**-5 #Hall coefficient\n", + "u=0.025 #mobility of hole\n", + "\n", + "r=Rh/u\n", + "\n", + "print\"Resistivity of P type silicon =\",\"{0:.3e}\".format(r),\"ohm-m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Resistivity of P type silicon = 9.000e-04 ohm-m\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.5,Page number 2-53" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "B=0.55 #magnetic field\n", + "d=4.5*10**-3 #distancebetween surface\n", + "J=500 #current density\n", + "n=10**20 #density\n", + "e=1.6*10**-19 #charge on electron\n", + "Rh=1/(n*e) #Hall coefficient\n", + "\n", + "Vh=Rh*B*J*d #Hall voltage\n", + "\n", + "print\"1) Hall voltage =\",round(Vh,4),\"Volts\"\n", + "\n", + "print\"2) Hall coefficient =\",(Rh),\"m^3/C\"\n", + "\n", + "u=0.17 #mobility of electrom\n", + "\n", + "m=math.atan(u*B)\n", + "\n", + "a=m*180/math.pi #conversion randian into degree\n", + "\n", + "print\"3) Hall angle =\",round(a,4),\"degree\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Hall voltage = 0.0773 Volts\n", + "2) Hall coefficient = 0.0625 m^3/C\n", + "3) Hall angle = 5.3416 degree\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.6,Page number 2-54" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Rh=3.66*10**-4 #Hall coefficient\n", + "r=8.93*10**-3 #resistivity \n", + "e=1.6*10**-19 #charge on electron\n", + "\n", + "#Hall coefficient Rh=1/(n*e)\n", + "\n", + "n=1/(Rh*e) #density\n", + "\n", + "print\"1) density(n) =\",round(n,4),\"/m^3\"\n", + "\n", + "u=Rh/r #mobility of electron\n", + "\n", + "print\"2) mobility (u) =\",round(u,4),\"m^2/v-s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) density(n) = 1.70765027322e+22 /m^3\n", + "2) mobility (u) = 0.041 m^2/v-s\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.7,Page number 2-55" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "B=0.2 #magnetic field\n", + "e=1.6*10**-19 #charge on electron\n", + "ue=0.39 #mobility of electron\n", + "l=0.01 #length\n", + "A=0.001*0.001 #cross section area of bar\n", + "V=1*10**-3 #Applied voltage\n", + "d=0.001 #sample of width \n", + "\n", + "r=1/(ue*e) #resistivity\n", + "R=r*l/A #resistance of Ge bar\n", + "\n", + "#using ohm's law\n", + "\n", + "I=V/R\n", + "Rh=r*ue #hall coefficient\n", + "\n", + "#using formulae for hall effect\n", + "\n", + "J=I/A #current density\n", + "Vh=Rh*B*J*d\n", + "\n", + "print\"Hall voltage =\",(Vh)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Hall voltage = 7.8e-06\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.24.1,Page number 2-55" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "x1=0.4 #difference between fermi level and conduction band(Ec-Ef)\n", + "T=300 #temp in kelvin\n", + "K=8.62*10**-5 #Boltzman constant in eV\n", + "\n", + "#ne=N*e**(-(Ec-Ef)/(K*T))\n", + "#ne is no of electron in conduction band\n", + "#since concentration of donor electron is doubled\n", + "\n", + "a=2 #ratio of no of electron\n", + "\n", + "#let x2 be the difference between new fermi level and conduction band(Ec-Ef')\n", + "\n", + "x2=-math.log(a)*(K*T)+x1 #arranging equation ne=N*e**(-(Ec-Ef)/(K*T))\n", + "\n", + "print\"Fermi level will be shifted towards conduction band by\",round(x2,4),\"eV\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Fermi level will be shifted towards conduction band by 0.3821 eV\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Applied_Physics-I_by_I_A_Shaikh/Chapter2__1.ipynb b/Applied_Physics-I_by_I_A_Shaikh/Chapter2__1.ipynb new file mode 100755 index 00000000..cb41afc6 --- /dev/null +++ b/Applied_Physics-I_by_I_A_Shaikh/Chapter2__1.ipynb @@ -0,0 +1,853 @@ +{ + "metadata": { + "celltoolbar": "Raw Cell Format", + "name": "", + "signature": "sha256:be03421cc765abd4c9572b7c61bb823243fbea415c12e649bb60ed73fc4375e6" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 2: Semiconductor Physics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21.1,Page number 2-47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "ro=1.72*10**-8 #resistivity of Cu\n", + "s=1/ro #conductivity of Cu\n", + "n=10.41*10**28 #no of electron per unit volume\n", + "e=1.6*10**-19 #charge on electron\n", + "\n", + "u=s/(n*e)\n", + "\n", + "print\"mobility of electron in Cu =\",\"{0:.3e}\".format(u),\"m^2/volt-sec\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "mobility of electron in Cu = 3.491e-03 m^2/volt-sec\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21.2,Page number 2-47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "m=63.5 #atomic weight\n", + "u=43.3 #mobility of electron\n", + "e=1.6*10**-19 #charge on electron\n", + "N=6.02*10**23 #Avogadro's number\n", + "d=8.96 #density\n", + "\n", + "Ad=N*d/m #Atomic density\n", + "\n", + "n=1*Ad\n", + "\n", + "ro=1/(n*e*u)\n", + "\n", + "print\"Resistivity of Cu =\",\"{0:.3e}\".format(ro),\"ohm-cm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Resistivity of Cu = 1.699e-06 ohm-cm\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21.3,Page number 2-47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "e=1.6*10**-19 #charge on electron\n", + "ne=2.5*10**19 #density of carriers\n", + "nh=ne #for intrinsic semiconductor\n", + "ue=0.39 #mobility of electron\n", + "uh=0.19 #mobility of hole\n", + "\n", + "s=ne*e*ue+nh*e*uh #conductivity of Ge\n", + "\n", + "ro=1.0/s #resistivity of Ge\n", + "\n", + "print\"Resistivity of Ge =\",round(ro,4),\"ohm-m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Resistivity of Ge = 0.431 ohm-m\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21.5,Page number 2-48" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Eg=1.2 #energy gap\n", + "T1=600 #temperature\n", + "T2=300 #temperature\n", + "\n", + "#since ue>>uh for intrinsic semiconductor\n", + "\n", + "#s=ni*e*ue\n", + "\n", + "K=8.62*10**-5 #Boltzman constant\n", + "\n", + "s=1l\n", + "\n", + "s1=s*exp((-Eg)/(2*K*T1))\n", + "\n", + "s2=s*exp((-Eg)/(2*K*T2))\n", + "\n", + "m=(s1/s2)\n", + "\n", + "print'Ratio between conductivity =',\"{0:.3e}\".format(m)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Ratio between conductivity = 1.092e+05\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21.6,Page number 2-49" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "c=5*10**28 #concentration of Si atoms\n", + "e=1.6*10**-19 #charge on electron\n", + "u=0.048 #mobility of hole\n", + "s=4.4*10**-4 #conductivity of Si\n", + "\n", + "#since millionth Si atom is replaced by an indium atom\n", + "\n", + "n=c*10**-6\n", + "\n", + "sp=u*e*n #conductivity of resultant\n", + "\n", + "print\"conductivity =\",(sp),\"mho/m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "conductivity = 384.0 mho/m\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21.7,Page number 2-49" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "m=28.1 #atomic weight of Si\n", + "e=1.6*10**-19 #charge on electron\n", + "N=6.02*10**26 #Avogadro's number\n", + "d=2.4*10**3 #density of Si\n", + "p=0.25 #resistivity\n", + "\n", + "#no. of Si atom/m**3\n", + "\n", + "Ad=N*d/m #Atomic density\n", + "\n", + "#impurity level is 0.01 ppm i.e. 1 atom in every 10**8 atoms of Si\n", + "\n", + "n=Ad/10**8 #no of impurity atoms\n", + "\n", + "#since each impurity produce 1 hole\n", + "\n", + "nh=n\n", + "\n", + "print\"1) hole concentration =\",round(n,4),\"holes/m^3\"\n", + "\n", + "up=1/(e*p*nh)\n", + "\n", + "print\"2) mobility =\",round(up,4),\"m^2/volt.sec\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) hole concentration = 5.14163701068e+20 holes/m^3\n", + "2) mobility = 0.0486 m^2/volt.sec\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.22.1,Page number 2-50" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "t=27 #temp in degree \n", + "T=t+273 #temp in kelvin\n", + "K=8.62*10**-5 #Boltzman constant in eV\n", + "Eg=1.12 #Energy band gap\n", + "\n", + "#For intrensic semiconductor (Ec-Ev)=Eg/2\n", + "\n", + "#let (Ec-Ev)=m\n", + "\n", + "m=Eg/2\n", + "\n", + "a=(m/(K*T))\n", + "\n", + "#probability f(Ec)=1/(1+exp((Ec-Ev)/(K*T))\n", + "\n", + "p=1/(1+exp(a))\n", + "\n", + "\n", + "print\"probability of an electron being thermally excited to conduction band=\",\"{0:.3e}\".format(p)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "probability of an electron being thermally excited to conduction band= 3.938e-10\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.22.2,Page number 2-50" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "T=300 #temp in kelvin\n", + "K=8.62*10**-5 #Boltzman constant in eV\n", + "m=0.012 #energy level(Ef-E)\n", + "\n", + "a=(m/(K*T))\n", + "\n", + "#probability f(Ec)=1/(1+exp((Ec-Ev)/(K*T))\n", + "\n", + "p=1.0/(1+exp(a))\n", + "\n", + "p1=1-p\n", + "\n", + "print\"probability of an energy level not being occupied by an electron=\",round(p1,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "probability of an energy level not being occupied by an electron= 0.614\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.22.3,Page number 2-51" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "t=20 #temp in degree \n", + "T=t+273 #temp in kelvin\n", + "K=8.62*10**-5 #Boltzman constant in eV\n", + "Eg=1.12 #Energy band gap\n", + "\n", + "#For intrensic semiconductor (Ec-Ev)=Eg/2\n", + "\n", + "#let (Ec-Ev)=m\n", + "\n", + "m=Eg/2\n", + "\n", + "a=(m/(K*T))\n", + "\n", + "#probability f(Ec)=1/(1+exp((Ec-Ev)/(K*T))\n", + "\n", + "p=1.0/(1+exp(a))\n", + "\n", + "\n", + "print\"probability of an electron being thermally excited to conduction band=\",\"{0:.3e}\".format(p)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "probability of an electron being thermally excited to conduction band= 2.348e-10\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.22.4,Page number 2-51" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "T=300 #temp in kelvin\n", + "K=8.62*10**-5 #Boltzman constant in eV\n", + "Eg=2.1 #Energy band gap\n", + "\n", + "#probability f(Ec)=1/(1+exp((Ec-Ev)/(K*T))\n", + "\n", + "m=K*T\n", + "\n", + "#for f(E)=0.99\n", + "\n", + "p1=0.99\n", + "\n", + "b=1.0-(1.0/p1)\n", + "\n", + "a=math.log(b) #a=(E-2.1)/m\n", + "\n", + "E=2.1+m*a\n", + "\n", + "print\"1) Energy for which probability is 0.99=\",(E),\"eV\"\n", + "\n", + "#for f(E)=0.01\n", + "\n", + "p2=0.01\n", + "\n", + "b2=1-1.0/p2\n", + "\n", + "a1=math.log(b2) #a=(E-2.1)/m\n", + "\n", + "E1=2.1+m*a1\n", + "\n", + "print\"2)Energy for which probability is 0.01=\",(E1),\"eV\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "ename": "ValueError", + "evalue": "math domain error", + "output_type": "pyerr", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m<ipython-input-4-0fb7e85ec399>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m 17\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1.0\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1.0\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mp1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 18\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 19\u001b[1;33m \u001b[0ma\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mmath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mb\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;31m#a=(E-2.1)/m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 20\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 21\u001b[0m \u001b[0mE\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m2.1\u001b[0m\u001b[1;33m+\u001b[0m\u001b[0mm\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mValueError\u001b[0m: math domain error" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.1,Page number 2-52" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "ni=2.4*10**19 #density of intrensic semiconductor\n", + "n=4.4*10**28 #no atom in Ge crystal\n", + "Nd=n/10**6 #density\n", + "Na=Nd\n", + "e=1.6*10**-19 #charge on electron\n", + "T=300 #temerature at N.T.P.\n", + "K=1.38*10**-23 #Boltzman constant\n", + "\n", + "Vo=(K*T/e)*log(Na*Nd/(ni**2))\n", + "\n", + "print\"Potential barrier for Ge =\",round(Vo,4),\"Volts\"\n", + "\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Potential barrier for Ge = 0.3888 Volts\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.2,Page number 2-52" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "B=0.6 #magnetic field\n", + "d=5*10**-3 #distancebetween surface\n", + "J=500 #current density\n", + "Nd=10**21 #density\n", + "e=1.6*10**-19 #charge on electron\n", + "\n", + "Vh=(B*J*d)/(Nd*e) #due to Hall effect\n", + "\n", + "print\"Hall voltage =\",\"{0:.3e}\".format(Vh),\"Volts\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Hall voltage = 9.375e-03 Volts\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.3,Page number 2-53" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Rh=6*10**-7 #Hall coefficient\n", + "B=1.5 #magnetic field\n", + "I=200 #current in strip\n", + "W=1*10**-3 #thickness of strip\n", + "\n", + "Vh=Rh*(B*I)/W #due to Hall effect\n", + "\n", + "print\"Hall voltage =\",(Vh),\"Volt\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Hall voltage = 0.18 Volt\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.4,Page number 2-53" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Rh=2.25*10**-5 #Hall coefficient\n", + "u=0.025 #mobility of hole\n", + "\n", + "r=Rh/u\n", + "\n", + "print\"Resistivity of P type silicon =\",\"{0:.3e}\".format(r),\"ohm-m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Resistivity of P type silicon = 9.000e-04 ohm-m\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.5,Page number 2-53" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "B=0.55 #magnetic field\n", + "d=4.5*10**-3 #distancebetween surface\n", + "J=500 #current density\n", + "n=10**20 #density\n", + "e=1.6*10**-19 #charge on electron\n", + "Rh=1/(n*e) #Hall coefficient\n", + "\n", + "Vh=Rh*B*J*d #Hall voltage\n", + "\n", + "print\"1) Hall voltage =\",round(Vh,4),\"Volts\"\n", + "\n", + "print\"2) Hall coefficient =\",(Rh),\"m^3/C\"\n", + "\n", + "u=0.17 #mobility of electrom\n", + "\n", + "m=math.atan(u*B)\n", + "\n", + "a=m*180/math.pi #conversion randian into degree\n", + "\n", + "print\"3) Hall angle =\",round(a,4),\"degree\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Hall voltage = 0.0773 Volts\n", + "2) Hall coefficient = 0.0625 m^3/C\n", + "3) Hall angle = 5.3416 degree\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.6,Page number 2-54" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Rh=3.66*10**-4 #Hall coefficient\n", + "r=8.93*10**-3 #resistivity \n", + "e=1.6*10**-19 #charge on electron\n", + "\n", + "#Hall coefficient Rh=1/(n*e)\n", + "\n", + "n=1/(Rh*e) #density\n", + "\n", + "print\"1) density(n) =\",round(n,4),\"/m^3\"\n", + "\n", + "u=Rh/r #mobility of electron\n", + "\n", + "print\"2) mobility (u) =\",round(u,4),\"m^2/v-s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) density(n) = 1.70765027322e+22 /m^3\n", + "2) mobility (u) = 0.041 m^2/v-s\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.7,Page number 2-55" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "B=0.2 #magnetic field\n", + "e=1.6*10**-19 #charge on electron\n", + "ue=0.39 #mobility of electron\n", + "l=0.01 #length\n", + "A=0.001*0.001 #cross section area of bar\n", + "V=1*10**-3 #Applied voltage\n", + "d=0.001 #sample of width \n", + "\n", + "r=1/(ue*e) #resistivity\n", + "R=r*l/A #resistance of Ge bar\n", + "\n", + "#using ohm's law\n", + "\n", + "I=V/R\n", + "Rh=r*ue #hall coefficient\n", + "\n", + "#using formulae for hall effect\n", + "\n", + "J=I/A #current density\n", + "Vh=Rh*B*J*d\n", + "\n", + "print\"Hall voltage =\",(Vh)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Hall voltage = 7.8e-06\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.24.1,Page number 2-55" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "x1=0.4 #difference between fermi level and conduction band(Ec-Ef)\n", + "T=300 #temp in kelvin\n", + "K=8.62*10**-5 #Boltzman constant in eV\n", + "\n", + "#ne=N*e**(-(Ec-Ef)/(K*T))\n", + "#ne is no of electron in conduction band\n", + "#since concentration of donor electron is doubled\n", + "\n", + "a=2 #ratio of no of electron\n", + "\n", + "#let x2 be the difference between new fermi level and conduction band(Ec-Ef')\n", + "\n", + "x2=-math.log(a)*(K*T)+x1 #arranging equation ne=N*e**(-(Ec-Ef)/(K*T))\n", + "\n", + "print\"Fermi level will be shifted towards conduction band by\",round(x2,4),\"eV\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Fermi level will be shifted towards conduction band by 0.3821 eV\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Applied_Physics-I_by_I_A_Shaikh/Chapter3.ipynb b/Applied_Physics-I_by_I_A_Shaikh/Chapter3.ipynb new file mode 100755 index 00000000..7111a9da --- /dev/null +++ b/Applied_Physics-I_by_I_A_Shaikh/Chapter3.ipynb @@ -0,0 +1,1175 @@ +{ + "metadata": { + "celltoolbar": "Raw Cell Format", + "name": "", + "signature": "sha256:9dcf8c834afbbdba5cac9bfd61902345de5a5912fe35cd8c01ac3ee021a2040e" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 3: Dielectric And Magnetic Materials" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.1,Page number 3-35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "A=650*10**-6 #area\n", + "d=4*10**-3 #seperation of plate\n", + "Q=2*10**-10 #charge\n", + "er=3.5 #relative permitivity\n", + "\n", + "e0=8.85*10**-12 #absolute permitivity\n", + "\n", + "V=(Q*d)/(e0*er*A)\n", + "\n", + "print\"voltage across capacitor =\",round(V,4),\"Volt\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "voltage across capacitor = 39.7343 Volt\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.2,Page number 3-36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "A=2000*10**-6 #area\n", + "d=0.5*10**-6 #seperation of plate\n", + "er=8.0 #relative permitivity\n", + "e0=8.85*10**-12 #absolute permitivity\n", + "\n", + "C=(e0*er*A)/d\n", + "\n", + "print\"capacitance for capacitor =\",\"{0:.3e}\".format(C),\"Faraday\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "capacitance for capacitor = 2.832e-07 Faraday\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.3,Page number 3-36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "E=1000 #electric field\n", + "P=4.3*10**-8 #polarization\n", + "e0=8.854*10**-12 #absolute permitivity\n", + "er=(P/(e0*E))+1 #as P/E=e0(er-1)\n", + "\n", + "print\"relative permittivity =\",round(er,4)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "relative permittivity = 5.8566\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.4,Page number 3-36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#As C=e0*er*A/d\n", + "\n", + "e0=math.e #absolute permitivity\n", + "\n", + "Ag=1l\n", + "\n", + "Ap=Ag #Assuming Area of glass plate and plastic film is same\n", + "\n", + "#for glass\n", + "\n", + "erg=6 #relative permitivity\n", + "\n", + "dg=0.25 #thickness\n", + "\n", + "Cg=e0*erg*Ag/dg\n", + "\n", + "#for plastic film\n", + "\n", + "erp=3 #relative permitivity\n", + "\n", + "dp=0.1 #thickness\n", + "\n", + "Cp=e0*erp*Ap/dp\n", + "\n", + "m=Cg/Cp\n", + "\n", + "print\"since Cg/Cp=\",m\n", + "\n", + "print\"plastic film holds more charge\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "since Cg/Cp= 0.8\n", + "plastic film holds more charge\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.5,Page number 3-37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "N=2.7*10**25 #no of atoms per m**3\n", + "er=1.0000684 #dielectric constant of He atom at NTP\n", + "e0=8.854*10**-12 #absolute permitivity\n", + "\n", + "a=e0*(er-1.0)/N #electronic polarizability\n", + "\n", + "print\"1) electronic polarizability=\",\"{0:.3e}\".format(a)\n", + "\n", + "R=(a/(4*3.1472*e0))**(1.0/3) #radius of helium atom\n", + "\n", + "print\"2) radius of He atoms =\",\"{0:.3e}\".format(R),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) electronic polarizability= 2.243e-41\n", + "2) radius of He atoms = 5.860e-11 meter\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.6,Page number 3-37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "er=1.000014 #dielectric constant of He atom at NTP\n", + "Xe=er-1.0 #electric susceptibility\n", + "\n", + "print\"electric susceptibility =\",(Xe)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "electric susceptibility = 1.4e-05\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.7,Page number 3-37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "T=300 #temperature of paramagnetic material\n", + "X=3.7*10**-3 #susceptibility of material\n", + "\n", + "C=X*T #using Curie's law\n", + "\n", + "T1=250 #temperature\n", + "T2=600 #temperature\n", + "\n", + "u1=C/T1 #relative permeability of material at 250k\n", + "\n", + "u2=C/T2 #relative permeability of material at 350k\n", + "\n", + "print\"relative permeability at temp 250K=\",\"{0:.3e}\".format(u1)\n", + "\n", + "print\"relative permeability at temp 600K =\",\"{0:.3e}\".format(u2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "relative permeability at temp 250K= 4.440e-03\n", + "relative permeability at temp 600K = 1.850e-03\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.8,Page number 3-38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "u=0.8*10**-23 #magnetic dipole moment of an atom \n", + "B=0.8 #magnetic field\n", + "K=1.38*10**-23 #boltzmann constant\n", + "\n", + "T=(2*u*B)/(3*K) #temperature\n", + "\n", + "print\"Temperature at which average thermal energy of an atom is equal to magntic energy=\",round(T,4),\"K\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Temperature at which average thermal energy of an atom is equal to magntic energy= 0.3092 K\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.9,Page number 3-38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "B=0.5 #magnetic field\n", + "t=27 #temperature in degree celcius\n", + "T=273+t #temperature in kelvin\n", + "\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "\n", + "C=2*10**-3 #Curie's constant\n", + "\n", + "M=(C*B)/(u0*T) #magnetization of material\n", + "\n", + "print\"magnetization of paramagnetic material =\",round(M,4),\"A/m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "magnetization of paramagnetic material = 2.6526 A/m\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.10,Page number 3-38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "B=10.9*10**-5 #flux density\n", + "\n", + "H=B/u0 #magnetic field\n", + "\n", + "print\"Horizontal component of magnetic field =\",round(H,4),\"A-m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Horizontal component of magnetic field = 86.7394 A-m\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.11,Page number 3-39" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "phi=5.9*10**-3 #magnetic flux\n", + "ur=900 #relative permeability of material\n", + "n=700 #number of turns\n", + "\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "\n", + "A=60*10**-4 #cross section area of ring\n", + "\n", + "l=2 #mean circumference of ring\n", + "\n", + "B=phi/A #flux density\n", + "\n", + "H=B/(u0*ur) #magnetic field\n", + "\n", + "At=H*l #Amp-turns required\n", + "\n", + "I=At/n #current required\n", + "\n", + "print\"Current required to produce a flux=\",round(I,4),\"Amp\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Current required to produce a flux= 2.4842 Amp\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.12,Page number 3-39" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "phi=2.7*10**-3 #magnetic flux\n", + "A=25*10**-4 #cross section area of ring\n", + "r=25*10**-2 #mean circumference of ring\n", + "la=10**-3 #air gap\n", + "\n", + "ur=900 #relative permeability of material\n", + "n=400 #number of turns\n", + "\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "\n", + "d=40*10**-2 #mean diameter of ring\n", + "\n", + "li=2*math.pi*r #mean circumference of ring\n", + "\n", + "B=phi/A #flux density\n", + "\n", + "#for air gap\n", + "\n", + "Ha=B/(u0) #magnetic field for air gap\n", + "\n", + "#for iron ring\n", + "\n", + "Hi=B/(u0*ur) #magnetic field for iron ring\n", + "\n", + "#therefore, Amp turn in air gap\n", + "\n", + "Ata=Ha*la #Amp-turns required\n", + "\n", + "#therefore, Amp-turn in ring\n", + "\n", + "Ati=Hi*li #Amp-turns required\n", + "\n", + "#therrfore total mmf required\n", + "\n", + "mmf=Ata+Ati\n", + "\n", + "#Current required\n", + "\n", + "I=mmf/n #current required\n", + "\n", + "print\"Current required =\",round(I,4),\"Amp\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Current required = 5.8986 Amp\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.13,Page number 3-40" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n1=10 #no of turns per cm\n", + "i=2 #current\n", + "B=1 #flux density\n", + "\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "\n", + "n=n1*100 #no turns per m\n", + "\n", + "H=n*i\n", + "\n", + "print\"1) magnetic intensity =\",round(H,4),\"Amp-turn/meter\"\n", + "\n", + "#calculation for magnetization\n", + "\n", + "I=B/u0-H\n", + "\n", + "print\"2) magnetization =\",\"{0:.3e}\".format(I),\"Amp-turn/meter\"\n", + "\n", + "#relative permeability\n", + "\n", + "ur=B/(u0*H)\n", + "\n", + "print\"3) Relative Permeability of the ring =\",(int(ur))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) magnetic intensity = 2000.0 Amp-turn/meter\n", + "2) magnetization = 7.938e+05 Amp-turn/meter\n", + "3) Relative Permeability of the ring = 397\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.14,Page number 3-40" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "m=40 #wt of the core\n", + "d=7.5*10**3 #density of iron\n", + "n=100 #frequency\n", + "\n", + "V=m/d #volume of the iron core\n", + "\n", + "E1=3800*10**-1 #loss of energy in core per cycles/cc\n", + "\n", + "E2=E1*V #loss of energy in core per cycles\n", + "\n", + "N=60*n #no of cycles per minute\n", + "\n", + "E=E2*N #loss of energy per minute\n", + "\n", + "print\"Loss of energy per minute =\",(E),\"Joule\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Loss of energy per minute = 12160.0 Joule\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.15,Page number 3-40" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "l=30*10**-2 #length of ring\n", + "A=1*10**-4 #cross section area of ring\n", + "i=0.032 #current\n", + "\n", + "phi=2*10**-6 #magnetic flux\n", + "\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "\n", + "N=300 #no of turns in the coil\n", + "\n", + "#1) flux density\n", + "\n", + "B=phi/A #flux density\n", + "\n", + "print\"1) Flux density in the ring =\",(B),\"Wb/m**2\"\n", + "\n", + "#2) magnetic intensity of ring\n", + "\n", + "n=N/l #no of turns per unit length\n", + "\n", + "H=n*i #magnetic intensity\n", + "\n", + "print\"2) magnetic intensity =\",(H),\"Amp-turn/meter\"\n", + "\n", + "#3) permeability and relative permeability of the ring\n", + "\n", + "u=B/H\n", + "\n", + "print\"3) Permeability of the ring =\",\"{0:.3e}\".format(u),\"Wb/A-m\"\n", + "\n", + "ur=u/u0\n", + "\n", + "print\"4) Relative Permeability of the ring =\",round(ur,4)\n", + "\n", + "#4)Susceptibility\n", + "\n", + "Xm=ur-1\n", + "\n", + "print\"5) magnetic Susceptibility of the ring =\",round(Xm,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Flux density in the ring = 0.02 Wb/m**2\n", + "2) magnetic intensity = 32.0 Amp-turn/meter\n", + "3) Permeability of the ring = 6.250e-04 Wb/A-m\n", + "4) Relative Permeability of the ring = 497.3592\n", + "5) magnetic Susceptibility of the ring = 496.3592\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.16,Page number 3-41" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "E=3000 #loss of energy per cycle per cm**3\n", + "m=12*10**3 #wt of the core\n", + "d=7.5 #density of iron\n", + "n=50 #frequency\n", + "\n", + "V=m/d #volume of the core\n", + "\n", + "El=E*V*n*60*60 #loss of energy per hour\n", + "\n", + "print\"Loss of energy per hour =\",(El),\"Erg\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Loss of energy per hour = 8.64e+11 Erg\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.17,Page number 3-41" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=50 #frequency\n", + "V=10**-3 #volume of the specimen\n", + "\n", + "#Area of B-H loop\n", + "\n", + "A=0.5*10**3*1\n", + "\n", + "P=n*V*A\n", + "\n", + "print\"Hysteresis power loss =\",(P),\"Watt\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Hysteresis power loss = 25.0 Watt\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.18,Page number 3-42" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "phi=1.5*10**-4 #magnetic flux\n", + "\n", + "ur=900 #relative permeability of material\n", + "\n", + "n=600 #number of turns\n", + "\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "\n", + "A=5.8*10**-4 #cross section area of ring\n", + "\n", + "d=40*10**-2 #mean diameter of ring\n", + "\n", + "li=math.pi*d #mean circumference of ring\n", + "\n", + "la=5*10**-3 #air gap\n", + "\n", + "B=phi/A #flux density\n", + "\n", + "#for air gap\n", + "\n", + "Ha=B/(u0) #magnetic field for air gap\n", + "\n", + "#for iron ring\n", + "\n", + "Hi=B/(u0*ur) #magnetic field for iron ring\n", + "\n", + "#therefore, Amp turn in air gap\n", + "\n", + "Ata=Ha*la #Amp-turns required\n", + "\n", + "#therefore, Amp-turn in ring\n", + "\n", + "Ati=Hi*li #Amp-turns required\n", + "\n", + "#therrfore total mmf required\n", + "\n", + "mmf=Ata+Ati\n", + "\n", + "#Current required\n", + "\n", + "I=mmf/n #current required\n", + "\n", + "print\"Current required =\",round(I,4),\"Amp\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Current required = 2.194 Amp\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.19,Page number 3-42" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "la=1*10**-2 #air gap\n", + "r=0.5 #radius of ring\n", + "A=5*10**-4 #cross section area of ring\n", + "i=5 #current\n", + "u=6*10**-3 #permeability of iron\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "N=900 #no of turns in the coil\n", + "\n", + "#let reluctance of iron ring with air gap be S\n", + "\n", + "S=la/(u0*A)+(2*math.pi*r-la)/(u*A)\n", + "\n", + "print\"1) Reluctance =\",\"{0:.3e}\".format(S),\"A-T/Wb\"\n", + "\n", + "mmf=N*i\n", + "\n", + "print\"2) m.m.f =\",(mmf),\"Amp-turn\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Reluctance = 1.696e+07 A-T/Wb\n", + "2) m.m.f = 4500 Amp-turn\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.20,Page number 3-43" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#the magnetization force is given by,\n", + "#H=NI/l\n", + "\n", + "H=5*10**3 #coercivity of bar magnet\n", + "l=10*10**-2 #length of solenoid\n", + "N=50 #number of turns\n", + "\n", + "I=l*H/N\n", + "\n", + "print\"current =\",(I),\"Ampere\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "current = 10.0 Ampere\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.21,Page number 3-43" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "ur=380 #relative permeability of air\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "A=5*10**-4 #cross section area of ring\n", + "n=200 #number of turns\n", + "d=20*10**-2 #mean diameter of ring\n", + "\n", + "l=math.pi*d #mean circumference of ring\n", + "\n", + "phi=2*10**-3 #magnetic flux\n", + "\n", + "S=l/(u0*ur*A) #reluctance\n", + "\n", + "#using ohm's law for magnetic circuit\n", + "\n", + "#phi=N*I/S\n", + "\n", + "I=S*phi/n\n", + "\n", + "print\"1) Reluctance =\",\"{0:.3e}\".format(S),\"A-T/Wb\"\n", + "print\"2) current =\",round(I,4),\"Ampere\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Reluctance = 2.632e+06 A-T/Wb\n", + "2) current = 26.3158 Ampere\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.22,Page number 3-43" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "ur=1 #relative permeability of air\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "A=6*10**-4 #cross section area of torroid\n", + "n=500 #number of turns\n", + "r=15*10**-2 #radius of torroid\n", + "I=4 #current in coil\n", + "l=2*math.pi*r #mean circumference of torroid\n", + "MMF=n*I\n", + "\n", + "print\"1) MMF (NI) =\",(MMF),\"AT\"\n", + "\n", + "R=l/(u0*ur*A) #Reluctance\n", + "\n", + "print\"2) Reluctance (R) =\",\"{0:.3e}\".format(R),\"AT/Wb\"\n", + "\n", + "phi=MMF/R #flux\n", + "\n", + "print\"3) Magnetic flux =\",(phi),\"Wb\"\n", + "\n", + "B=phi/A #flux density\n", + "\n", + "print\"4) Flux density =\",\"{0:.3e}\".format(B),\"Wb/m**2\"\n", + "\n", + "H=B/(u0*ur) #magnetic field intensity\n", + "\n", + "print\"5) Magnetic field intensity =\",round(H,4),\"A/m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) MMF (NI) = 2000 AT\n", + "2) Reluctance (R) = 1.250e+09 AT/Wb\n", + "3) Magnetic flux = 1.6e-06 Wb\n", + "4) Flux density = 2.667e-03 Wb/m**2\n", + "5) Magnetic field intensity = 2122.0659 A/m\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.23,Page number 3-44" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "phi=10**-3 #magnetic flux\n", + "ur=1000 #relative permeability of iron\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "A=5*10**-4 #cross section area of ring\n", + "la=2*10**-3 #air gap\n", + "d=20*10**-3 #mean diameter of ring\n", + "\n", + "li=math.pi*d-la #mean circumference of ring\n", + "\n", + "#using KVL for magnetic circuit\n", + "\n", + "#AT(total)=AT(iron)+AT(air gap)\n", + "\n", + "ATt=(phi/(u0*A))*((li/ur)+la)\n", + "\n", + "print\"Number of Ampere-Turns required =\",round(ATt,0)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of Ampere-Turns required = 3280.0\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.24,Page number 3-44" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "X=0.5*10**-5 #susceptibility of material\n", + "\n", + "H=10**6 #magnetic field strength\n", + "\n", + "I=X*H #intensity of magnetization\n", + "\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "\n", + "B=u0*(H+I) #flux density\n", + "\n", + "print\"1) intensity magnetization =\",(I),\"Amp/m\"\n", + "\n", + "print\"2) flux density in the material =\",round(B,4),\"wb/m**2\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) intensity magnetization = 5.0 Amp/m\n", + "2) flux density in the material = 1.2566 wb/m**2\n" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Applied_Physics-I_by_I_A_Shaikh/Chapter3_1.ipynb b/Applied_Physics-I_by_I_A_Shaikh/Chapter3_1.ipynb new file mode 100755 index 00000000..7111a9da --- /dev/null +++ b/Applied_Physics-I_by_I_A_Shaikh/Chapter3_1.ipynb @@ -0,0 +1,1175 @@ +{ + "metadata": { + "celltoolbar": "Raw Cell Format", + "name": "", + "signature": "sha256:9dcf8c834afbbdba5cac9bfd61902345de5a5912fe35cd8c01ac3ee021a2040e" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 3: Dielectric And Magnetic Materials" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.1,Page number 3-35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "A=650*10**-6 #area\n", + "d=4*10**-3 #seperation of plate\n", + "Q=2*10**-10 #charge\n", + "er=3.5 #relative permitivity\n", + "\n", + "e0=8.85*10**-12 #absolute permitivity\n", + "\n", + "V=(Q*d)/(e0*er*A)\n", + "\n", + "print\"voltage across capacitor =\",round(V,4),\"Volt\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "voltage across capacitor = 39.7343 Volt\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.2,Page number 3-36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "A=2000*10**-6 #area\n", + "d=0.5*10**-6 #seperation of plate\n", + "er=8.0 #relative permitivity\n", + "e0=8.85*10**-12 #absolute permitivity\n", + "\n", + "C=(e0*er*A)/d\n", + "\n", + "print\"capacitance for capacitor =\",\"{0:.3e}\".format(C),\"Faraday\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "capacitance for capacitor = 2.832e-07 Faraday\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.3,Page number 3-36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "E=1000 #electric field\n", + "P=4.3*10**-8 #polarization\n", + "e0=8.854*10**-12 #absolute permitivity\n", + "er=(P/(e0*E))+1 #as P/E=e0(er-1)\n", + "\n", + "print\"relative permittivity =\",round(er,4)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "relative permittivity = 5.8566\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.4,Page number 3-36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#As C=e0*er*A/d\n", + "\n", + "e0=math.e #absolute permitivity\n", + "\n", + "Ag=1l\n", + "\n", + "Ap=Ag #Assuming Area of glass plate and plastic film is same\n", + "\n", + "#for glass\n", + "\n", + "erg=6 #relative permitivity\n", + "\n", + "dg=0.25 #thickness\n", + "\n", + "Cg=e0*erg*Ag/dg\n", + "\n", + "#for plastic film\n", + "\n", + "erp=3 #relative permitivity\n", + "\n", + "dp=0.1 #thickness\n", + "\n", + "Cp=e0*erp*Ap/dp\n", + "\n", + "m=Cg/Cp\n", + "\n", + "print\"since Cg/Cp=\",m\n", + "\n", + "print\"plastic film holds more charge\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "since Cg/Cp= 0.8\n", + "plastic film holds more charge\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.5,Page number 3-37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "N=2.7*10**25 #no of atoms per m**3\n", + "er=1.0000684 #dielectric constant of He atom at NTP\n", + "e0=8.854*10**-12 #absolute permitivity\n", + "\n", + "a=e0*(er-1.0)/N #electronic polarizability\n", + "\n", + "print\"1) electronic polarizability=\",\"{0:.3e}\".format(a)\n", + "\n", + "R=(a/(4*3.1472*e0))**(1.0/3) #radius of helium atom\n", + "\n", + "print\"2) radius of He atoms =\",\"{0:.3e}\".format(R),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) electronic polarizability= 2.243e-41\n", + "2) radius of He atoms = 5.860e-11 meter\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.6,Page number 3-37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "er=1.000014 #dielectric constant of He atom at NTP\n", + "Xe=er-1.0 #electric susceptibility\n", + "\n", + "print\"electric susceptibility =\",(Xe)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "electric susceptibility = 1.4e-05\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.7,Page number 3-37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "T=300 #temperature of paramagnetic material\n", + "X=3.7*10**-3 #susceptibility of material\n", + "\n", + "C=X*T #using Curie's law\n", + "\n", + "T1=250 #temperature\n", + "T2=600 #temperature\n", + "\n", + "u1=C/T1 #relative permeability of material at 250k\n", + "\n", + "u2=C/T2 #relative permeability of material at 350k\n", + "\n", + "print\"relative permeability at temp 250K=\",\"{0:.3e}\".format(u1)\n", + "\n", + "print\"relative permeability at temp 600K =\",\"{0:.3e}\".format(u2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "relative permeability at temp 250K= 4.440e-03\n", + "relative permeability at temp 600K = 1.850e-03\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.8,Page number 3-38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "u=0.8*10**-23 #magnetic dipole moment of an atom \n", + "B=0.8 #magnetic field\n", + "K=1.38*10**-23 #boltzmann constant\n", + "\n", + "T=(2*u*B)/(3*K) #temperature\n", + "\n", + "print\"Temperature at which average thermal energy of an atom is equal to magntic energy=\",round(T,4),\"K\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Temperature at which average thermal energy of an atom is equal to magntic energy= 0.3092 K\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.9,Page number 3-38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "B=0.5 #magnetic field\n", + "t=27 #temperature in degree celcius\n", + "T=273+t #temperature in kelvin\n", + "\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "\n", + "C=2*10**-3 #Curie's constant\n", + "\n", + "M=(C*B)/(u0*T) #magnetization of material\n", + "\n", + "print\"magnetization of paramagnetic material =\",round(M,4),\"A/m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "magnetization of paramagnetic material = 2.6526 A/m\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.10,Page number 3-38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "B=10.9*10**-5 #flux density\n", + "\n", + "H=B/u0 #magnetic field\n", + "\n", + "print\"Horizontal component of magnetic field =\",round(H,4),\"A-m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Horizontal component of magnetic field = 86.7394 A-m\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.11,Page number 3-39" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "phi=5.9*10**-3 #magnetic flux\n", + "ur=900 #relative permeability of material\n", + "n=700 #number of turns\n", + "\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "\n", + "A=60*10**-4 #cross section area of ring\n", + "\n", + "l=2 #mean circumference of ring\n", + "\n", + "B=phi/A #flux density\n", + "\n", + "H=B/(u0*ur) #magnetic field\n", + "\n", + "At=H*l #Amp-turns required\n", + "\n", + "I=At/n #current required\n", + "\n", + "print\"Current required to produce a flux=\",round(I,4),\"Amp\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Current required to produce a flux= 2.4842 Amp\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.12,Page number 3-39" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "phi=2.7*10**-3 #magnetic flux\n", + "A=25*10**-4 #cross section area of ring\n", + "r=25*10**-2 #mean circumference of ring\n", + "la=10**-3 #air gap\n", + "\n", + "ur=900 #relative permeability of material\n", + "n=400 #number of turns\n", + "\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "\n", + "d=40*10**-2 #mean diameter of ring\n", + "\n", + "li=2*math.pi*r #mean circumference of ring\n", + "\n", + "B=phi/A #flux density\n", + "\n", + "#for air gap\n", + "\n", + "Ha=B/(u0) #magnetic field for air gap\n", + "\n", + "#for iron ring\n", + "\n", + "Hi=B/(u0*ur) #magnetic field for iron ring\n", + "\n", + "#therefore, Amp turn in air gap\n", + "\n", + "Ata=Ha*la #Amp-turns required\n", + "\n", + "#therefore, Amp-turn in ring\n", + "\n", + "Ati=Hi*li #Amp-turns required\n", + "\n", + "#therrfore total mmf required\n", + "\n", + "mmf=Ata+Ati\n", + "\n", + "#Current required\n", + "\n", + "I=mmf/n #current required\n", + "\n", + "print\"Current required =\",round(I,4),\"Amp\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Current required = 5.8986 Amp\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.13,Page number 3-40" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n1=10 #no of turns per cm\n", + "i=2 #current\n", + "B=1 #flux density\n", + "\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "\n", + "n=n1*100 #no turns per m\n", + "\n", + "H=n*i\n", + "\n", + "print\"1) magnetic intensity =\",round(H,4),\"Amp-turn/meter\"\n", + "\n", + "#calculation for magnetization\n", + "\n", + "I=B/u0-H\n", + "\n", + "print\"2) magnetization =\",\"{0:.3e}\".format(I),\"Amp-turn/meter\"\n", + "\n", + "#relative permeability\n", + "\n", + "ur=B/(u0*H)\n", + "\n", + "print\"3) Relative Permeability of the ring =\",(int(ur))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) magnetic intensity = 2000.0 Amp-turn/meter\n", + "2) magnetization = 7.938e+05 Amp-turn/meter\n", + "3) Relative Permeability of the ring = 397\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.14,Page number 3-40" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "m=40 #wt of the core\n", + "d=7.5*10**3 #density of iron\n", + "n=100 #frequency\n", + "\n", + "V=m/d #volume of the iron core\n", + "\n", + "E1=3800*10**-1 #loss of energy in core per cycles/cc\n", + "\n", + "E2=E1*V #loss of energy in core per cycles\n", + "\n", + "N=60*n #no of cycles per minute\n", + "\n", + "E=E2*N #loss of energy per minute\n", + "\n", + "print\"Loss of energy per minute =\",(E),\"Joule\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Loss of energy per minute = 12160.0 Joule\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.15,Page number 3-40" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "l=30*10**-2 #length of ring\n", + "A=1*10**-4 #cross section area of ring\n", + "i=0.032 #current\n", + "\n", + "phi=2*10**-6 #magnetic flux\n", + "\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "\n", + "N=300 #no of turns in the coil\n", + "\n", + "#1) flux density\n", + "\n", + "B=phi/A #flux density\n", + "\n", + "print\"1) Flux density in the ring =\",(B),\"Wb/m**2\"\n", + "\n", + "#2) magnetic intensity of ring\n", + "\n", + "n=N/l #no of turns per unit length\n", + "\n", + "H=n*i #magnetic intensity\n", + "\n", + "print\"2) magnetic intensity =\",(H),\"Amp-turn/meter\"\n", + "\n", + "#3) permeability and relative permeability of the ring\n", + "\n", + "u=B/H\n", + "\n", + "print\"3) Permeability of the ring =\",\"{0:.3e}\".format(u),\"Wb/A-m\"\n", + "\n", + "ur=u/u0\n", + "\n", + "print\"4) Relative Permeability of the ring =\",round(ur,4)\n", + "\n", + "#4)Susceptibility\n", + "\n", + "Xm=ur-1\n", + "\n", + "print\"5) magnetic Susceptibility of the ring =\",round(Xm,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Flux density in the ring = 0.02 Wb/m**2\n", + "2) magnetic intensity = 32.0 Amp-turn/meter\n", + "3) Permeability of the ring = 6.250e-04 Wb/A-m\n", + "4) Relative Permeability of the ring = 497.3592\n", + "5) magnetic Susceptibility of the ring = 496.3592\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.16,Page number 3-41" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "E=3000 #loss of energy per cycle per cm**3\n", + "m=12*10**3 #wt of the core\n", + "d=7.5 #density of iron\n", + "n=50 #frequency\n", + "\n", + "V=m/d #volume of the core\n", + "\n", + "El=E*V*n*60*60 #loss of energy per hour\n", + "\n", + "print\"Loss of energy per hour =\",(El),\"Erg\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Loss of energy per hour = 8.64e+11 Erg\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.17,Page number 3-41" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=50 #frequency\n", + "V=10**-3 #volume of the specimen\n", + "\n", + "#Area of B-H loop\n", + "\n", + "A=0.5*10**3*1\n", + "\n", + "P=n*V*A\n", + "\n", + "print\"Hysteresis power loss =\",(P),\"Watt\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Hysteresis power loss = 25.0 Watt\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.18,Page number 3-42" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "phi=1.5*10**-4 #magnetic flux\n", + "\n", + "ur=900 #relative permeability of material\n", + "\n", + "n=600 #number of turns\n", + "\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "\n", + "A=5.8*10**-4 #cross section area of ring\n", + "\n", + "d=40*10**-2 #mean diameter of ring\n", + "\n", + "li=math.pi*d #mean circumference of ring\n", + "\n", + "la=5*10**-3 #air gap\n", + "\n", + "B=phi/A #flux density\n", + "\n", + "#for air gap\n", + "\n", + "Ha=B/(u0) #magnetic field for air gap\n", + "\n", + "#for iron ring\n", + "\n", + "Hi=B/(u0*ur) #magnetic field for iron ring\n", + "\n", + "#therefore, Amp turn in air gap\n", + "\n", + "Ata=Ha*la #Amp-turns required\n", + "\n", + "#therefore, Amp-turn in ring\n", + "\n", + "Ati=Hi*li #Amp-turns required\n", + "\n", + "#therrfore total mmf required\n", + "\n", + "mmf=Ata+Ati\n", + "\n", + "#Current required\n", + "\n", + "I=mmf/n #current required\n", + "\n", + "print\"Current required =\",round(I,4),\"Amp\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Current required = 2.194 Amp\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.19,Page number 3-42" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "la=1*10**-2 #air gap\n", + "r=0.5 #radius of ring\n", + "A=5*10**-4 #cross section area of ring\n", + "i=5 #current\n", + "u=6*10**-3 #permeability of iron\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "N=900 #no of turns in the coil\n", + "\n", + "#let reluctance of iron ring with air gap be S\n", + "\n", + "S=la/(u0*A)+(2*math.pi*r-la)/(u*A)\n", + "\n", + "print\"1) Reluctance =\",\"{0:.3e}\".format(S),\"A-T/Wb\"\n", + "\n", + "mmf=N*i\n", + "\n", + "print\"2) m.m.f =\",(mmf),\"Amp-turn\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Reluctance = 1.696e+07 A-T/Wb\n", + "2) m.m.f = 4500 Amp-turn\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.20,Page number 3-43" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#the magnetization force is given by,\n", + "#H=NI/l\n", + "\n", + "H=5*10**3 #coercivity of bar magnet\n", + "l=10*10**-2 #length of solenoid\n", + "N=50 #number of turns\n", + "\n", + "I=l*H/N\n", + "\n", + "print\"current =\",(I),\"Ampere\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "current = 10.0 Ampere\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.21,Page number 3-43" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "ur=380 #relative permeability of air\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "A=5*10**-4 #cross section area of ring\n", + "n=200 #number of turns\n", + "d=20*10**-2 #mean diameter of ring\n", + "\n", + "l=math.pi*d #mean circumference of ring\n", + "\n", + "phi=2*10**-3 #magnetic flux\n", + "\n", + "S=l/(u0*ur*A) #reluctance\n", + "\n", + "#using ohm's law for magnetic circuit\n", + "\n", + "#phi=N*I/S\n", + "\n", + "I=S*phi/n\n", + "\n", + "print\"1) Reluctance =\",\"{0:.3e}\".format(S),\"A-T/Wb\"\n", + "print\"2) current =\",round(I,4),\"Ampere\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Reluctance = 2.632e+06 A-T/Wb\n", + "2) current = 26.3158 Ampere\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.22,Page number 3-43" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "ur=1 #relative permeability of air\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "A=6*10**-4 #cross section area of torroid\n", + "n=500 #number of turns\n", + "r=15*10**-2 #radius of torroid\n", + "I=4 #current in coil\n", + "l=2*math.pi*r #mean circumference of torroid\n", + "MMF=n*I\n", + "\n", + "print\"1) MMF (NI) =\",(MMF),\"AT\"\n", + "\n", + "R=l/(u0*ur*A) #Reluctance\n", + "\n", + "print\"2) Reluctance (R) =\",\"{0:.3e}\".format(R),\"AT/Wb\"\n", + "\n", + "phi=MMF/R #flux\n", + "\n", + "print\"3) Magnetic flux =\",(phi),\"Wb\"\n", + "\n", + "B=phi/A #flux density\n", + "\n", + "print\"4) Flux density =\",\"{0:.3e}\".format(B),\"Wb/m**2\"\n", + "\n", + "H=B/(u0*ur) #magnetic field intensity\n", + "\n", + "print\"5) Magnetic field intensity =\",round(H,4),\"A/m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) MMF (NI) = 2000 AT\n", + "2) Reluctance (R) = 1.250e+09 AT/Wb\n", + "3) Magnetic flux = 1.6e-06 Wb\n", + "4) Flux density = 2.667e-03 Wb/m**2\n", + "5) Magnetic field intensity = 2122.0659 A/m\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.23,Page number 3-44" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "phi=10**-3 #magnetic flux\n", + "ur=1000 #relative permeability of iron\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "A=5*10**-4 #cross section area of ring\n", + "la=2*10**-3 #air gap\n", + "d=20*10**-3 #mean diameter of ring\n", + "\n", + "li=math.pi*d-la #mean circumference of ring\n", + "\n", + "#using KVL for magnetic circuit\n", + "\n", + "#AT(total)=AT(iron)+AT(air gap)\n", + "\n", + "ATt=(phi/(u0*A))*((li/ur)+la)\n", + "\n", + "print\"Number of Ampere-Turns required =\",round(ATt,0)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of Ampere-Turns required = 3280.0\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.24,Page number 3-44" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "X=0.5*10**-5 #susceptibility of material\n", + "\n", + "H=10**6 #magnetic field strength\n", + "\n", + "I=X*H #intensity of magnetization\n", + "\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "\n", + "B=u0*(H+I) #flux density\n", + "\n", + "print\"1) intensity magnetization =\",(I),\"Amp/m\"\n", + "\n", + "print\"2) flux density in the material =\",round(B,4),\"wb/m**2\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) intensity magnetization = 5.0 Amp/m\n", + "2) flux density in the material = 1.2566 wb/m**2\n" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Applied_Physics-I_by_I_A_Shaikh/Chapter3_2.ipynb b/Applied_Physics-I_by_I_A_Shaikh/Chapter3_2.ipynb new file mode 100644 index 00000000..7111a9da --- /dev/null +++ b/Applied_Physics-I_by_I_A_Shaikh/Chapter3_2.ipynb @@ -0,0 +1,1175 @@ +{ + "metadata": { + "celltoolbar": "Raw Cell Format", + "name": "", + "signature": "sha256:9dcf8c834afbbdba5cac9bfd61902345de5a5912fe35cd8c01ac3ee021a2040e" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 3: Dielectric And Magnetic Materials" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.1,Page number 3-35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "A=650*10**-6 #area\n", + "d=4*10**-3 #seperation of plate\n", + "Q=2*10**-10 #charge\n", + "er=3.5 #relative permitivity\n", + "\n", + "e0=8.85*10**-12 #absolute permitivity\n", + "\n", + "V=(Q*d)/(e0*er*A)\n", + "\n", + "print\"voltage across capacitor =\",round(V,4),\"Volt\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "voltage across capacitor = 39.7343 Volt\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.2,Page number 3-36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "A=2000*10**-6 #area\n", + "d=0.5*10**-6 #seperation of plate\n", + "er=8.0 #relative permitivity\n", + "e0=8.85*10**-12 #absolute permitivity\n", + "\n", + "C=(e0*er*A)/d\n", + "\n", + "print\"capacitance for capacitor =\",\"{0:.3e}\".format(C),\"Faraday\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "capacitance for capacitor = 2.832e-07 Faraday\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.3,Page number 3-36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "E=1000 #electric field\n", + "P=4.3*10**-8 #polarization\n", + "e0=8.854*10**-12 #absolute permitivity\n", + "er=(P/(e0*E))+1 #as P/E=e0(er-1)\n", + "\n", + "print\"relative permittivity =\",round(er,4)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "relative permittivity = 5.8566\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.4,Page number 3-36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#As C=e0*er*A/d\n", + "\n", + "e0=math.e #absolute permitivity\n", + "\n", + "Ag=1l\n", + "\n", + "Ap=Ag #Assuming Area of glass plate and plastic film is same\n", + "\n", + "#for glass\n", + "\n", + "erg=6 #relative permitivity\n", + "\n", + "dg=0.25 #thickness\n", + "\n", + "Cg=e0*erg*Ag/dg\n", + "\n", + "#for plastic film\n", + "\n", + "erp=3 #relative permitivity\n", + "\n", + "dp=0.1 #thickness\n", + "\n", + "Cp=e0*erp*Ap/dp\n", + "\n", + "m=Cg/Cp\n", + "\n", + "print\"since Cg/Cp=\",m\n", + "\n", + "print\"plastic film holds more charge\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "since Cg/Cp= 0.8\n", + "plastic film holds more charge\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.5,Page number 3-37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "N=2.7*10**25 #no of atoms per m**3\n", + "er=1.0000684 #dielectric constant of He atom at NTP\n", + "e0=8.854*10**-12 #absolute permitivity\n", + "\n", + "a=e0*(er-1.0)/N #electronic polarizability\n", + "\n", + "print\"1) electronic polarizability=\",\"{0:.3e}\".format(a)\n", + "\n", + "R=(a/(4*3.1472*e0))**(1.0/3) #radius of helium atom\n", + "\n", + "print\"2) radius of He atoms =\",\"{0:.3e}\".format(R),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) electronic polarizability= 2.243e-41\n", + "2) radius of He atoms = 5.860e-11 meter\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.6,Page number 3-37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "er=1.000014 #dielectric constant of He atom at NTP\n", + "Xe=er-1.0 #electric susceptibility\n", + "\n", + "print\"electric susceptibility =\",(Xe)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "electric susceptibility = 1.4e-05\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.7,Page number 3-37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "T=300 #temperature of paramagnetic material\n", + "X=3.7*10**-3 #susceptibility of material\n", + "\n", + "C=X*T #using Curie's law\n", + "\n", + "T1=250 #temperature\n", + "T2=600 #temperature\n", + "\n", + "u1=C/T1 #relative permeability of material at 250k\n", + "\n", + "u2=C/T2 #relative permeability of material at 350k\n", + "\n", + "print\"relative permeability at temp 250K=\",\"{0:.3e}\".format(u1)\n", + "\n", + "print\"relative permeability at temp 600K =\",\"{0:.3e}\".format(u2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "relative permeability at temp 250K= 4.440e-03\n", + "relative permeability at temp 600K = 1.850e-03\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.8,Page number 3-38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "u=0.8*10**-23 #magnetic dipole moment of an atom \n", + "B=0.8 #magnetic field\n", + "K=1.38*10**-23 #boltzmann constant\n", + "\n", + "T=(2*u*B)/(3*K) #temperature\n", + "\n", + "print\"Temperature at which average thermal energy of an atom is equal to magntic energy=\",round(T,4),\"K\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Temperature at which average thermal energy of an atom is equal to magntic energy= 0.3092 K\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.9,Page number 3-38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "B=0.5 #magnetic field\n", + "t=27 #temperature in degree celcius\n", + "T=273+t #temperature in kelvin\n", + "\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "\n", + "C=2*10**-3 #Curie's constant\n", + "\n", + "M=(C*B)/(u0*T) #magnetization of material\n", + "\n", + "print\"magnetization of paramagnetic material =\",round(M,4),\"A/m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "magnetization of paramagnetic material = 2.6526 A/m\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.10,Page number 3-38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "B=10.9*10**-5 #flux density\n", + "\n", + "H=B/u0 #magnetic field\n", + "\n", + "print\"Horizontal component of magnetic field =\",round(H,4),\"A-m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Horizontal component of magnetic field = 86.7394 A-m\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.11,Page number 3-39" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "phi=5.9*10**-3 #magnetic flux\n", + "ur=900 #relative permeability of material\n", + "n=700 #number of turns\n", + "\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "\n", + "A=60*10**-4 #cross section area of ring\n", + "\n", + "l=2 #mean circumference of ring\n", + "\n", + "B=phi/A #flux density\n", + "\n", + "H=B/(u0*ur) #magnetic field\n", + "\n", + "At=H*l #Amp-turns required\n", + "\n", + "I=At/n #current required\n", + "\n", + "print\"Current required to produce a flux=\",round(I,4),\"Amp\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Current required to produce a flux= 2.4842 Amp\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.12,Page number 3-39" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "phi=2.7*10**-3 #magnetic flux\n", + "A=25*10**-4 #cross section area of ring\n", + "r=25*10**-2 #mean circumference of ring\n", + "la=10**-3 #air gap\n", + "\n", + "ur=900 #relative permeability of material\n", + "n=400 #number of turns\n", + "\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "\n", + "d=40*10**-2 #mean diameter of ring\n", + "\n", + "li=2*math.pi*r #mean circumference of ring\n", + "\n", + "B=phi/A #flux density\n", + "\n", + "#for air gap\n", + "\n", + "Ha=B/(u0) #magnetic field for air gap\n", + "\n", + "#for iron ring\n", + "\n", + "Hi=B/(u0*ur) #magnetic field for iron ring\n", + "\n", + "#therefore, Amp turn in air gap\n", + "\n", + "Ata=Ha*la #Amp-turns required\n", + "\n", + "#therefore, Amp-turn in ring\n", + "\n", + "Ati=Hi*li #Amp-turns required\n", + "\n", + "#therrfore total mmf required\n", + "\n", + "mmf=Ata+Ati\n", + "\n", + "#Current required\n", + "\n", + "I=mmf/n #current required\n", + "\n", + "print\"Current required =\",round(I,4),\"Amp\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Current required = 5.8986 Amp\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.13,Page number 3-40" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n1=10 #no of turns per cm\n", + "i=2 #current\n", + "B=1 #flux density\n", + "\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "\n", + "n=n1*100 #no turns per m\n", + "\n", + "H=n*i\n", + "\n", + "print\"1) magnetic intensity =\",round(H,4),\"Amp-turn/meter\"\n", + "\n", + "#calculation for magnetization\n", + "\n", + "I=B/u0-H\n", + "\n", + "print\"2) magnetization =\",\"{0:.3e}\".format(I),\"Amp-turn/meter\"\n", + "\n", + "#relative permeability\n", + "\n", + "ur=B/(u0*H)\n", + "\n", + "print\"3) Relative Permeability of the ring =\",(int(ur))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) magnetic intensity = 2000.0 Amp-turn/meter\n", + "2) magnetization = 7.938e+05 Amp-turn/meter\n", + "3) Relative Permeability of the ring = 397\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.14,Page number 3-40" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "m=40 #wt of the core\n", + "d=7.5*10**3 #density of iron\n", + "n=100 #frequency\n", + "\n", + "V=m/d #volume of the iron core\n", + "\n", + "E1=3800*10**-1 #loss of energy in core per cycles/cc\n", + "\n", + "E2=E1*V #loss of energy in core per cycles\n", + "\n", + "N=60*n #no of cycles per minute\n", + "\n", + "E=E2*N #loss of energy per minute\n", + "\n", + "print\"Loss of energy per minute =\",(E),\"Joule\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Loss of energy per minute = 12160.0 Joule\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.15,Page number 3-40" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "l=30*10**-2 #length of ring\n", + "A=1*10**-4 #cross section area of ring\n", + "i=0.032 #current\n", + "\n", + "phi=2*10**-6 #magnetic flux\n", + "\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "\n", + "N=300 #no of turns in the coil\n", + "\n", + "#1) flux density\n", + "\n", + "B=phi/A #flux density\n", + "\n", + "print\"1) Flux density in the ring =\",(B),\"Wb/m**2\"\n", + "\n", + "#2) magnetic intensity of ring\n", + "\n", + "n=N/l #no of turns per unit length\n", + "\n", + "H=n*i #magnetic intensity\n", + "\n", + "print\"2) magnetic intensity =\",(H),\"Amp-turn/meter\"\n", + "\n", + "#3) permeability and relative permeability of the ring\n", + "\n", + "u=B/H\n", + "\n", + "print\"3) Permeability of the ring =\",\"{0:.3e}\".format(u),\"Wb/A-m\"\n", + "\n", + "ur=u/u0\n", + "\n", + "print\"4) Relative Permeability of the ring =\",round(ur,4)\n", + "\n", + "#4)Susceptibility\n", + "\n", + "Xm=ur-1\n", + "\n", + "print\"5) magnetic Susceptibility of the ring =\",round(Xm,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Flux density in the ring = 0.02 Wb/m**2\n", + "2) magnetic intensity = 32.0 Amp-turn/meter\n", + "3) Permeability of the ring = 6.250e-04 Wb/A-m\n", + "4) Relative Permeability of the ring = 497.3592\n", + "5) magnetic Susceptibility of the ring = 496.3592\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.16,Page number 3-41" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "E=3000 #loss of energy per cycle per cm**3\n", + "m=12*10**3 #wt of the core\n", + "d=7.5 #density of iron\n", + "n=50 #frequency\n", + "\n", + "V=m/d #volume of the core\n", + "\n", + "El=E*V*n*60*60 #loss of energy per hour\n", + "\n", + "print\"Loss of energy per hour =\",(El),\"Erg\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Loss of energy per hour = 8.64e+11 Erg\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.17,Page number 3-41" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=50 #frequency\n", + "V=10**-3 #volume of the specimen\n", + "\n", + "#Area of B-H loop\n", + "\n", + "A=0.5*10**3*1\n", + "\n", + "P=n*V*A\n", + "\n", + "print\"Hysteresis power loss =\",(P),\"Watt\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Hysteresis power loss = 25.0 Watt\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.18,Page number 3-42" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "phi=1.5*10**-4 #magnetic flux\n", + "\n", + "ur=900 #relative permeability of material\n", + "\n", + "n=600 #number of turns\n", + "\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "\n", + "A=5.8*10**-4 #cross section area of ring\n", + "\n", + "d=40*10**-2 #mean diameter of ring\n", + "\n", + "li=math.pi*d #mean circumference of ring\n", + "\n", + "la=5*10**-3 #air gap\n", + "\n", + "B=phi/A #flux density\n", + "\n", + "#for air gap\n", + "\n", + "Ha=B/(u0) #magnetic field for air gap\n", + "\n", + "#for iron ring\n", + "\n", + "Hi=B/(u0*ur) #magnetic field for iron ring\n", + "\n", + "#therefore, Amp turn in air gap\n", + "\n", + "Ata=Ha*la #Amp-turns required\n", + "\n", + "#therefore, Amp-turn in ring\n", + "\n", + "Ati=Hi*li #Amp-turns required\n", + "\n", + "#therrfore total mmf required\n", + "\n", + "mmf=Ata+Ati\n", + "\n", + "#Current required\n", + "\n", + "I=mmf/n #current required\n", + "\n", + "print\"Current required =\",round(I,4),\"Amp\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Current required = 2.194 Amp\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.19,Page number 3-42" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "la=1*10**-2 #air gap\n", + "r=0.5 #radius of ring\n", + "A=5*10**-4 #cross section area of ring\n", + "i=5 #current\n", + "u=6*10**-3 #permeability of iron\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "N=900 #no of turns in the coil\n", + "\n", + "#let reluctance of iron ring with air gap be S\n", + "\n", + "S=la/(u0*A)+(2*math.pi*r-la)/(u*A)\n", + "\n", + "print\"1) Reluctance =\",\"{0:.3e}\".format(S),\"A-T/Wb\"\n", + "\n", + "mmf=N*i\n", + "\n", + "print\"2) m.m.f =\",(mmf),\"Amp-turn\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Reluctance = 1.696e+07 A-T/Wb\n", + "2) m.m.f = 4500 Amp-turn\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.20,Page number 3-43" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#the magnetization force is given by,\n", + "#H=NI/l\n", + "\n", + "H=5*10**3 #coercivity of bar magnet\n", + "l=10*10**-2 #length of solenoid\n", + "N=50 #number of turns\n", + "\n", + "I=l*H/N\n", + "\n", + "print\"current =\",(I),\"Ampere\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "current = 10.0 Ampere\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.21,Page number 3-43" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "ur=380 #relative permeability of air\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "A=5*10**-4 #cross section area of ring\n", + "n=200 #number of turns\n", + "d=20*10**-2 #mean diameter of ring\n", + "\n", + "l=math.pi*d #mean circumference of ring\n", + "\n", + "phi=2*10**-3 #magnetic flux\n", + "\n", + "S=l/(u0*ur*A) #reluctance\n", + "\n", + "#using ohm's law for magnetic circuit\n", + "\n", + "#phi=N*I/S\n", + "\n", + "I=S*phi/n\n", + "\n", + "print\"1) Reluctance =\",\"{0:.3e}\".format(S),\"A-T/Wb\"\n", + "print\"2) current =\",round(I,4),\"Ampere\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Reluctance = 2.632e+06 A-T/Wb\n", + "2) current = 26.3158 Ampere\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.22,Page number 3-43" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "ur=1 #relative permeability of air\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "A=6*10**-4 #cross section area of torroid\n", + "n=500 #number of turns\n", + "r=15*10**-2 #radius of torroid\n", + "I=4 #current in coil\n", + "l=2*math.pi*r #mean circumference of torroid\n", + "MMF=n*I\n", + "\n", + "print\"1) MMF (NI) =\",(MMF),\"AT\"\n", + "\n", + "R=l/(u0*ur*A) #Reluctance\n", + "\n", + "print\"2) Reluctance (R) =\",\"{0:.3e}\".format(R),\"AT/Wb\"\n", + "\n", + "phi=MMF/R #flux\n", + "\n", + "print\"3) Magnetic flux =\",(phi),\"Wb\"\n", + "\n", + "B=phi/A #flux density\n", + "\n", + "print\"4) Flux density =\",\"{0:.3e}\".format(B),\"Wb/m**2\"\n", + "\n", + "H=B/(u0*ur) #magnetic field intensity\n", + "\n", + "print\"5) Magnetic field intensity =\",round(H,4),\"A/m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) MMF (NI) = 2000 AT\n", + "2) Reluctance (R) = 1.250e+09 AT/Wb\n", + "3) Magnetic flux = 1.6e-06 Wb\n", + "4) Flux density = 2.667e-03 Wb/m**2\n", + "5) Magnetic field intensity = 2122.0659 A/m\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.23,Page number 3-44" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "phi=10**-3 #magnetic flux\n", + "ur=1000 #relative permeability of iron\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "A=5*10**-4 #cross section area of ring\n", + "la=2*10**-3 #air gap\n", + "d=20*10**-3 #mean diameter of ring\n", + "\n", + "li=math.pi*d-la #mean circumference of ring\n", + "\n", + "#using KVL for magnetic circuit\n", + "\n", + "#AT(total)=AT(iron)+AT(air gap)\n", + "\n", + "ATt=(phi/(u0*A))*((li/ur)+la)\n", + "\n", + "print\"Number of Ampere-Turns required =\",round(ATt,0)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of Ampere-Turns required = 3280.0\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17.24,Page number 3-44" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "X=0.5*10**-5 #susceptibility of material\n", + "\n", + "H=10**6 #magnetic field strength\n", + "\n", + "I=X*H #intensity of magnetization\n", + "\n", + "u0=4*math.pi*10**-7 #permeability of free space\n", + "\n", + "B=u0*(H+I) #flux density\n", + "\n", + "print\"1) intensity magnetization =\",(I),\"Amp/m\"\n", + "\n", + "print\"2) flux density in the material =\",round(B,4),\"wb/m**2\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) intensity magnetization = 5.0 Amp/m\n", + "2) flux density in the material = 1.2566 wb/m**2\n" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Applied_Physics-I_by_I_A_Shaikh/Chapter4.ipynb b/Applied_Physics-I_by_I_A_Shaikh/Chapter4.ipynb new file mode 100755 index 00000000..ded2d042 --- /dev/null +++ b/Applied_Physics-I_by_I_A_Shaikh/Chapter4.ipynb @@ -0,0 +1,1309 @@ +{ + "metadata": { + "celltoolbar": "Raw Cell Format", + "name": "", + "signature": "sha256:c8b4bc6a0f384361dda4e7989c0d96facf075884a24ed18090bbb83730c8fbed" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 4: Acoustics and Ultrasonics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.11.1,Page number 4-17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given data\n", + "d=8900.0 #density\n", + "Y=20.8*10**10 #Young's modulus\n", + "n=40*10**3 #frequency of wave\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "l=(k/(2*n))*math.sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "print\"length =\",round(l,4),\"meter\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "length = 0.0604 meter\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.12.1,Page number 4-20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given data\n", + "\n", + "d=2.65*10**3 #density\n", + "Y=8*10**10 #Young's modulus\n", + "n=1*10**6 #frequency of wave\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "t=(k/(2*n))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "print\"thickness =\",round(t,4),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "thickness = 0.0027 meter\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.1,Page number 4-25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data\n", + "l=20 #length of room\n", + "b=15 #bredth of room\n", + "h=10 #height of room\n", + "V=l*b*h #volume of room\n", + "a=0.106 #absorption coefficient\n", + "\n", + "S=2*(l*b+b*h+h*l) #surface area of hall\n", + "\n", + "T=(0.161*V)/(a*S) #Reverberation time,using Sabine's formula\n", + "\n", + "print\"Reverberation time =\",round(T,4),\"sec\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Reverberation time = 3.5051 sec\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.2,Page number 4-26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "m=1j #original sound intensity\n", + "n=1000*1j #increased intensity value\n", + "\n", + "l=10*log10(n/m) #change in intensity level\n", + "\n", + "print\"change in intensity level =\",l,\"dB\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "change in intensity level = (30+0j) dB\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.3,Page number 4-26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "S1=220 #wall area\n", + "a1=0.03 #absorption coefficient for the wall\n", + "S2=120 #floor area\n", + "a2=0.8 #absorption coefficient for the floor\n", + "S3=120 #ceiling area\n", + "a3=0.06 #absorption coefficient for the ceiling\n", + "V=600 #volume of room\n", + "\n", + "S=S1+S2+S3 #total surface area\n", + "\n", + "a=(a1*S1+a2*S2+a3*S3)/S #average sound absorption coefficient\n", + "\n", + "print\"1) average sound absorption coefficient =\",round(a,4)\n", + "\n", + "T=(0.161*V)/(a*S) #Reverberation time,using Sabine's formula\n", + "\n", + "print\"2) Reverberation time =\",round(T,4),\"sec\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) average sound absorption coefficient = 0.2387\n", + "2) Reverberation time = 0.8798 sec\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.4,Page number 4-27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given data\n", + "\n", + "V=5500 #volume\n", + "T=2.3 #Reverberation time\n", + "S=750 #sound absorption coefficient\n", + "a=(0.161*V)/(S*T) #using Sabine's formula\n", + "\n", + "print\"average absorption coefficient =\",round(a,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "average absorption coefficient = 0.5133\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.5,Page number 4-27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "l=20 #length of room\n", + "b=12 #bredth of room\n", + "h=12 #height of room\n", + "V=l*b*h #volume of room\n", + "S=2*(l*b+b*h+h*l) #surface area of hall\n", + "T1=2.5 #Reverberation time\n", + "\n", + "a=(0.161*V)/(T1*S) #using Sabine's formula\n", + "\n", + "print\"1) average absorption coefficient =\",round(a,4)\n", + "\n", + "a1=0.5 #absorption coefficient\n", + "T2=2 #Reverberation time\n", + "\n", + "S1=(0.161*V/(a1-a))*(1.0/T2-1.0/T1)\n", + "\n", + "print\"2) carpet area required =\",round(S1,4),\"m^2\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) average absorption coefficient = 0.1486\n", + "2) carpet area required = 131.958 m^2\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.6,Page number 4-28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Ac=10*12 #area of carpet covering entire floor\n", + "ac=0.06 #absorption coefficient of carpet\n", + "\n", + "aS1=Ac*ac #absorption due to carpet\n", + "\n", + "Af=10*12 #area of false celling\n", + "af=0.03 #absorption coefficient of celling\n", + "\n", + "aS2=Af*af #absorption due to celling\n", + "\n", + "As=100*1 #area of cushioned sets\n", + "a_cush=1 #absorption coefficient of cushion sets\n", + "\n", + "aS3=As*a_cush #absorption due to cusion sets\n", + "\n", + "Aw=346*1 #area of walls covered with absorbent\n", + "aw=0.2 #absorption coefficient of walls\n", + "\n", + "aS4=Aw*aw #absorption due to walls\n", + "\n", + "Ad=346*1 #area of wooden door\n", + "ad=0.2 #absorption coefficient of wooden door\n", + "\n", + "aS5=Ad*ad #absorption due to wooden door\n", + "\n", + "aS=aS1+aS2+aS3+aS4 #total absorption\n", + "\n", + "ap=0.46 #absorption coefficient of audience/person\n", + "l=12 #assuming length of wall\n", + "b=10 #assuming breadth of wall\n", + "h=8 #assuming height of wall\n", + "\n", + "V=l*b*h #volume of hall\n", + "\n", + "#case 1 :(no one inside/emptey hall)\n", + "\n", + "T1=(0.161*V)/aS #reverberation time\n", + "\n", + "print\" 1)reverberation time of empty hall =\",round(T1,4),\"sec\"\n", + "\n", + "#case 2 :(50 person inside hall)\n", + "\n", + "T2=(0.161*V)/(aS+50*0.46) #reverberation time\n", + "\n", + "print\" 2)reverberation time of hall with 50 person =\",round(T2,4),\"sec\"\n", + "\n", + "#case 2 :(100 person inside hall/full capacity of hall)\n", + "\n", + "T3=(0.161*V)/(aS+100*0.46) #reverberation time\n", + "\n", + "print\" 3)reverberation time of hall with 100 person =\",round(T3,4),\"sec\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " 1)reverberation time of empty hall = 0.8587 sec\n", + " 2)reverberation time of hall with 50 person = 0.7614 sec\n", + " 3)reverberation time of hall with 100 person = 0.6839 sec\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.7,Page number 4-30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "l=20 #length of room\n", + "b=15 #bredth of room\n", + "h=5 #height of room\n", + "\n", + "V=l*b*h #volume of room\n", + "S=2*(l*b+b*h+h*l) #surface area of hall\n", + "\n", + "T=3.5 #Reverberation time\n", + "\n", + "a=(0.161*V)/(T*S) #using Sabine's formula\n", + "\n", + "print\"1) average absorption coefficient =\",round(a,4)\n", + "\n", + "avg=a*S #average total absorption\n", + "\n", + "print\"2) average total absorption =\",round(avg,4),\"m^2.s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) average absorption coefficient = 0.0726\n", + "2) average total absorption = 69.0 m^2.s\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.8,Page number 4-30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "l=20 #length of room\n", + "b=15 #bredth of room\n", + "h=10 #height of room\n", + "\n", + "V=l*b*h #volume of room\n", + "\n", + "a=0.1 #absorption coefficient\n", + "\n", + "S=2*(l*b+b*h+h*l) #surface area of hall\n", + "\n", + "T1=(0.161*V)/(a*S) #Reverberation time,using Sabine's formula\n", + "\n", + "print\"1) Reverberation time =\",round(T1,4),\"sec\"\n", + "\n", + "a2=0.66 #absorption coefficient of curtain cloth\n", + "\n", + "S2=100 #surface area of a curtain cloth\n", + "\n", + "T2=(0.161*V)/(a*S+a2*S2*2) #Reverberation time,using Sabine's formula\n", + "\n", + "T=T1-T2 #change in Reverberation time\n", + "\n", + "print\"2) change in Reverberation time =\",round(T,4),\"sec\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Reverberation time = 3.7154 sec\n", + "2) change in Reverberation time = 1.8719 sec\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.9,Page number 4-30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "S1=220 #wall area\n", + "a1=0.03 #absorption coefficient for the wall\n", + "S2=120 #floor area\n", + "a2=0.8 #absorption coefficient for the floor\n", + "S3=120 #ceiling area\n", + "a3=0.06 #absorption coefficient for the ceiling\n", + "V=600 #volume of room\n", + "\n", + "S=S1+S2+S3 #total surface area\n", + "a=(a1*S1+a2*S2+a3*S3)/S #average sound absorption coefficient\n", + "\n", + "print\"1) average sound absorption coefficient =\",round(a,4)\n", + "\n", + "T=(0.161*V)/(a*S) #Reverberation time,using Sabine's formula\n", + "\n", + "print\"2) Reverberation time =\",round(T,4),\"sec\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) average sound absorption coefficient = 0.2387\n", + "2) Reverberation time = 0.8798 sec\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.10,Page number 4-31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "f=0.07*10**6 #frequency\n", + "t=0.65 #time\n", + "v=1700 #velocity of sound\n", + "\n", + "d=v*t/2 #depth of seabed\n", + "\n", + "print\"1) depth of seabed =\",round(d,4),\"meter\"\n", + "\n", + "lamda=v/f #wavelength\n", + "\n", + "print\"2) wavelength =\",round(lamda,4),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) depth of seabed = 552.5 meter\n", + "2) wavelength = 0.0243 meter\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.11,Page number 4-31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "t=1*10**-3 #thicknesss of crystal\n", + "d=2.65*10**3 #density\n", + "Y=8*10**10 #Young's modulus\n", + "k=1 #consider 1st harmonic\n", + "\n", + "n=(k/(2*t))*sqrt(Y/d) #formula of natural frequency\n", + "\n", + "print\" natural frequency =\",\"{0:.3e}\".format(n),\"Hz\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " natural frequency = 2.747e+06 Hz\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.12,Page number 4-32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "d=2650 #density\n", + "Y=8*10**10 #Young's modulus\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "#case 1\n", + "\n", + "n1=3.8*10**6 #frequency of wave\n", + "\n", + "t1=(k/(2*n1))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "print\"1) thickness =\",\"{0:.3e}\".format(t1),\"meter\"\n", + "\n", + "#case 2\n", + "\n", + "n2=300*10**3 #frequency of wave\n", + "\n", + "t2=(k/(2*n2))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "print\"2) thickness =\",\"{0:.3e}\".format(t2),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) thickness = 7.230e-04 meter\n", + "2) thickness = 9.157e-03 meter\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.13,Page number 4-32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "d=2650 #density\n", + "Y=8*10**10 #Young's modulus\n", + "n=2*10**6 #frequency of wave\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "t=(k/(2*n))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "print\"thickness =\",\"{0:.3e}\".format(t),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "thickness = 1.374e-03 meter\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.14,Page number 4-33" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "f=50*10**3 #frequency\n", + "v1=348 #velocity of ultrasound in atmosphere\n", + "v2=1392 #velocity of ultrasound in sea water\n", + "t=2.0 #time difference\n", + "\n", + "#distance is constant hence v1*t1=v2*t2\n", + "\n", + "m=v2/v1 #assuming constant as m\n", + "\n", + "#(t1-t2=d) and (t1=m*t2) therefore\n", + "\n", + "t2=t/(m-1)\n", + "\n", + "d=v2*t2 #distance between two ship\n", + "\n", + "print\"distance between two ships =\",round(d,4),\"meter\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "distance between two ships = 928.0 meter\n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.15,Page number 4-34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#for case1\n", + "t1=2*10**-3 #thicknesss of plate\n", + "d=2.65*10**3 #density\n", + "Y=8*10**10 #Young's modulus\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "n1=(k/(2*t1))*sqrt(Y/d) #formula of natural frequency\n", + "\n", + "print\"1)natural frequency =\",\"{0:.3e}\".format(n1),\"Hz\"\n", + "\n", + "#for case2\n", + "\n", + "n2=3*10**6 #frequency\n", + "\n", + "t2=(k/(2*n2))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "t=t1-t2 #change in thickness\n", + "\n", + "print\"2)change in thickness =\",\"{0:.3e}\".format(t),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)natural frequency = 1.374e+06 Hz\n", + "2)change in thickness = 1.084e-03 meter\n" + ] + } + ], + "prompt_number": 29 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.16,Page number 4-34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "S=10 #salinity\n", + "t=2 #time\n", + "T=20 #temperature\n", + "\n", + "v=1510+1.14*S+4.21*T-0.037*T**2 #velocity of ultrasound in sea\n", + "\n", + "d=v*t/2 #depth of sea bed\n", + "\n", + "print\"depth of sea bed =\",round(d,4),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "depth of sea bed = 1590.8 meter\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.17,Page number 4-35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "S=29 #salinity\n", + "t=2 #time\n", + "l=0.01 #wavelength\n", + "T=30 #temperature\n", + "\n", + "v=1510+1.14*S+4.21*T-0.037*T**2 #velocity of ultrasound in sea\n", + "\n", + "d=v*t/2 #depth of sea bed\n", + "\n", + "print\"1)depth of sea bed =\",round(d,4),\"meter\"\n", + "\n", + "f=v/l #frequency\n", + "\n", + "print\"2) frequency =\",\"{0:.3e}\".format(f),\"Hz\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)depth of sea bed = 1636.06 meter\n", + "2) frequency = 1.636e+05 Hz\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.18,Page number 4-35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "v1=5.9*10**3 #velocity of UW in mild steel\n", + "v2=4.3*10**3 #velocity of UW in brass\n", + "t2=15*10**-3 #thickness of brass plate\n", + "\n", + "t1=v2*t2/v1 #since ve;ocity is inversly proportional to thickness\n", + "\n", + "print\"real thickness =\",\"{0:.3e}\".format(t1),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "real thickness = 1.093e-02 meter\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.19,Page number 4-36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "t1=4*10**-3 #thickness of 1st crystal\n", + "n1=400*10**3 #frequency of 1st crystal\n", + "n2=500*10**3 #frequency of 2nd crystal\n", + "\n", + "t2=n1*t1/n2 #since frquency is inversly proportional to thickness\n", + "\n", + "print\"thickness of 2nd crystal =\",\"{0:.3e}\".format(t2),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "thickness of 2nd crystal = 3.200e-03 meter\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.20,Page number 4-36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "t2=30*10**-6 #pulse arrival time of defective steel bar\n", + "t1=80*10**-6 #pulse arrival time of non defective steel bar\n", + "d=40*10**-2 #bar thickness\n", + "\n", + "x=(t2/t1)*d\n", + "\n", + "print\"distance at which defect has occurred =\",round(x,4),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "distance at which defect has occurred = 0.15 meter\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.21,Page number 4-37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "d=18*10**-3 #thickness\n", + "v=5.9*10**3 #velocity\n", + "\n", + "t=(2*d)/v #echo time\n", + "\n", + "print\"echo time =\",\"{0:.3e}\".format(t),\"sec\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "echo time = 6.102e-06 sec\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.22,Page number 4-37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "t=1*10**-3 #thickness of quartz crystal\n", + "\n", + "#given t=l/2\n", + "\n", + "l=t*2 #wavelength\n", + "Y=7.9*10**10 #young's module of crystal\n", + "p=2650 #density of crystal\n", + "\n", + "v=sqrt(Y/p) #velocity of vibration\n", + "\n", + "n=v/l #frequency of vibration\n", + "\n", + "print\"frquency of vibration =\",\"{0:.3e}\".format(n),\"Hz\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "frquency of vibration = 2.730e+06 Hz\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.23,Page number 4-38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "#given data\n", + "\n", + "d=7.23*10**3 #density\n", + "Y=11.6*10**10 #Young's modulus\n", + "n=20*10**3 #frequency of wave\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "l=(k/(2*n))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "print\"length =\",\"{0:.3e}\".format(l),\"meter\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "length = 1.001e-01 meter\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.24,Page number 4-38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#for case1\n", + "t1=2*10**-3 #thicknesss of plate\n", + "d=2.65*10**3 #density\n", + "Y=8*10**10 #Young's modulus\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "n1=(k/(2*t1))*sqrt(Y/d) #formula of natural frequency\n", + "\n", + "print\"1)natural frequency =\",\"{0:.3e}\".format(n1),\"Hz\"\n", + "\n", + "#for case2\n", + "\n", + "n2=3*10**6 #frequency\n", + "\n", + "t2=(k/(2*n2))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "t=t1-t2 #change in thickness\n", + "\n", + "print\"2)change in thickness =\",\"{0:.3e}\".format(t),\"meter\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)natural frequency = 1.374e+06 Hz\n", + "2)change in thickness = 1.084e-03 meter\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.25,Page number 4-39" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "l=20 #length of room\n", + "b=15 #bredth of room\n", + "h=10 #height of room\n", + "\n", + "V=l*b*h #volume of room\n", + "S=2*(l*b+b*h+h*l) #surface area of hall\n", + "\n", + "T=3 #Reverberation time\n", + "\n", + "a=(0.161*V)/(T*S) #using Sabine's formula\n", + "\n", + "print\"1) average absorption coefficient =\",round(a,4)\n", + "\n", + "m=a*S #total absorption\n", + "\n", + "print\"2) total absorption of surface =\",round(m,4),\"m**2/sec\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) average absorption coefficient = 0.1238\n", + "2) total absorption of surface = 161.0 m**2/sec\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.26,Page number 4-39" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#for case1\n", + "t1=1.8*10**-3 #thicknesss of plate\n", + "d=2.65*10**3 #density\n", + "Y=8*10**10 #Young's modulus\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "n1=(k/(2*t1))*sqrt(Y/d) #formula of natural frequency\n", + "\n", + "print\"1)natural frequency =\",\"{0:.3e}\".format(n1),\"Hz\"\n", + "\n", + "#for case2\n", + "\n", + "n2=2*10**6 #frequency\n", + "\n", + "t2=(k/(2*n2))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "t=t1-t2 #change in thickness\n", + "\n", + "print\"2)change in thickness =\",\"{0:.3e}\".format(t),\"meter\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)natural frequency = 1.526e+06 Hz\n", + "2)change in thickness = 4.264e-04 meter\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.27,Page number 4-39" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=0.4999*10**6 #frequency\n", + "t=5.5*10**-3 #thicknesss of plate\n", + "d=2.65*10**3 #density\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "Y=4*(t**2)*(n**2)*d/k #arranging formula of natural frequency\n", + "\n", + "print\"Youngs modulus =\",\"{0:.3e}\".format(Y),\"N/m**2\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Youngs modulus = 8.013e+10 N/m**2\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Applied_Physics-I_by_I_A_Shaikh/Chapter4_1.ipynb b/Applied_Physics-I_by_I_A_Shaikh/Chapter4_1.ipynb new file mode 100755 index 00000000..ded2d042 --- /dev/null +++ b/Applied_Physics-I_by_I_A_Shaikh/Chapter4_1.ipynb @@ -0,0 +1,1309 @@ +{ + "metadata": { + "celltoolbar": "Raw Cell Format", + "name": "", + "signature": "sha256:c8b4bc6a0f384361dda4e7989c0d96facf075884a24ed18090bbb83730c8fbed" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 4: Acoustics and Ultrasonics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.11.1,Page number 4-17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given data\n", + "d=8900.0 #density\n", + "Y=20.8*10**10 #Young's modulus\n", + "n=40*10**3 #frequency of wave\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "l=(k/(2*n))*math.sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "print\"length =\",round(l,4),\"meter\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "length = 0.0604 meter\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.12.1,Page number 4-20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given data\n", + "\n", + "d=2.65*10**3 #density\n", + "Y=8*10**10 #Young's modulus\n", + "n=1*10**6 #frequency of wave\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "t=(k/(2*n))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "print\"thickness =\",round(t,4),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "thickness = 0.0027 meter\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.1,Page number 4-25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data\n", + "l=20 #length of room\n", + "b=15 #bredth of room\n", + "h=10 #height of room\n", + "V=l*b*h #volume of room\n", + "a=0.106 #absorption coefficient\n", + "\n", + "S=2*(l*b+b*h+h*l) #surface area of hall\n", + "\n", + "T=(0.161*V)/(a*S) #Reverberation time,using Sabine's formula\n", + "\n", + "print\"Reverberation time =\",round(T,4),\"sec\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Reverberation time = 3.5051 sec\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.2,Page number 4-26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "m=1j #original sound intensity\n", + "n=1000*1j #increased intensity value\n", + "\n", + "l=10*log10(n/m) #change in intensity level\n", + "\n", + "print\"change in intensity level =\",l,\"dB\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "change in intensity level = (30+0j) dB\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.3,Page number 4-26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "S1=220 #wall area\n", + "a1=0.03 #absorption coefficient for the wall\n", + "S2=120 #floor area\n", + "a2=0.8 #absorption coefficient for the floor\n", + "S3=120 #ceiling area\n", + "a3=0.06 #absorption coefficient for the ceiling\n", + "V=600 #volume of room\n", + "\n", + "S=S1+S2+S3 #total surface area\n", + "\n", + "a=(a1*S1+a2*S2+a3*S3)/S #average sound absorption coefficient\n", + "\n", + "print\"1) average sound absorption coefficient =\",round(a,4)\n", + "\n", + "T=(0.161*V)/(a*S) #Reverberation time,using Sabine's formula\n", + "\n", + "print\"2) Reverberation time =\",round(T,4),\"sec\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) average sound absorption coefficient = 0.2387\n", + "2) Reverberation time = 0.8798 sec\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.4,Page number 4-27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given data\n", + "\n", + "V=5500 #volume\n", + "T=2.3 #Reverberation time\n", + "S=750 #sound absorption coefficient\n", + "a=(0.161*V)/(S*T) #using Sabine's formula\n", + "\n", + "print\"average absorption coefficient =\",round(a,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "average absorption coefficient = 0.5133\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.5,Page number 4-27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "l=20 #length of room\n", + "b=12 #bredth of room\n", + "h=12 #height of room\n", + "V=l*b*h #volume of room\n", + "S=2*(l*b+b*h+h*l) #surface area of hall\n", + "T1=2.5 #Reverberation time\n", + "\n", + "a=(0.161*V)/(T1*S) #using Sabine's formula\n", + "\n", + "print\"1) average absorption coefficient =\",round(a,4)\n", + "\n", + "a1=0.5 #absorption coefficient\n", + "T2=2 #Reverberation time\n", + "\n", + "S1=(0.161*V/(a1-a))*(1.0/T2-1.0/T1)\n", + "\n", + "print\"2) carpet area required =\",round(S1,4),\"m^2\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) average absorption coefficient = 0.1486\n", + "2) carpet area required = 131.958 m^2\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.6,Page number 4-28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Ac=10*12 #area of carpet covering entire floor\n", + "ac=0.06 #absorption coefficient of carpet\n", + "\n", + "aS1=Ac*ac #absorption due to carpet\n", + "\n", + "Af=10*12 #area of false celling\n", + "af=0.03 #absorption coefficient of celling\n", + "\n", + "aS2=Af*af #absorption due to celling\n", + "\n", + "As=100*1 #area of cushioned sets\n", + "a_cush=1 #absorption coefficient of cushion sets\n", + "\n", + "aS3=As*a_cush #absorption due to cusion sets\n", + "\n", + "Aw=346*1 #area of walls covered with absorbent\n", + "aw=0.2 #absorption coefficient of walls\n", + "\n", + "aS4=Aw*aw #absorption due to walls\n", + "\n", + "Ad=346*1 #area of wooden door\n", + "ad=0.2 #absorption coefficient of wooden door\n", + "\n", + "aS5=Ad*ad #absorption due to wooden door\n", + "\n", + "aS=aS1+aS2+aS3+aS4 #total absorption\n", + "\n", + "ap=0.46 #absorption coefficient of audience/person\n", + "l=12 #assuming length of wall\n", + "b=10 #assuming breadth of wall\n", + "h=8 #assuming height of wall\n", + "\n", + "V=l*b*h #volume of hall\n", + "\n", + "#case 1 :(no one inside/emptey hall)\n", + "\n", + "T1=(0.161*V)/aS #reverberation time\n", + "\n", + "print\" 1)reverberation time of empty hall =\",round(T1,4),\"sec\"\n", + "\n", + "#case 2 :(50 person inside hall)\n", + "\n", + "T2=(0.161*V)/(aS+50*0.46) #reverberation time\n", + "\n", + "print\" 2)reverberation time of hall with 50 person =\",round(T2,4),\"sec\"\n", + "\n", + "#case 2 :(100 person inside hall/full capacity of hall)\n", + "\n", + "T3=(0.161*V)/(aS+100*0.46) #reverberation time\n", + "\n", + "print\" 3)reverberation time of hall with 100 person =\",round(T3,4),\"sec\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " 1)reverberation time of empty hall = 0.8587 sec\n", + " 2)reverberation time of hall with 50 person = 0.7614 sec\n", + " 3)reverberation time of hall with 100 person = 0.6839 sec\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.7,Page number 4-30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "l=20 #length of room\n", + "b=15 #bredth of room\n", + "h=5 #height of room\n", + "\n", + "V=l*b*h #volume of room\n", + "S=2*(l*b+b*h+h*l) #surface area of hall\n", + "\n", + "T=3.5 #Reverberation time\n", + "\n", + "a=(0.161*V)/(T*S) #using Sabine's formula\n", + "\n", + "print\"1) average absorption coefficient =\",round(a,4)\n", + "\n", + "avg=a*S #average total absorption\n", + "\n", + "print\"2) average total absorption =\",round(avg,4),\"m^2.s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) average absorption coefficient = 0.0726\n", + "2) average total absorption = 69.0 m^2.s\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.8,Page number 4-30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "l=20 #length of room\n", + "b=15 #bredth of room\n", + "h=10 #height of room\n", + "\n", + "V=l*b*h #volume of room\n", + "\n", + "a=0.1 #absorption coefficient\n", + "\n", + "S=2*(l*b+b*h+h*l) #surface area of hall\n", + "\n", + "T1=(0.161*V)/(a*S) #Reverberation time,using Sabine's formula\n", + "\n", + "print\"1) Reverberation time =\",round(T1,4),\"sec\"\n", + "\n", + "a2=0.66 #absorption coefficient of curtain cloth\n", + "\n", + "S2=100 #surface area of a curtain cloth\n", + "\n", + "T2=(0.161*V)/(a*S+a2*S2*2) #Reverberation time,using Sabine's formula\n", + "\n", + "T=T1-T2 #change in Reverberation time\n", + "\n", + "print\"2) change in Reverberation time =\",round(T,4),\"sec\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Reverberation time = 3.7154 sec\n", + "2) change in Reverberation time = 1.8719 sec\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.9,Page number 4-30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "S1=220 #wall area\n", + "a1=0.03 #absorption coefficient for the wall\n", + "S2=120 #floor area\n", + "a2=0.8 #absorption coefficient for the floor\n", + "S3=120 #ceiling area\n", + "a3=0.06 #absorption coefficient for the ceiling\n", + "V=600 #volume of room\n", + "\n", + "S=S1+S2+S3 #total surface area\n", + "a=(a1*S1+a2*S2+a3*S3)/S #average sound absorption coefficient\n", + "\n", + "print\"1) average sound absorption coefficient =\",round(a,4)\n", + "\n", + "T=(0.161*V)/(a*S) #Reverberation time,using Sabine's formula\n", + "\n", + "print\"2) Reverberation time =\",round(T,4),\"sec\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) average sound absorption coefficient = 0.2387\n", + "2) Reverberation time = 0.8798 sec\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.10,Page number 4-31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "f=0.07*10**6 #frequency\n", + "t=0.65 #time\n", + "v=1700 #velocity of sound\n", + "\n", + "d=v*t/2 #depth of seabed\n", + "\n", + "print\"1) depth of seabed =\",round(d,4),\"meter\"\n", + "\n", + "lamda=v/f #wavelength\n", + "\n", + "print\"2) wavelength =\",round(lamda,4),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) depth of seabed = 552.5 meter\n", + "2) wavelength = 0.0243 meter\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.11,Page number 4-31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "t=1*10**-3 #thicknesss of crystal\n", + "d=2.65*10**3 #density\n", + "Y=8*10**10 #Young's modulus\n", + "k=1 #consider 1st harmonic\n", + "\n", + "n=(k/(2*t))*sqrt(Y/d) #formula of natural frequency\n", + "\n", + "print\" natural frequency =\",\"{0:.3e}\".format(n),\"Hz\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " natural frequency = 2.747e+06 Hz\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.12,Page number 4-32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "d=2650 #density\n", + "Y=8*10**10 #Young's modulus\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "#case 1\n", + "\n", + "n1=3.8*10**6 #frequency of wave\n", + "\n", + "t1=(k/(2*n1))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "print\"1) thickness =\",\"{0:.3e}\".format(t1),\"meter\"\n", + "\n", + "#case 2\n", + "\n", + "n2=300*10**3 #frequency of wave\n", + "\n", + "t2=(k/(2*n2))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "print\"2) thickness =\",\"{0:.3e}\".format(t2),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) thickness = 7.230e-04 meter\n", + "2) thickness = 9.157e-03 meter\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.13,Page number 4-32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "d=2650 #density\n", + "Y=8*10**10 #Young's modulus\n", + "n=2*10**6 #frequency of wave\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "t=(k/(2*n))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "print\"thickness =\",\"{0:.3e}\".format(t),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "thickness = 1.374e-03 meter\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.14,Page number 4-33" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "f=50*10**3 #frequency\n", + "v1=348 #velocity of ultrasound in atmosphere\n", + "v2=1392 #velocity of ultrasound in sea water\n", + "t=2.0 #time difference\n", + "\n", + "#distance is constant hence v1*t1=v2*t2\n", + "\n", + "m=v2/v1 #assuming constant as m\n", + "\n", + "#(t1-t2=d) and (t1=m*t2) therefore\n", + "\n", + "t2=t/(m-1)\n", + "\n", + "d=v2*t2 #distance between two ship\n", + "\n", + "print\"distance between two ships =\",round(d,4),\"meter\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "distance between two ships = 928.0 meter\n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.15,Page number 4-34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#for case1\n", + "t1=2*10**-3 #thicknesss of plate\n", + "d=2.65*10**3 #density\n", + "Y=8*10**10 #Young's modulus\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "n1=(k/(2*t1))*sqrt(Y/d) #formula of natural frequency\n", + "\n", + "print\"1)natural frequency =\",\"{0:.3e}\".format(n1),\"Hz\"\n", + "\n", + "#for case2\n", + "\n", + "n2=3*10**6 #frequency\n", + "\n", + "t2=(k/(2*n2))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "t=t1-t2 #change in thickness\n", + "\n", + "print\"2)change in thickness =\",\"{0:.3e}\".format(t),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)natural frequency = 1.374e+06 Hz\n", + "2)change in thickness = 1.084e-03 meter\n" + ] + } + ], + "prompt_number": 29 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.16,Page number 4-34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "S=10 #salinity\n", + "t=2 #time\n", + "T=20 #temperature\n", + "\n", + "v=1510+1.14*S+4.21*T-0.037*T**2 #velocity of ultrasound in sea\n", + "\n", + "d=v*t/2 #depth of sea bed\n", + "\n", + "print\"depth of sea bed =\",round(d,4),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "depth of sea bed = 1590.8 meter\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.17,Page number 4-35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "S=29 #salinity\n", + "t=2 #time\n", + "l=0.01 #wavelength\n", + "T=30 #temperature\n", + "\n", + "v=1510+1.14*S+4.21*T-0.037*T**2 #velocity of ultrasound in sea\n", + "\n", + "d=v*t/2 #depth of sea bed\n", + "\n", + "print\"1)depth of sea bed =\",round(d,4),\"meter\"\n", + "\n", + "f=v/l #frequency\n", + "\n", + "print\"2) frequency =\",\"{0:.3e}\".format(f),\"Hz\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)depth of sea bed = 1636.06 meter\n", + "2) frequency = 1.636e+05 Hz\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.18,Page number 4-35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "v1=5.9*10**3 #velocity of UW in mild steel\n", + "v2=4.3*10**3 #velocity of UW in brass\n", + "t2=15*10**-3 #thickness of brass plate\n", + "\n", + "t1=v2*t2/v1 #since ve;ocity is inversly proportional to thickness\n", + "\n", + "print\"real thickness =\",\"{0:.3e}\".format(t1),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "real thickness = 1.093e-02 meter\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.19,Page number 4-36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "t1=4*10**-3 #thickness of 1st crystal\n", + "n1=400*10**3 #frequency of 1st crystal\n", + "n2=500*10**3 #frequency of 2nd crystal\n", + "\n", + "t2=n1*t1/n2 #since frquency is inversly proportional to thickness\n", + "\n", + "print\"thickness of 2nd crystal =\",\"{0:.3e}\".format(t2),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "thickness of 2nd crystal = 3.200e-03 meter\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.20,Page number 4-36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "t2=30*10**-6 #pulse arrival time of defective steel bar\n", + "t1=80*10**-6 #pulse arrival time of non defective steel bar\n", + "d=40*10**-2 #bar thickness\n", + "\n", + "x=(t2/t1)*d\n", + "\n", + "print\"distance at which defect has occurred =\",round(x,4),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "distance at which defect has occurred = 0.15 meter\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.21,Page number 4-37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "d=18*10**-3 #thickness\n", + "v=5.9*10**3 #velocity\n", + "\n", + "t=(2*d)/v #echo time\n", + "\n", + "print\"echo time =\",\"{0:.3e}\".format(t),\"sec\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "echo time = 6.102e-06 sec\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.22,Page number 4-37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "t=1*10**-3 #thickness of quartz crystal\n", + "\n", + "#given t=l/2\n", + "\n", + "l=t*2 #wavelength\n", + "Y=7.9*10**10 #young's module of crystal\n", + "p=2650 #density of crystal\n", + "\n", + "v=sqrt(Y/p) #velocity of vibration\n", + "\n", + "n=v/l #frequency of vibration\n", + "\n", + "print\"frquency of vibration =\",\"{0:.3e}\".format(n),\"Hz\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "frquency of vibration = 2.730e+06 Hz\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.23,Page number 4-38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "#given data\n", + "\n", + "d=7.23*10**3 #density\n", + "Y=11.6*10**10 #Young's modulus\n", + "n=20*10**3 #frequency of wave\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "l=(k/(2*n))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "print\"length =\",\"{0:.3e}\".format(l),\"meter\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "length = 1.001e-01 meter\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.24,Page number 4-38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#for case1\n", + "t1=2*10**-3 #thicknesss of plate\n", + "d=2.65*10**3 #density\n", + "Y=8*10**10 #Young's modulus\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "n1=(k/(2*t1))*sqrt(Y/d) #formula of natural frequency\n", + "\n", + "print\"1)natural frequency =\",\"{0:.3e}\".format(n1),\"Hz\"\n", + "\n", + "#for case2\n", + "\n", + "n2=3*10**6 #frequency\n", + "\n", + "t2=(k/(2*n2))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "t=t1-t2 #change in thickness\n", + "\n", + "print\"2)change in thickness =\",\"{0:.3e}\".format(t),\"meter\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)natural frequency = 1.374e+06 Hz\n", + "2)change in thickness = 1.084e-03 meter\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.25,Page number 4-39" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "l=20 #length of room\n", + "b=15 #bredth of room\n", + "h=10 #height of room\n", + "\n", + "V=l*b*h #volume of room\n", + "S=2*(l*b+b*h+h*l) #surface area of hall\n", + "\n", + "T=3 #Reverberation time\n", + "\n", + "a=(0.161*V)/(T*S) #using Sabine's formula\n", + "\n", + "print\"1) average absorption coefficient =\",round(a,4)\n", + "\n", + "m=a*S #total absorption\n", + "\n", + "print\"2) total absorption of surface =\",round(m,4),\"m**2/sec\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) average absorption coefficient = 0.1238\n", + "2) total absorption of surface = 161.0 m**2/sec\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.26,Page number 4-39" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#for case1\n", + "t1=1.8*10**-3 #thicknesss of plate\n", + "d=2.65*10**3 #density\n", + "Y=8*10**10 #Young's modulus\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "n1=(k/(2*t1))*sqrt(Y/d) #formula of natural frequency\n", + "\n", + "print\"1)natural frequency =\",\"{0:.3e}\".format(n1),\"Hz\"\n", + "\n", + "#for case2\n", + "\n", + "n2=2*10**6 #frequency\n", + "\n", + "t2=(k/(2*n2))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "t=t1-t2 #change in thickness\n", + "\n", + "print\"2)change in thickness =\",\"{0:.3e}\".format(t),\"meter\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)natural frequency = 1.526e+06 Hz\n", + "2)change in thickness = 4.264e-04 meter\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.27,Page number 4-39" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=0.4999*10**6 #frequency\n", + "t=5.5*10**-3 #thicknesss of plate\n", + "d=2.65*10**3 #density\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "Y=4*(t**2)*(n**2)*d/k #arranging formula of natural frequency\n", + "\n", + "print\"Youngs modulus =\",\"{0:.3e}\".format(Y),\"N/m**2\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Youngs modulus = 8.013e+10 N/m**2\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Applied_Physics-I_by_I_A_Shaikh/Chapter4_2.ipynb b/Applied_Physics-I_by_I_A_Shaikh/Chapter4_2.ipynb new file mode 100644 index 00000000..ded2d042 --- /dev/null +++ b/Applied_Physics-I_by_I_A_Shaikh/Chapter4_2.ipynb @@ -0,0 +1,1309 @@ +{ + "metadata": { + "celltoolbar": "Raw Cell Format", + "name": "", + "signature": "sha256:c8b4bc6a0f384361dda4e7989c0d96facf075884a24ed18090bbb83730c8fbed" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 4: Acoustics and Ultrasonics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.11.1,Page number 4-17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given data\n", + "d=8900.0 #density\n", + "Y=20.8*10**10 #Young's modulus\n", + "n=40*10**3 #frequency of wave\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "l=(k/(2*n))*math.sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "print\"length =\",round(l,4),\"meter\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "length = 0.0604 meter\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.12.1,Page number 4-20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given data\n", + "\n", + "d=2.65*10**3 #density\n", + "Y=8*10**10 #Young's modulus\n", + "n=1*10**6 #frequency of wave\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "t=(k/(2*n))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "print\"thickness =\",round(t,4),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "thickness = 0.0027 meter\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.1,Page number 4-25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data\n", + "l=20 #length of room\n", + "b=15 #bredth of room\n", + "h=10 #height of room\n", + "V=l*b*h #volume of room\n", + "a=0.106 #absorption coefficient\n", + "\n", + "S=2*(l*b+b*h+h*l) #surface area of hall\n", + "\n", + "T=(0.161*V)/(a*S) #Reverberation time,using Sabine's formula\n", + "\n", + "print\"Reverberation time =\",round(T,4),\"sec\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Reverberation time = 3.5051 sec\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.2,Page number 4-26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "m=1j #original sound intensity\n", + "n=1000*1j #increased intensity value\n", + "\n", + "l=10*log10(n/m) #change in intensity level\n", + "\n", + "print\"change in intensity level =\",l,\"dB\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "change in intensity level = (30+0j) dB\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.3,Page number 4-26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "S1=220 #wall area\n", + "a1=0.03 #absorption coefficient for the wall\n", + "S2=120 #floor area\n", + "a2=0.8 #absorption coefficient for the floor\n", + "S3=120 #ceiling area\n", + "a3=0.06 #absorption coefficient for the ceiling\n", + "V=600 #volume of room\n", + "\n", + "S=S1+S2+S3 #total surface area\n", + "\n", + "a=(a1*S1+a2*S2+a3*S3)/S #average sound absorption coefficient\n", + "\n", + "print\"1) average sound absorption coefficient =\",round(a,4)\n", + "\n", + "T=(0.161*V)/(a*S) #Reverberation time,using Sabine's formula\n", + "\n", + "print\"2) Reverberation time =\",round(T,4),\"sec\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) average sound absorption coefficient = 0.2387\n", + "2) Reverberation time = 0.8798 sec\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.4,Page number 4-27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given data\n", + "\n", + "V=5500 #volume\n", + "T=2.3 #Reverberation time\n", + "S=750 #sound absorption coefficient\n", + "a=(0.161*V)/(S*T) #using Sabine's formula\n", + "\n", + "print\"average absorption coefficient =\",round(a,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "average absorption coefficient = 0.5133\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.5,Page number 4-27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "l=20 #length of room\n", + "b=12 #bredth of room\n", + "h=12 #height of room\n", + "V=l*b*h #volume of room\n", + "S=2*(l*b+b*h+h*l) #surface area of hall\n", + "T1=2.5 #Reverberation time\n", + "\n", + "a=(0.161*V)/(T1*S) #using Sabine's formula\n", + "\n", + "print\"1) average absorption coefficient =\",round(a,4)\n", + "\n", + "a1=0.5 #absorption coefficient\n", + "T2=2 #Reverberation time\n", + "\n", + "S1=(0.161*V/(a1-a))*(1.0/T2-1.0/T1)\n", + "\n", + "print\"2) carpet area required =\",round(S1,4),\"m^2\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) average absorption coefficient = 0.1486\n", + "2) carpet area required = 131.958 m^2\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.6,Page number 4-28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Ac=10*12 #area of carpet covering entire floor\n", + "ac=0.06 #absorption coefficient of carpet\n", + "\n", + "aS1=Ac*ac #absorption due to carpet\n", + "\n", + "Af=10*12 #area of false celling\n", + "af=0.03 #absorption coefficient of celling\n", + "\n", + "aS2=Af*af #absorption due to celling\n", + "\n", + "As=100*1 #area of cushioned sets\n", + "a_cush=1 #absorption coefficient of cushion sets\n", + "\n", + "aS3=As*a_cush #absorption due to cusion sets\n", + "\n", + "Aw=346*1 #area of walls covered with absorbent\n", + "aw=0.2 #absorption coefficient of walls\n", + "\n", + "aS4=Aw*aw #absorption due to walls\n", + "\n", + "Ad=346*1 #area of wooden door\n", + "ad=0.2 #absorption coefficient of wooden door\n", + "\n", + "aS5=Ad*ad #absorption due to wooden door\n", + "\n", + "aS=aS1+aS2+aS3+aS4 #total absorption\n", + "\n", + "ap=0.46 #absorption coefficient of audience/person\n", + "l=12 #assuming length of wall\n", + "b=10 #assuming breadth of wall\n", + "h=8 #assuming height of wall\n", + "\n", + "V=l*b*h #volume of hall\n", + "\n", + "#case 1 :(no one inside/emptey hall)\n", + "\n", + "T1=(0.161*V)/aS #reverberation time\n", + "\n", + "print\" 1)reverberation time of empty hall =\",round(T1,4),\"sec\"\n", + "\n", + "#case 2 :(50 person inside hall)\n", + "\n", + "T2=(0.161*V)/(aS+50*0.46) #reverberation time\n", + "\n", + "print\" 2)reverberation time of hall with 50 person =\",round(T2,4),\"sec\"\n", + "\n", + "#case 2 :(100 person inside hall/full capacity of hall)\n", + "\n", + "T3=(0.161*V)/(aS+100*0.46) #reverberation time\n", + "\n", + "print\" 3)reverberation time of hall with 100 person =\",round(T3,4),\"sec\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " 1)reverberation time of empty hall = 0.8587 sec\n", + " 2)reverberation time of hall with 50 person = 0.7614 sec\n", + " 3)reverberation time of hall with 100 person = 0.6839 sec\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.7,Page number 4-30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "l=20 #length of room\n", + "b=15 #bredth of room\n", + "h=5 #height of room\n", + "\n", + "V=l*b*h #volume of room\n", + "S=2*(l*b+b*h+h*l) #surface area of hall\n", + "\n", + "T=3.5 #Reverberation time\n", + "\n", + "a=(0.161*V)/(T*S) #using Sabine's formula\n", + "\n", + "print\"1) average absorption coefficient =\",round(a,4)\n", + "\n", + "avg=a*S #average total absorption\n", + "\n", + "print\"2) average total absorption =\",round(avg,4),\"m^2.s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) average absorption coefficient = 0.0726\n", + "2) average total absorption = 69.0 m^2.s\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.8,Page number 4-30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "l=20 #length of room\n", + "b=15 #bredth of room\n", + "h=10 #height of room\n", + "\n", + "V=l*b*h #volume of room\n", + "\n", + "a=0.1 #absorption coefficient\n", + "\n", + "S=2*(l*b+b*h+h*l) #surface area of hall\n", + "\n", + "T1=(0.161*V)/(a*S) #Reverberation time,using Sabine's formula\n", + "\n", + "print\"1) Reverberation time =\",round(T1,4),\"sec\"\n", + "\n", + "a2=0.66 #absorption coefficient of curtain cloth\n", + "\n", + "S2=100 #surface area of a curtain cloth\n", + "\n", + "T2=(0.161*V)/(a*S+a2*S2*2) #Reverberation time,using Sabine's formula\n", + "\n", + "T=T1-T2 #change in Reverberation time\n", + "\n", + "print\"2) change in Reverberation time =\",round(T,4),\"sec\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Reverberation time = 3.7154 sec\n", + "2) change in Reverberation time = 1.8719 sec\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.9,Page number 4-30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "S1=220 #wall area\n", + "a1=0.03 #absorption coefficient for the wall\n", + "S2=120 #floor area\n", + "a2=0.8 #absorption coefficient for the floor\n", + "S3=120 #ceiling area\n", + "a3=0.06 #absorption coefficient for the ceiling\n", + "V=600 #volume of room\n", + "\n", + "S=S1+S2+S3 #total surface area\n", + "a=(a1*S1+a2*S2+a3*S3)/S #average sound absorption coefficient\n", + "\n", + "print\"1) average sound absorption coefficient =\",round(a,4)\n", + "\n", + "T=(0.161*V)/(a*S) #Reverberation time,using Sabine's formula\n", + "\n", + "print\"2) Reverberation time =\",round(T,4),\"sec\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) average sound absorption coefficient = 0.2387\n", + "2) Reverberation time = 0.8798 sec\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.10,Page number 4-31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "f=0.07*10**6 #frequency\n", + "t=0.65 #time\n", + "v=1700 #velocity of sound\n", + "\n", + "d=v*t/2 #depth of seabed\n", + "\n", + "print\"1) depth of seabed =\",round(d,4),\"meter\"\n", + "\n", + "lamda=v/f #wavelength\n", + "\n", + "print\"2) wavelength =\",round(lamda,4),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) depth of seabed = 552.5 meter\n", + "2) wavelength = 0.0243 meter\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.11,Page number 4-31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "t=1*10**-3 #thicknesss of crystal\n", + "d=2.65*10**3 #density\n", + "Y=8*10**10 #Young's modulus\n", + "k=1 #consider 1st harmonic\n", + "\n", + "n=(k/(2*t))*sqrt(Y/d) #formula of natural frequency\n", + "\n", + "print\" natural frequency =\",\"{0:.3e}\".format(n),\"Hz\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " natural frequency = 2.747e+06 Hz\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.12,Page number 4-32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "d=2650 #density\n", + "Y=8*10**10 #Young's modulus\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "#case 1\n", + "\n", + "n1=3.8*10**6 #frequency of wave\n", + "\n", + "t1=(k/(2*n1))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "print\"1) thickness =\",\"{0:.3e}\".format(t1),\"meter\"\n", + "\n", + "#case 2\n", + "\n", + "n2=300*10**3 #frequency of wave\n", + "\n", + "t2=(k/(2*n2))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "print\"2) thickness =\",\"{0:.3e}\".format(t2),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) thickness = 7.230e-04 meter\n", + "2) thickness = 9.157e-03 meter\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.13,Page number 4-32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "d=2650 #density\n", + "Y=8*10**10 #Young's modulus\n", + "n=2*10**6 #frequency of wave\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "t=(k/(2*n))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "print\"thickness =\",\"{0:.3e}\".format(t),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "thickness = 1.374e-03 meter\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.14,Page number 4-33" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "f=50*10**3 #frequency\n", + "v1=348 #velocity of ultrasound in atmosphere\n", + "v2=1392 #velocity of ultrasound in sea water\n", + "t=2.0 #time difference\n", + "\n", + "#distance is constant hence v1*t1=v2*t2\n", + "\n", + "m=v2/v1 #assuming constant as m\n", + "\n", + "#(t1-t2=d) and (t1=m*t2) therefore\n", + "\n", + "t2=t/(m-1)\n", + "\n", + "d=v2*t2 #distance between two ship\n", + "\n", + "print\"distance between two ships =\",round(d,4),\"meter\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "distance between two ships = 928.0 meter\n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.15,Page number 4-34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#for case1\n", + "t1=2*10**-3 #thicknesss of plate\n", + "d=2.65*10**3 #density\n", + "Y=8*10**10 #Young's modulus\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "n1=(k/(2*t1))*sqrt(Y/d) #formula of natural frequency\n", + "\n", + "print\"1)natural frequency =\",\"{0:.3e}\".format(n1),\"Hz\"\n", + "\n", + "#for case2\n", + "\n", + "n2=3*10**6 #frequency\n", + "\n", + "t2=(k/(2*n2))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "t=t1-t2 #change in thickness\n", + "\n", + "print\"2)change in thickness =\",\"{0:.3e}\".format(t),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)natural frequency = 1.374e+06 Hz\n", + "2)change in thickness = 1.084e-03 meter\n" + ] + } + ], + "prompt_number": 29 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.16,Page number 4-34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "S=10 #salinity\n", + "t=2 #time\n", + "T=20 #temperature\n", + "\n", + "v=1510+1.14*S+4.21*T-0.037*T**2 #velocity of ultrasound in sea\n", + "\n", + "d=v*t/2 #depth of sea bed\n", + "\n", + "print\"depth of sea bed =\",round(d,4),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "depth of sea bed = 1590.8 meter\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.17,Page number 4-35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "S=29 #salinity\n", + "t=2 #time\n", + "l=0.01 #wavelength\n", + "T=30 #temperature\n", + "\n", + "v=1510+1.14*S+4.21*T-0.037*T**2 #velocity of ultrasound in sea\n", + "\n", + "d=v*t/2 #depth of sea bed\n", + "\n", + "print\"1)depth of sea bed =\",round(d,4),\"meter\"\n", + "\n", + "f=v/l #frequency\n", + "\n", + "print\"2) frequency =\",\"{0:.3e}\".format(f),\"Hz\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)depth of sea bed = 1636.06 meter\n", + "2) frequency = 1.636e+05 Hz\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.18,Page number 4-35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "v1=5.9*10**3 #velocity of UW in mild steel\n", + "v2=4.3*10**3 #velocity of UW in brass\n", + "t2=15*10**-3 #thickness of brass plate\n", + "\n", + "t1=v2*t2/v1 #since ve;ocity is inversly proportional to thickness\n", + "\n", + "print\"real thickness =\",\"{0:.3e}\".format(t1),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "real thickness = 1.093e-02 meter\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.19,Page number 4-36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "t1=4*10**-3 #thickness of 1st crystal\n", + "n1=400*10**3 #frequency of 1st crystal\n", + "n2=500*10**3 #frequency of 2nd crystal\n", + "\n", + "t2=n1*t1/n2 #since frquency is inversly proportional to thickness\n", + "\n", + "print\"thickness of 2nd crystal =\",\"{0:.3e}\".format(t2),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "thickness of 2nd crystal = 3.200e-03 meter\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.20,Page number 4-36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "t2=30*10**-6 #pulse arrival time of defective steel bar\n", + "t1=80*10**-6 #pulse arrival time of non defective steel bar\n", + "d=40*10**-2 #bar thickness\n", + "\n", + "x=(t2/t1)*d\n", + "\n", + "print\"distance at which defect has occurred =\",round(x,4),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "distance at which defect has occurred = 0.15 meter\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.21,Page number 4-37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "d=18*10**-3 #thickness\n", + "v=5.9*10**3 #velocity\n", + "\n", + "t=(2*d)/v #echo time\n", + "\n", + "print\"echo time =\",\"{0:.3e}\".format(t),\"sec\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "echo time = 6.102e-06 sec\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.22,Page number 4-37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "t=1*10**-3 #thickness of quartz crystal\n", + "\n", + "#given t=l/2\n", + "\n", + "l=t*2 #wavelength\n", + "Y=7.9*10**10 #young's module of crystal\n", + "p=2650 #density of crystal\n", + "\n", + "v=sqrt(Y/p) #velocity of vibration\n", + "\n", + "n=v/l #frequency of vibration\n", + "\n", + "print\"frquency of vibration =\",\"{0:.3e}\".format(n),\"Hz\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "frquency of vibration = 2.730e+06 Hz\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.23,Page number 4-38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "#given data\n", + "\n", + "d=7.23*10**3 #density\n", + "Y=11.6*10**10 #Young's modulus\n", + "n=20*10**3 #frequency of wave\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "l=(k/(2*n))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "print\"length =\",\"{0:.3e}\".format(l),\"meter\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "length = 1.001e-01 meter\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.24,Page number 4-38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#for case1\n", + "t1=2*10**-3 #thicknesss of plate\n", + "d=2.65*10**3 #density\n", + "Y=8*10**10 #Young's modulus\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "n1=(k/(2*t1))*sqrt(Y/d) #formula of natural frequency\n", + "\n", + "print\"1)natural frequency =\",\"{0:.3e}\".format(n1),\"Hz\"\n", + "\n", + "#for case2\n", + "\n", + "n2=3*10**6 #frequency\n", + "\n", + "t2=(k/(2*n2))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "t=t1-t2 #change in thickness\n", + "\n", + "print\"2)change in thickness =\",\"{0:.3e}\".format(t),\"meter\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)natural frequency = 1.374e+06 Hz\n", + "2)change in thickness = 1.084e-03 meter\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.25,Page number 4-39" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "l=20 #length of room\n", + "b=15 #bredth of room\n", + "h=10 #height of room\n", + "\n", + "V=l*b*h #volume of room\n", + "S=2*(l*b+b*h+h*l) #surface area of hall\n", + "\n", + "T=3 #Reverberation time\n", + "\n", + "a=(0.161*V)/(T*S) #using Sabine's formula\n", + "\n", + "print\"1) average absorption coefficient =\",round(a,4)\n", + "\n", + "m=a*S #total absorption\n", + "\n", + "print\"2) total absorption of surface =\",round(m,4),\"m**2/sec\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) average absorption coefficient = 0.1238\n", + "2) total absorption of surface = 161.0 m**2/sec\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.26,Page number 4-39" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#for case1\n", + "t1=1.8*10**-3 #thicknesss of plate\n", + "d=2.65*10**3 #density\n", + "Y=8*10**10 #Young's modulus\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "n1=(k/(2*t1))*sqrt(Y/d) #formula of natural frequency\n", + "\n", + "print\"1)natural frequency =\",\"{0:.3e}\".format(n1),\"Hz\"\n", + "\n", + "#for case2\n", + "\n", + "n2=2*10**6 #frequency\n", + "\n", + "t2=(k/(2*n2))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "t=t1-t2 #change in thickness\n", + "\n", + "print\"2)change in thickness =\",\"{0:.3e}\".format(t),\"meter\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)natural frequency = 1.526e+06 Hz\n", + "2)change in thickness = 4.264e-04 meter\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.27,Page number 4-39" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=0.4999*10**6 #frequency\n", + "t=5.5*10**-3 #thicknesss of plate\n", + "d=2.65*10**3 #density\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "Y=4*(t**2)*(n**2)*d/k #arranging formula of natural frequency\n", + "\n", + "print\"Youngs modulus =\",\"{0:.3e}\".format(Y),\"N/m**2\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Youngs modulus = 8.013e+10 N/m**2\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Applied_Physics-I_by_I_A_Shaikh/README.txt b/Applied_Physics-I_by_I_A_Shaikh/README.txt new file mode 100644 index 00000000..525c6847 --- /dev/null +++ b/Applied_Physics-I_by_I_A_Shaikh/README.txt @@ -0,0 +1,10 @@ +Contributed By: ajinkya khair +Course: be +College/Institute/Organization: V.E.S.I.T. +Department/Designation: Electronic and telecommunication +Book Title: Applied Physics-I +Author: I A Shaikh +Publisher: Tech-max Publication, Pune +Year of publication: 2013 +Isbn: 9789350770641 +Edition: 7
\ No newline at end of file diff --git a/Applied_Physics-I_by_I_A_Shaikh/chapter1.ipynb b/Applied_Physics-I_by_I_A_Shaikh/chapter1.ipynb new file mode 100755 index 00000000..b2a76d3e --- /dev/null +++ b/Applied_Physics-I_by_I_A_Shaikh/chapter1.ipynb @@ -0,0 +1,2525 @@ +{ + "metadata": { + "celltoolbar": "Raw Cell Format", + "name": "", + "signature": "sha256:3e9b00b8b544a24032a4bb804cb876f45a5efd85913287f396a56723a0eb1a09" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 1: Crystallography" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.3.1,Page number 1-14" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "A=26.98 #atomic weight of Al\n", + "N=6.023*10**26 #Avogadro's number\n", + "p=2700 #Density\n", + "n=4 #FCC structure\n", + "\n", + "a=(n*A/(N*p))**(1./3)\n", + "\n", + "print\"Unit cell dimension of Al=\",\"{0:.3e}\".format(a),\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Unit cell dimension of Al= 4.049e-10 m\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.3.2,Page number 1-15" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "As=28.1 #atomic weight of Si\n", + "Ag=69.7 #atomic weight of Ga\n", + "Aa=74.9 #atomic weight of As\n", + "a_s=5.43*10**-8 #lattice constant of Si\n", + "aga=5.65*10**-8 #lattice constant of GaAs\n", + "ns=8 #no of atoms/unit cell in Si\n", + "nga=4 #no of atoms/unit cell in GaAs\n", + "N=6.023*10**23 #Avogadro's number\n", + "\n", + "#p=(n*A)/(N*a**3) this is formula for density\n", + "\n", + "#for Si\n", + "\n", + "ps=(ns*As)/(N*a_s**3)\n", + "\n", + "print\"1) Density of Si=\",round(ps,4),\"gm/cm^3\"\n", + "\n", + "#for GaAs\n", + "\n", + "Aga=Ag+Aa #molecular wt of GaAs\n", + "\n", + "pga=(nga*Aga)/(N*aga**3)\n", + "\n", + "print\"2) Density of GaAs=\",round(pga,4),\"gm/cm^3\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Density of Si= 2.3312 gm/cm^3\n", + "2) Density of GaAs= 5.3244 gm/cm^3\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.3.3,Page number 1-16" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "A=63.5 #atomic weight of Cu\n", + "N=6.023*10**23 #Avogadro's number\n", + "n=4 #FCC structure\n", + "r=1.28*10**-8 #atomic radius of Cu\n", + "\n", + "#for FCC\n", + "\n", + "a=4*r/(sqrt(2)) #lattice constant\n", + "p=(n*A)/(N*a**3)\n", + "\n", + "print\"Density of Cu=\",round(p,4),\"gm/cm^3\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Density of Cu= 8.887 gm/cm^3\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.3.4,Page number 1-17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "A=50 #atomic weight of chromium\n", + "N=6.023*10**23 #Avogadro's number\n", + "p=5.96 #Density\n", + "n=2 #BCC structure\n", + "\n", + "#step 1 : claculation for lattice constant (a)\n", + "\n", + "a=(n*A/(N*p))**(1./3)\n", + "\n", + "#step 2 : radius of an atom in BCC\n", + "\n", + "r=sqrt(3)*a/4\n", + "\n", + "#step 3 : Atomic packing factor (APF)\n", + "\n", + "APF=n*((4./3)*math.pi*r**3)/a**3\n", + "\n", + "print\"Atomic packing factor (APF)=\",round(APF,4)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Atomic packing factor (APF)= 0.6802\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.3.5,Page number 1-17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "A=120 #atomic weight of chromium\n", + "N=6.023*10**23 #Avogadro's number\n", + "p=5.2 #Density\n", + "n=2 #BCC structure\n", + "m=20 #mass\n", + "\n", + "#step 1 : claculation for volume of unit cell(a**3)\n", + "\n", + "a=(n*A/(N*p))\n", + "\n", + "#step 2 : volume of 20 gm of the element\n", + "\n", + "v=m/p\n", + "\n", + "#step 3 :no of unit cell\n", + "\n", + "x=v/a\n", + "\n", + "print\"no of unit cell=\",\"{0:.3e}\".format(x)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "no of unit cell= 5.019e+22\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.3.6,Page number 1-18" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "A=132.91 #atomic weight of chromium\n", + "N=6.023*10**26 #Avogadro's number\n", + "p=1900 #Density\n", + "a=6.14*10**-10 #lattice constant\n", + "\n", + "#step 1 : type of structure\n", + "\n", + "n=(p*N*a**3)/A\n", + "\n", + "print\"n =\",round(n)\n", + "\n", + "print\"BCC structure\"\n", + "\n", + "#step 2: no of atoms/m**3\n", + "\n", + "x=n/a**3\n", + "\n", + "print\"no of atoms/m^3=\",\"{0:.3e}\".format(x)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "n = 2.0\n", + "BCC structure\n", + "no of atoms/m^3= 8.610e+27\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.3.7,Page number 1-18" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "a=0.4049*10**-9 #lattice constant\n", + "t=0.006*10**-2 #thickness of Al foil\n", + "A=50*10**-4 #Area of foil\n", + "\n", + "V1=a**3 #volume of unit cell\n", + "\n", + "V=A*t #volume of the foil\n", + "\n", + "N=V/V1 #no of unit cell in the foil\n", + "\n", + "print\"no of unit cell in the foil=\",\"{0:.3e}\".format(N)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "no of unit cell in the foil= 4.519e+21\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.5.1,Page number 1-29" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#refer diagram from textbook\n", + "\n", + "#on joining centre of 3 anions,an equilateral triangle is formed and on joining centres of any anion and cation a right angle triangle ABC os formed\n", + "\n", + "#where AC=rc+ra\n", + "\n", + "#and BC=ra\n", + "\n", + "#m(angle (ACB))=30 degree\n", + "\n", + "#therefore cos (30)=ra/(rc+ra)\n", + "\n", + "#assume rc/ra=r\n", + "\n", + "r=(1.0-math.cos(30.0*math.pi/180))/math.cos(math.pi*30/180) #by arrangimg terms we get value of r\n", + "\n", + "print\"critical radius ratio of ligancy 3=\",round(r,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "critical radius ratio of ligancy 3= 0.1547\n" + ] + } + ], + "prompt_number": 33 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.5.2,Page number 1-30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#refer diagram from textbook\n", + "\n", + "#in the said arrangement a cation is squeezed into 4 anions in a plane and 5th anion is in upper layer and 6th in bottom layer \n", + "\n", + "#join cation anion centres E and B and complete the triangle EBF\n", + "\n", + "#in triangle EBF m(angle F)=90 and EF=BF\n", + "\n", + "#m(angle B)=m(angle E)=45\n", + "\n", + "#and EB=rc+ra and BF=ra\n", + "\n", + "#cos(45)=ra/(rc+ra)\n", + "\n", + "#assume rc/ra=r\n", + "\n", + "p=math.cos(45*math.pi/180)\n", + "r=(1-p)/math.cos(45*math.pi/180) #by arrangimg terms we get value of r\n", + "\n", + "print\"critical radius ratio for ligancy 6 =\",round(r,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "critical radius ratio for ligancy 6 = 0.4142\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.5.3,Page number 1-30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#refer diagram from textbook\n", + "\n", + "#since plane is square hence it is same as ligancy 6\n", + "\n", + "#in the said arrangement a cation is squeezed into 4 anions in a plane and 5th anion is in upper layer and 6th in bottom layer \n", + "\n", + "#join cation anion centres E and B and complete the triangle EBF\n", + "\n", + "#in triangle EBF m(angle F)=90 and EF=BF\n", + "\n", + "#m(angle B)=m(angle E)=45\n", + "\n", + "#and EB=rc+ra and BF=ra\n", + "\n", + "#cos(45)=ra/(rc+ra)\n", + "\n", + "#assume rc/ra=r\n", + "\n", + "r=(1-math.cos(45*math.pi/180))/math.cos(45*math.pi/180) #by arrangimg terms we get value of r\n", + "\n", + "print\"critical radius ratio for ligancy 8 =\",round(r,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "critical radius ratio for ligancy 8 = 0.4142\n" + ] + } + ], + "prompt_number": 38 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.5.4,Page number 1-31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#a tetrahedron CAEH can be considered with C as the apex of the tetrahedron.\n", + "\n", + "#the edges AE,AH and EH of the tetrahedron will then be the face of the cube faces ABEF,ADHF,EFHG resp.\n", + "\n", + "#from fig\n", + "\n", + "#AO=ra+rc and AJ=ra\n", + "\n", + "#AE=root(2)*a and AG=root(3)*a\n", + "\n", + "#AO/AJ=AG/AE=(ra+rc)/ra=root(3)*a/root(2)*a\n", + "\n", + "#assume rc/ra=r\n", + "r=(math.sqrt(3)-math.sqrt(2))/math.sqrt(2)\n", + "\n", + "print\"critical radius ratio for ligancy 4 = \",round(r,4)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "critical radius ratio for ligancy 4 = 0.2247\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.5.5,Page number 1-32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#ligancy 8 represents cubic arrangment .8 anions are at the corners and touch along cube edgs.Along the body diagonal the central cation and the corner anion are in contact.\n", + "\n", + "#cube edge=2*ra\n", + "\n", + "#refer diagram from textbook\n", + "\n", + "#and body diagonal=root(3)*cube edge=root(3)[2*(rc+ra)]\n", + "\n", + "#assume rc/ra=r\n", + "\n", + "r=math.sqrt(3)-1.0\n", + "\n", + "print\"critical radius ratio of ligancy 8=\",round(r,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "critical radius ratio of ligancy 8= 0.7321\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.5.6,Page number 1-32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#for an ionic crystal exibiting HCP structure the arrangment of ions refere from textbook\n", + "\n", + "#at centre we have a cation with radius rc=OA\n", + "\n", + "#it is an touch with 6 anions with radius ra=AB\n", + "\n", + "#OB=OC=ra+rc\n", + "\n", + "#intrangle ODB ,m(angle (OBC))=60 degree ,m(angle (ODB))=90 degree\n", + "\n", + "#therefore cos(60)=BD/OB=AB/(OA+OB)=ra/(rc+ra)\n", + "\n", + "#assume rc/ra=r\n", + "\n", + "r=(1.-math.cos(60*math.pi/180))/math.cos(60*math.pi/180) #by arrangimg terms we get value of r\n", + "\n", + "print\"critical radius ratio 0f HCP structure=\",round(r,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "critical radius ratio 0f HCP structure= 1.0\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.6.2,Page number 1-35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#intercept of planeare in proportion a,b/3,2*c\n", + "\n", + "#as a,b and c are basic vectors the proportin of intercepts 1:1/3:2\n", + "\n", + "#therefore reciprocal\n", + "\n", + "r1=1\n", + "\n", + "r2=3\n", + "\n", + "r3=1./2\n", + "\n", + "#taking LCM of 2 and 1 is 2\n", + "\n", + "l=2\n", + "\n", + "m1=(l*r1)\n", + "\n", + "m2=(l*r2)\n", + "\n", + "m3=(l*r3)\n", + "\n", + "print\"miler indices=\",m3,m2,m1\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "miler indices= 1.0 6 2\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.6.4,Page number 1-38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "r=1.414 #atomic radius in amstrong unit\n", + "\n", + "#for FCC structure\n", + "\n", + "a=4*r/math.sqrt(2)\n", + "\n", + "#part 1: plane(2,0,0)\n", + "\n", + "#the interplanar spacing of plane\n", + "\n", + "h1=2\n", + "k1=0\n", + "l1=0\n", + "\n", + "#we know that d=a/sqrt(h**2+k**2+l**2)\n", + "\n", + "d1=a/sqrt(h1**2+k1**2+l1**2)\n", + "\n", + "print\"1)interplanar spacing for (2,0,0) plane=\",round(d1,4),\"amstrong\"\n", + "\n", + "#part 2: plane(1,1,1)\n", + "\n", + "#the interplanar spacing of plane\n", + "\n", + "h2=1\n", + "k2=1\n", + "l2=1\n", + "\n", + "#we know that d=a/sqrt(h**2+k**2+l**2)\n", + "\n", + "d2=a/sqrt(h2**2+k2**2+l2**2)\n", + "\n", + "print\"2)interplanar spacing for(1,1,1) plane=\",round(d2,4),\"amstrong\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)interplanar spacing for (2,0,0) plane= 1.9997 amstrong\n", + "2)interplanar spacing for(1,1,1) plane= 2.3091 amstrong\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.1,Page number 1-58" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=4 #FCC structure\n", + "ro=2180 #density of NaCl\n", + "M=23+35.5 #molecular weight of NaCl\n", + "N=6.023*10**26 #Avogadro's number\n", + "\n", + "a=((n*M)/(N*ro))**(1.0/3)\n", + "\n", + "print\"Lattice constant=\",\"{0:.3e}\".format(a),\"m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Lattice constant= 5.627e-10 m\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.2,Page number 1-58" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=4 #FCC structure\n", + "ro=8.9 #density of Cu atom\n", + "A=63.55 #atomic weight of Cu atom\n", + "N=6.023*10**23 #Avogadro's number\n", + "\n", + "a=((n*A)/(N*ro))**(1./3)\n", + "\n", + "print\"1) Lattice constant=\",\"{0:.3e}\".format(a),\"cm\"\n", + "\n", + "r=math.sqrt(2)*a/4 #radius of Cu atom\n", + "\n", + "d=2*r #diameter of Cu atom\n", + "\n", + "print\"2) Diameter of Cu atom=\",\"{0:.3e}\".format(d),\"cm\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Lattice constant= 3.620e-08 cm\n", + "2) Diameter of Cu atom= 2.559e-08 cm\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.3,Page number 1-59" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=8 #diamond structure\n", + "A=12.01 #atomic wt\n", + "N=6.023*10**23 #Avogadro's number\n", + "a=3.75*10**-8 #lattice constant of diamond\n", + "\n", + "ro=(n*A)/(N*(a**3))\n", + "\n", + "print\"Density of diamond=\",round(ro,4),\"gm/cc\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Density of diamond= 3.025 gm/cc\n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.4,Page number 1-59" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#intercept of planeare in proportion 3a:4b:infinity (plane parallel to z axis)\n", + "\n", + "#as a,b and c are basic vectors the proportin of intercepts 3:4:infinity\n", + "\n", + "#therefore reciprocal\n", + "\n", + "r1=1./3\n", + "r2=1./4\n", + "r3=0\n", + "\n", + "#taking LCM of 3 and 4 i.e. 12\n", + "\n", + "l=12\n", + "\n", + "m1=(l*r1)\n", + "\n", + "m2=(l*r2)\n", + "\n", + "m3=(l*r3)\n", + "\n", + "print\"miler indices=\",(m3,m2,m1)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "miler indices= (0, 3.0, 4.0)\n" + ] + } + ], + "prompt_number": 29 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.5,Page number 1-59" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#intercept of planeare in proportion 3a:-2b:3/2c\n", + "\n", + "#as a,b and c are basic vectors the proportin of intercepts 3:-2:3/2\n", + "\n", + "#therefore reciprocal\n", + "\n", + "r1=1./3\n", + "r2=-1./2\n", + "r3=2./3\n", + "\n", + "#taking LCM of 3, 2 and 3/2 is 6\n", + "\n", + "l=6\n", + "\n", + "m1=(l*r1)\n", + "\n", + "m2=(l*r2)\n", + "\n", + "m3=(l*r3)\n", + "\n", + "print\"miler indices=\",(m3,m2,m1)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "miler indices= (4.0, -3.0, 2.0)\n" + ] + } + ], + "prompt_number": 31 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.6,Page number 1-59" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#if a plane cut at length m,n,p on the three crystal axes,then\n", + "\n", + "#m:n:p=xa:yb:zc\n", + "\n", + "#when primitive vectors of unit cell and numbers x,y,z,are related to miller indices (h,k,l)of the plane by relation\n", + "\n", + "#1/x:1/y:1/z=h:k:l\n", + "\n", + "#since a=b=c (crystal is simple cubic)\n", + "\n", + "#and (h,k,l)=(1,2,3)\n", + "\n", + "#therefore reciprocal\n", + "\n", + "r1=1./1\n", + "r2=1./2\n", + "r3=1./3\n", + "\n", + "#taking LCM of 1 ,2 and 3 is 6\n", + "\n", + "l=6\n", + "\n", + "m=(l*r1)\n", + "\n", + "n=(l*r2)\n", + "\n", + "p=(l*r3)\n", + "\n", + "print\"ratio of intercepts=\",(m,n,p)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "ratio of intercepts= (6.0, 3.0, 2.0)\n" + ] + } + ], + "prompt_number": 35 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.7,Page number 1-60" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#primitive vectors\n", + "\n", + "a=1.2 #in amstrong unit\n", + "b=1.8 #in amstrong unit\n", + "c=2 #in amstrong unit\n", + "\n", + "#miller indices of the plane\n", + "\n", + "h=2\n", + "k=3\n", + "l=1\n", + "\n", + "#therefore intercepts are a/h,b/k,c/l\n", + "\n", + "x=a/h\n", + "y=b/k\n", + "z=c/l\n", + "\n", + "#this gives intercepts along x axis as x amstrong but it is given tthat plane cut x axis at 1.2 amstrong .\n", + "\n", + "t=1.2/x\n", + "\n", + "#this shows that the plane under consideration is another plane which is parallel to it(to keep miller indices same)\n", + "\n", + "n=t*y #Y intercept\n", + "\n", + "p=t*z #Z intercept\n", + "\n", + "print\"1) Y intercept=\",n,\"amstrong\"\n", + "\n", + "print\"2)Z intercept=\",p,\"amstrong\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Y intercept= 1.2 amstrong\n", + "2)Z intercept= 4.0 amstrong\n" + ] + } + ], + "prompt_number": 37 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.8,Page number 1-61" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#the interplanar spacing of plane\n", + "\n", + "h=1\n", + "k=1\n", + "l=0\n", + "d=2 #interpanar spacing in amstrong unit\n", + "\n", + "#we know that d=a/sqrt(h**2+k**2+l**2) therefore\n", + "\n", + "a=d*math.sqrt(h**2+k**2+l**2)\n", + "\n", + "#for FCC structure\n", + "\n", + "r=math.sqrt(2)*a/4\n", + "\n", + "print\"radius r=\",(r),\"amstrong\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "radius r= 1.0 amstrong\n" + ] + } + ], + "prompt_number": 39 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.9,Page number 1-61" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=4 #for FCC structure\n", + "\n", + "#the interplanar spacing of plane\n", + "\n", + "h=1\n", + "k=1\n", + "l=1\n", + "d=2.08*10**-10 #distance\n", + "A=63.54 #atomic weight of Cu\n", + "N=6.023*10**26 #amstrong no\n", + "\n", + "#we know that d=a/sqrt(h**2+k**2+l**2) therefore\n", + "\n", + "a=d*math.sqrt(h**2+k**2+l**2)\n", + "\n", + "#also (a**3*q)=n*A/N\n", + "\n", + "q=n*A/(N*a**3)\n", + "\n", + "print\"1)density=\",round(q,4),\"kg/m^3\"\n", + "\n", + "#for FCC structure\n", + "\n", + "r=math.sqrt(2)*a/4\n", + "\n", + "d=r*2\n", + "\n", + "print\"2)radius r=\",\"{0:.3e}\".format(r),\"m\"\n", + "\n", + "print\"3)diameter d=\",\"{0:.3e}\".format(d),\"m\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)density= 9024.4855 kg/m^3\n", + "2)radius r= 1.274e-10 m\n", + "3)diameter d= 2.547e-10 m\n" + ] + } + ], + "prompt_number": 44 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.10,Page number 1-62" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "A=63.546 #atomic weight of Cu\n", + "N=6.023*10**26 #Avogadro's number\n", + "p=8930 #Density\n", + "n=1.23 #no.of electron per atom\n", + "\n", + "#density=mass/volume\n", + "\n", + "#therfore 1/volume=density/mass\n", + "\n", + "#since electron concentration is needed, let us find out no of atoms/volume(x)\n", + "\n", + "x=N*p/A\n", + "\n", + "#now one atom contribute n=1.23 electron\n", + "\n", + "#therefore x atoms contribute y no of free electron\n", + "\n", + "y=x*n\n", + "\n", + "print\"free electron concentration=\",\"{0:.3e}\".format(y),\"electron/m^3\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "free electron concentration= 1.041e+29 electron/m^3\n" + ] + } + ], + "prompt_number": 46 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.11,Page number 1-62" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#primitive vectors\n", + "\n", + "a=1.5 #in amstrong unit\n", + "b=2 #in amstrong unit\n", + "c=4. #in amstrong unit\n", + "\n", + "#miller indices of the plane\n", + "\n", + "h=3\n", + "k=2\n", + "l=6\n", + "\n", + "#therefore intercepts are a/h,b/k,c/l\n", + "\n", + "x=a/h\n", + "y=b/k\n", + "z=c/l\n", + "\n", + "#this gives intercepts along x axis as x amstrong but it is given that plane cut x axis at 1.2 amstrong .\n", + "\n", + "t=1.5/x\n", + "\n", + "#this shows that the plane under consideration is another plane which is parallel to it(to keep miller indices same)\n", + "\n", + "n=t*y #Y intercept\n", + "\n", + "p=t*z #Z intercept\n", + "\n", + "print\"1) Y intercept=\",(n),\"amstrong\"\n", + "\n", + "print\"2)Z intercept=\",(p),\"amstrong\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Y intercept= 3.0 amstrong\n", + "2)Z intercept= 2.0 amstrong\n" + ] + } + ], + "prompt_number": 48 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.12,Page number 1-63" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "ro=7.87 #density of metal\n", + "A=55.85 #atomic wt of metal\n", + "N=6.023*10**23 #Avogadro's number\n", + "a=2.9*10**-8 #lattice constant of metal\n", + "\n", + "n=(N*(a**3)*ro)/A\n", + "\n", + "print\"Number of atom per unit cell of a metal=\",round(n,0)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of atom per unit cell of a metal= 2.0\n" + ] + } + ], + "prompt_number": 52 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.13,Page number 1-63" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=2 #BCC structure\n", + "ro=9.6*10**2 #density of sodium crystal\n", + "A=23 #atomic weight of sodium crystal\n", + "N=6.023*10**26 #Avogadro's number\n", + "\n", + "a=((n*A)/(N*ro))**(1./3)\n", + "\n", + "print\"Lattice constant=\",\"{0:.3e}\".format(a),\"m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Lattice constant= 4.301e-10 m\n" + ] + } + ], + "prompt_number": 50 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.15,Page number 1-64" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "ro=2.7*10**3 #density of metal\n", + "A=27 #atomic wt of metal\n", + "N=6.023*10**26 #Avogadro's number\n", + "a=4.05*10**-10 #lattice constant of metal\n", + "\n", + "n=(N*(a**3)*ro)/A\n", + "\n", + "print\"1) Number of atom per unit cell of a metal=\",round(n,0)\n", + "\n", + "r=math.sqrt(2)*a/4 #radius of metal\n", + "\n", + "print\"2) atomic radius of a metal=\",\"{0:.3e}\".format(r),\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Number of atom per unit cell of a metal= 4.0\n", + "2) atomic radius of a metal= 1.432e-10 m\n" + ] + } + ], + "prompt_number": 56 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.16,Page number 1-64" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=2 #BCC structure\n", + "ro=5.98*10**3 #density of chromium\n", + "A=50 #atomic wt of chromium\n", + "N=6.023*10**26 #Avogadro's number\n", + "\n", + "a=((n*A)/(N*ro))**(1./3)\n", + "\n", + "print\"1) Lattice constant=\",\"{0:.3e}\".format(a),\"m\"\n", + "\n", + "#for BCC\n", + "\n", + "r=math.sqrt(3)*a/4 #radius of chromium\n", + "\n", + "APF=(n*(4./3)*math.pi*(r**3))/(a**3)\n", + "\n", + "print\"2) A.P.F. for chromium=\",round(APF,4)\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Lattice constant= 3.028e-10 m\n", + "2) A.P.F. for chromium= 0.6802\n" + ] + } + ], + "prompt_number": 60 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.17,Page number 1-65" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=4 #FCC structure\n", + "ro=6250 #density\n", + "M=60.2 #molecular weight\n", + "N=6.023*10**26 #Avogadro's number\n", + "\n", + "a=((n*M)/(N*ro))**(1./3)\n", + "\n", + "print\"Lattice constant=\",\"{0:.3e}\".format(a),\"m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Lattice constant= 3.999e-10 m\n" + ] + } + ], + "prompt_number": 62 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.19,Page number 1-66" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "a=2.82*10**-9 #lattice constant\n", + "n=2 #FCC crystal\n", + "t=17.167 #glancing angle in degree\n", + "q=math.pi/180*t #glancing angle in radians\n", + "\n", + "#assuming reflection in (1,0,0) plane\n", + "\n", + "h=1\n", + "k=0\n", + "l=0\n", + "\n", + "d=a/math.sqrt(h**2+k**2+l**2)\n", + "\n", + "#using Bragg's law , 2*d*sin(q)=n*la\n", + "\n", + "la=2*d*sin(q)/n\n", + "\n", + "print\"wavlength of X-ray=\",\"{0:.3e}\".format(la),\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "wavlength of X-ray= 8.323e-10 m\n" + ] + } + ], + "prompt_number": 64 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.20,Page number 1-66" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=8 #Diamond structure\n", + "ro=2.33*10**3 #density of diamond\n", + "M=28.9 #atomic weight of diamond\n", + "N=6.023*10**26 #Avogadro's number\n", + "\n", + "a=((n*M)/(N*ro))**(1./3)\n", + "\n", + "print\"1) Lattice constant=\",\"{0:.3e}\".format(a),\"m\"\n", + "\n", + "r=math.sqrt(3)*a/8 #radius of diamond structure\n", + "\n", + "print\"2) atomic radius of a metal=\",\"{0:.3e}\".format(r),\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Lattice constant= 5.482e-10 m\n", + "2) atomic radius of a metal= 1.187e-10 m\n" + ] + } + ], + "prompt_number": 66 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.21,Page number 1-66" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=2 #BCC structure\n", + "ro=8.57*10**3 #density of chromium\n", + "d=2.86*10**-10 #nearest atoms distance\n", + "\n", + "#d=sqrt(3)/2*a\n", + "\n", + "a=2*d/math.sqrt(3)\n", + "\n", + "#now use formulae a**3*ro=n*A/N\n", + "\n", + "#therefore a**3*ro/n=mass of unit cell/(no of atoms pre unit cell)=mass of one atom\n", + "\n", + "m=a**3*ro/n\n", + "\n", + "print\"mass of one atom=\",\"{0:.3e}\".format(m),\"kg\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "mass of one atom= 1.543e-25 kg\n" + ] + } + ], + "prompt_number": 68 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.1,Page number 1-68" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "d=4.255*10**-10 #interplaner spacing\n", + "l=1.549*10**-10 #wavelength of x ray\n", + "\n", + "#part 1: for smallest glancing angle(n=1)\n", + "\n", + "n1=1\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "q=math.degrees(math.asin(n1*l/(2*d)))\n", + "\n", + "print\"1)glancing angle=\",round(q,4),\"degree\"\n", + "\n", + "#part 2: for highst order\n", + "\n", + "#for highest order sin(q) not exceed one i.e maximum value is one\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "n2=2*d/l #since sin(q)is one\n", + "\n", + "print\"2)highest order possible =\",math.floor(n2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)glancing angle= 10.4875 degree\n", + "2)highest order possible = 5.0\n" + ] + } + ], + "prompt_number": 70 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.2,Page number 1-69" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "a=2.125*10**-10 #lattice constant\n", + "d=a/2 #interplaner spacing\n", + "n=2 #second order maximum\n", + "l=0.592*10**-10 #wavelength of rock salt crystal\n", + "\n", + "#using Bragg's law\n", + "\n", + "q=math.degrees(math.asin((n*l)/(2*d))) #glancing angle\n", + "\n", + "print\"glancing angle=\",round(q,4),\"degree\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "glancing angle= 33.8608 degree\n" + ] + } + ], + "prompt_number": 72 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.3,Page number 1-69" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n1=1 #for 1st order\n", + "n2=2 #for 2nd order\n", + "t=3.4 #angle where 1st order reflection done\n", + "t1=t*math.pi/180 #convert degree to radian\n", + "\n", + "m=math.sin(t1)\n", + "\n", + "#but from Bragg's law\n", + "\n", + "#n*l=2*d*sin(t)\n", + "\n", + "#for for constant distance(d) and wavelength(l) \n", + "\n", + "#order(n) is directly proportionl to sine of angle i.e (sin(t))\n", + "\n", + "#n1/n2=sin(t1)/sin(t2)\n", + "\n", + "#assume sin(t2)=a\n", + "\n", + "a=n2/n1*m\n", + "\n", + "t2=math.degrees(math.asin(a)) #taking sin inverese in degree\n", + "\n", + "print\"second order reflection take place at an angle=\",round(t2,4),\"degree\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "second order reflection take place at an angle= 6.812 degree\n" + ] + } + ], + "prompt_number": 75 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.4,Page number 1-70" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "V=50*10**3 #operating voltage of x-ray\n", + "M=74.6 #molecular weight\n", + "p=1.99*10**3 #density\n", + "n=4 #no of atoms per unit cell(for FCC structure)\n", + "h=6.63*10**-34 #plank's constant\n", + "c=3*10**8 #velocity \n", + "e=1.6*10**-19 #charge on electron\n", + "N=6.023*10**26 #Avogadro's number\n", + "\n", + "#step 1:clculating shortest wavelength\n", + "\n", + "l=h*c/(e*V)\n", + "\n", + "print\"1)shortest wavelength=\",(l),\"m\"\n", + "\n", + "#step:2 calculating distance(d)\n", + "\n", + "#now a**3*p=n*M/N therefore,\n", + "\n", + "a=(n*M/(N*p))**(1./3)\n", + "\n", + "#since KCl is ionic crystal herefore,\n", + "\n", + "d=a/2\n", + "\n", + "#step 3: calculaing glancing angle\n", + "\n", + "#using Bragg's law\n", + "\n", + "#n*l=2*d*sin(t)\n", + "\n", + "#assume sin(t)=a, wavelength is minimum i.e l and n=1\n", + "\n", + "n=1\n", + "\n", + "a=n*l/(2*d)\n", + "\n", + "t=math.degrees(math.asin(a)) #taking sin inverese in degree\n", + "\n", + "print\"2) glancing angle=\",round(t,4),\"degree\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)shortest wavelength= 2.48625e-11 m\n", + "2) glancing angle= 2.265 degree\n" + ] + } + ], + "prompt_number": 77 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.5,Page number 1-70" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=1.0 #first order maximum\n", + "l=0.82*10**-10 #wavelength of X ray\n", + "qd=7.0 #glancing angle in degree\n", + "qm=51./60 #glancing angle in minute\n", + "qs=48./3600 #glancing angle in second\n", + "\n", + "q=qd+qm+qs #total glancin angle in degree\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "d=n*l/(2*math.sin(q*math.pi/180))\n", + "\n", + "a=3*10**-10 #lattice constant\n", + "\n", + "#we know that d=a/root(h**2+k**2+l**2)\n", + "\n", + "#assume root(h**2+k**2+l**2) =m\n", + "\n", + "#arranging terms we get\n", + "\n", + "m=a/d\n", + "\n", + "print\"square root(h**2+k**2+l**2)=\",round(m,0)\n", + "\n", + "print\"hence possible solutions are (100),(010),(001)\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "square root(h**2+k**2+l**2)= 1.0\n", + "hence possible solutions are (100),(010),(001)\n" + ] + } + ], + "prompt_number": 90 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.6,Page number 1-71" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=1 #first order maximum\n", + "l=1j #wavelength of X ray\n", + "\n", + "#part 1:for(100)\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "q1=5.4 #glancing angle in degree\n", + "\n", + "dl1=n*l/(2*math.sin(q1*math.pi/180))\n", + "\n", + "#part 2:for(110)\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "q2=7.6 #glancing angle in degree\n", + "\n", + "dl2=n*l/(2*math.sin(q2*math.pi/180))\n", + "\n", + "#part 3:for(111)\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "q3=9.4 #glancing angle in degree\n", + "\n", + "dl3=n*l/(2*math.sin(q3*math.pi/180))\n", + "\n", + "#for taking ratio divide all dl by dl1\n", + "\n", + "d1=dl1/dl1\n", + "\n", + "d2=dl2/dl1\n", + "\n", + "d3=dl3/dl1\n", + "\n", + "print\"cubic lattice structure is=\",d1,d2,d3" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " cubic lattice structure is= (1+0j) (0.711559669333+0j) (0.576199350225+0j)\n" + ] + } + ], + "prompt_number": 94 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.7,Page number 1-71" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=1 #first order maximum\n", + "l=1.54*10**-10 #wavelength of rock salt crystal\n", + "q=21.7 #glancing angle in degree\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "d=n*l/(2*math.sin(q*math.pi/180))\n", + "\n", + "print\"lattice constant of crystal=\",\"{0:.3e}\".format(d),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "lattice constant of crystal= 2.083e-10 meter\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.8,Page number 1-72" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "a=2.814*10**-10 #lattice constant\n", + "\n", + "#the interplanar spacing of plane\n", + "\n", + "h=1\n", + "k=0\n", + "l=0\n", + "\n", + "d=a/math.sqrt(h**2+k**2+l**2)\n", + "\n", + "n=2 #first order maximum\n", + "\n", + "l=0.714*10**-10 #wavelength of X-ray crystal\n", + "\n", + "#using Bragg's law\n", + "\n", + "q=math.degrees(math.asin((n*l)/(2*d))) #glancing angle\n", + "\n", + "print\"glancing angle=\",round(q,4),\"degree\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "glancing angle= 14.6984 degree\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.9,Page number 1-72" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "d=2.82*10**-10 #interplaner spacing\n", + "t=10 #glancing angle\n", + "\n", + "#for part 1\n", + "\n", + "n=1 #first order maximum\n", + "\n", + "#using Bragg's law n*l=2*d*sin(t)\n", + "\n", + "l=2*d*math.sin(math.pi*t/180)/n\n", + "\n", + "print\"1)wavelength=\",\"{0:.3e}\".format(l),\"meter\"\n", + "\n", + "#for part 2\n", + "\n", + "n1=2\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "q=math.degrees(math.asin(n1*l/(2*d)))\n", + "\n", + "print\"2)glancing angle=\",round(q,4),\"degree\"\n", + "\n", + "#for part 3\n", + "\n", + "#for highest order sin(q) not exceed one i.e maximum value is one\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "n2=2*d/l #since sin(q)is one\n", + "\n", + "print\"3)highest order possible =\",(floor(n2))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)wavelength= 9.794e-11 meter\n", + "2)glancing angle= 20.322 degree\n", + "3)highest order possible = 5.0\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.10,Page number 1-73" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#for line -A\n", + "\n", + "n1=1 #1st order maximum\n", + "q1=30 #glancing angle in degree\n", + "\n", + "#using Bragg's law for line A n1*l1=2*d1*sin(q1)\n", + "\n", + "#d1=n1*l1/(2*sin(q1))\n", + "\n", + "#for line B\n", + "\n", + "l2=0.97 #wavelength in amstrong unit\n", + "n2=3 #1st order maximum\n", + "q2=60 #glancing angle in degree\n", + "\n", + "#using Bragg's law for line B n2*l2=2*d2*sin(q2)\n", + "\n", + "#since for both lines A and B we use same plane of same crystal,therefore\n", + "\n", + "#d1=d2\n", + "\n", + "#therefore equution became n2*l2=2*n1*l1/(2*sin(q1))*sin(q2)\n", + "\n", + "#by arranging terms we get\n", + "\n", + "\n", + "l1=n2*l2*2*math.sin(q1*math.pi/180)/(2*n1*math.sin(q2*math.pi/180))\n", + "\n", + "print\"wavelength of the line A=\",round(l1,4),\"amstrong\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "wavelength of the line A= 1.6801 amstrong\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.11,Page number 1-74" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=1.0 #first order minimum\n", + "d=5.5*10**-11 #atomic spacing\n", + "e=1.6*10**-19 #charge on one electron\n", + "Ee=10*10**3 #energy in eV\n", + "E=e*Ee #energy in Joule\n", + "m=9.1*10**-31 #mass of elelctron\n", + "h=6.63*10**-34 #plank's constant\n", + "\n", + "l=h/math.sqrt(2*m*E) #wavelength\n", + "\n", + "#using Bragg's law\n", + "\n", + "q=math.degrees(math.asin((n*l)/(2*d))) #glancing angle\n", + "\n", + "print\"glancing angle=\",round(q,4),\"degree\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "glancing angle= 6.4129 degree\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.12,Page number 1-74" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "a=2.814*10**-10 #lattice constant\n", + "\n", + "#for rock salt\n", + "\n", + "d=a/2 #interplaner spacing\n", + "\n", + "n=1 #first order maximum\n", + "\n", + "l=1.541*10**-10 #wavelength of rock salt crystal\n", + "\n", + "#using Bragg's law\n", + "\n", + "q=math.degrees(math.asin((n*l)/(2*d))) #glancing angl\n", + "\n", + "print\"glancing angle=\",round(q,4),\"degree\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "glancing angle= 33.2038 degree\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.16.1,Page number 1-75" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Ev=1.08 #average energy required to creaet a vacancy\n", + "k=1.38*10**-23 #boltzman constant in J/K\n", + "e=1.6*10**-19 #charge on 1 electron\n", + "\n", + "K=k/e #boltzman constant in eV/K\n", + "\n", + "#for a low concentration of vacancies a relation is\n", + "\n", + "#n=Nexp(-Ev/KT)\n", + "\n", + "#since total no atom is 1 hence N=1\n", + "\n", + "#at 1000k\n", + "\n", + "T1=1000 #temperature\n", + "\n", + "n1=math.exp(-Ev/(K*T1))\n", + "\n", + "#at 500k\n", + "\n", + "T2=500 #temperature\n", + "\n", + "n2=math.exp(-Ev/(K*T2))\n", + "\n", + "v=(n1)/(n2) #ratio of vacancies\n", + "\n", + "print\"ratio of vacancies=\",round(v,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "ratio of vacancies= 274234.5745\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.16.2,Page number 1-75" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Ev=1.95 #average energy required to creaet a vacancy\n", + "k=1.38*10**-23 #boltzman constant in J/K\n", + "e=1.6*10**-19 #charge on 1 electron\n", + "K=k/e #boltzman constant in eV/K\n", + "T=500 #temperature\n", + "\n", + "#for a low concentration of vacancies a relation is\n", + "\n", + "#n=Nexp(-Ev/KT)\n", + "\n", + "m=math.exp(-Ev/(K*T)) #ratio of no of vacancies to no of atoms n/N\n", + "\n", + "print\"ratio of no of vacancies to no of atoms=\",\"{0:.3e}\".format(m)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "ratio of no of vacancies to no of atoms= 2.303e-20\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.16.3,Page number 1-76" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Ev=1.8 #average energy required to creaet a vacancy\n", + "k=1.38*10**-23 #boltzman constant in J/K\n", + "e=1.6*10**-19 #charge on 1 electron\n", + "K=k/e #boltzman constant in eV/K\n", + "\n", + "#for a low concentration of vacancies a relation is\n", + "\n", + "#n=Nexp(-Ev/KT)\n", + "\n", + "#ratio of vacancy is n/N assume be r=exp(-Ev/KT)\n", + "\n", + "#since total no atom is 1 hence N=1\n", + "\n", + "#at 1000k\n", + "\n", + "t1=-119 #temperature in degree\n", + "T1=t1+273 #temperature in kelvine\n", + "r1=math.exp(-Ev/(K*T1))\n", + "\n", + "print\"1)ratio of vacancies at -119 degree=\",\"{0:.3e}\".format(r1)\n", + "\n", + "#at 500k\n", + "\n", + "t2=80 #temperature in degree\n", + "\n", + "T2=t2+273 #temperature in kelvine\n", + "\n", + "r2=exp(-Ev/(K*T2))\n", + "\n", + "v=(r1)/(r2) #ratio of vacancies\n", + "\n", + "print\"2)ratio of vacancies at 80 degree=\",\"{0:.3e}\".format(r2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)ratio of vacancies at -119 degree= 1.399e-59\n", + "2)ratio of vacancies at 80 degree= 2.110e-26\n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.16.4,Page number 1-76" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Ev=1.5 #energy of formaton of frankel defect\n", + "k=1.38*10**-23 #boltzman constant in J/K\n", + "e=1.6*10**-19 #charge on 1 electron\n", + "K=k/e #boltzman constant in eV/K\n", + "T=700 #temperature\n", + "N=6.023*10**26 #avogadro's no\n", + "\n", + "#for a low concentration of vacancies a relation is\n", + "\n", + "#n=Nexp(-Ev/KT)\n", + "\n", + "m=math.exp(-Ev/(2*K*T)) #ratio of no of vacancies to no of atoms n/N\n", + "\n", + "qs=5.56 #specific density\n", + "q=5.56*10**3 #real density ke/m**3\n", + "M=0.143 #molecular weight in kg/m**3\n", + "ma=M/N #mass of one molecule\n", + "v=ma/q #vol of one molecule\n", + "\n", + "#v volume containe 1 molecule\n", + "\n", + "#therefore 1 m**3 containe x molecule\n", + "\n", + "x=1./v\n", + "d=m*x #defect per m**3\n", + "dm=d*10**-9 #defect per mm**3\n", + "\n", + "print\"number of frankel defects per mm^3=\",\"{0:.3e}\".format(dm)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "number of frankel defects per mm^3= 9.432e+16\n" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Applied_Physics-I_by_I_A_Shaikh/chapter1_1.ipynb b/Applied_Physics-I_by_I_A_Shaikh/chapter1_1.ipynb new file mode 100644 index 00000000..b2a76d3e --- /dev/null +++ b/Applied_Physics-I_by_I_A_Shaikh/chapter1_1.ipynb @@ -0,0 +1,2525 @@ +{ + "metadata": { + "celltoolbar": "Raw Cell Format", + "name": "", + "signature": "sha256:3e9b00b8b544a24032a4bb804cb876f45a5efd85913287f396a56723a0eb1a09" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 1: Crystallography" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.3.1,Page number 1-14" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "A=26.98 #atomic weight of Al\n", + "N=6.023*10**26 #Avogadro's number\n", + "p=2700 #Density\n", + "n=4 #FCC structure\n", + "\n", + "a=(n*A/(N*p))**(1./3)\n", + "\n", + "print\"Unit cell dimension of Al=\",\"{0:.3e}\".format(a),\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Unit cell dimension of Al= 4.049e-10 m\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.3.2,Page number 1-15" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "As=28.1 #atomic weight of Si\n", + "Ag=69.7 #atomic weight of Ga\n", + "Aa=74.9 #atomic weight of As\n", + "a_s=5.43*10**-8 #lattice constant of Si\n", + "aga=5.65*10**-8 #lattice constant of GaAs\n", + "ns=8 #no of atoms/unit cell in Si\n", + "nga=4 #no of atoms/unit cell in GaAs\n", + "N=6.023*10**23 #Avogadro's number\n", + "\n", + "#p=(n*A)/(N*a**3) this is formula for density\n", + "\n", + "#for Si\n", + "\n", + "ps=(ns*As)/(N*a_s**3)\n", + "\n", + "print\"1) Density of Si=\",round(ps,4),\"gm/cm^3\"\n", + "\n", + "#for GaAs\n", + "\n", + "Aga=Ag+Aa #molecular wt of GaAs\n", + "\n", + "pga=(nga*Aga)/(N*aga**3)\n", + "\n", + "print\"2) Density of GaAs=\",round(pga,4),\"gm/cm^3\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Density of Si= 2.3312 gm/cm^3\n", + "2) Density of GaAs= 5.3244 gm/cm^3\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.3.3,Page number 1-16" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "A=63.5 #atomic weight of Cu\n", + "N=6.023*10**23 #Avogadro's number\n", + "n=4 #FCC structure\n", + "r=1.28*10**-8 #atomic radius of Cu\n", + "\n", + "#for FCC\n", + "\n", + "a=4*r/(sqrt(2)) #lattice constant\n", + "p=(n*A)/(N*a**3)\n", + "\n", + "print\"Density of Cu=\",round(p,4),\"gm/cm^3\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Density of Cu= 8.887 gm/cm^3\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.3.4,Page number 1-17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "A=50 #atomic weight of chromium\n", + "N=6.023*10**23 #Avogadro's number\n", + "p=5.96 #Density\n", + "n=2 #BCC structure\n", + "\n", + "#step 1 : claculation for lattice constant (a)\n", + "\n", + "a=(n*A/(N*p))**(1./3)\n", + "\n", + "#step 2 : radius of an atom in BCC\n", + "\n", + "r=sqrt(3)*a/4\n", + "\n", + "#step 3 : Atomic packing factor (APF)\n", + "\n", + "APF=n*((4./3)*math.pi*r**3)/a**3\n", + "\n", + "print\"Atomic packing factor (APF)=\",round(APF,4)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Atomic packing factor (APF)= 0.6802\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.3.5,Page number 1-17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "A=120 #atomic weight of chromium\n", + "N=6.023*10**23 #Avogadro's number\n", + "p=5.2 #Density\n", + "n=2 #BCC structure\n", + "m=20 #mass\n", + "\n", + "#step 1 : claculation for volume of unit cell(a**3)\n", + "\n", + "a=(n*A/(N*p))\n", + "\n", + "#step 2 : volume of 20 gm of the element\n", + "\n", + "v=m/p\n", + "\n", + "#step 3 :no of unit cell\n", + "\n", + "x=v/a\n", + "\n", + "print\"no of unit cell=\",\"{0:.3e}\".format(x)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "no of unit cell= 5.019e+22\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.3.6,Page number 1-18" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "A=132.91 #atomic weight of chromium\n", + "N=6.023*10**26 #Avogadro's number\n", + "p=1900 #Density\n", + "a=6.14*10**-10 #lattice constant\n", + "\n", + "#step 1 : type of structure\n", + "\n", + "n=(p*N*a**3)/A\n", + "\n", + "print\"n =\",round(n)\n", + "\n", + "print\"BCC structure\"\n", + "\n", + "#step 2: no of atoms/m**3\n", + "\n", + "x=n/a**3\n", + "\n", + "print\"no of atoms/m^3=\",\"{0:.3e}\".format(x)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "n = 2.0\n", + "BCC structure\n", + "no of atoms/m^3= 8.610e+27\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.3.7,Page number 1-18" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "a=0.4049*10**-9 #lattice constant\n", + "t=0.006*10**-2 #thickness of Al foil\n", + "A=50*10**-4 #Area of foil\n", + "\n", + "V1=a**3 #volume of unit cell\n", + "\n", + "V=A*t #volume of the foil\n", + "\n", + "N=V/V1 #no of unit cell in the foil\n", + "\n", + "print\"no of unit cell in the foil=\",\"{0:.3e}\".format(N)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "no of unit cell in the foil= 4.519e+21\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.5.1,Page number 1-29" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#refer diagram from textbook\n", + "\n", + "#on joining centre of 3 anions,an equilateral triangle is formed and on joining centres of any anion and cation a right angle triangle ABC os formed\n", + "\n", + "#where AC=rc+ra\n", + "\n", + "#and BC=ra\n", + "\n", + "#m(angle (ACB))=30 degree\n", + "\n", + "#therefore cos (30)=ra/(rc+ra)\n", + "\n", + "#assume rc/ra=r\n", + "\n", + "r=(1.0-math.cos(30.0*math.pi/180))/math.cos(math.pi*30/180) #by arrangimg terms we get value of r\n", + "\n", + "print\"critical radius ratio of ligancy 3=\",round(r,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "critical radius ratio of ligancy 3= 0.1547\n" + ] + } + ], + "prompt_number": 33 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.5.2,Page number 1-30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#refer diagram from textbook\n", + "\n", + "#in the said arrangement a cation is squeezed into 4 anions in a plane and 5th anion is in upper layer and 6th in bottom layer \n", + "\n", + "#join cation anion centres E and B and complete the triangle EBF\n", + "\n", + "#in triangle EBF m(angle F)=90 and EF=BF\n", + "\n", + "#m(angle B)=m(angle E)=45\n", + "\n", + "#and EB=rc+ra and BF=ra\n", + "\n", + "#cos(45)=ra/(rc+ra)\n", + "\n", + "#assume rc/ra=r\n", + "\n", + "p=math.cos(45*math.pi/180)\n", + "r=(1-p)/math.cos(45*math.pi/180) #by arrangimg terms we get value of r\n", + "\n", + "print\"critical radius ratio for ligancy 6 =\",round(r,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "critical radius ratio for ligancy 6 = 0.4142\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.5.3,Page number 1-30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#refer diagram from textbook\n", + "\n", + "#since plane is square hence it is same as ligancy 6\n", + "\n", + "#in the said arrangement a cation is squeezed into 4 anions in a plane and 5th anion is in upper layer and 6th in bottom layer \n", + "\n", + "#join cation anion centres E and B and complete the triangle EBF\n", + "\n", + "#in triangle EBF m(angle F)=90 and EF=BF\n", + "\n", + "#m(angle B)=m(angle E)=45\n", + "\n", + "#and EB=rc+ra and BF=ra\n", + "\n", + "#cos(45)=ra/(rc+ra)\n", + "\n", + "#assume rc/ra=r\n", + "\n", + "r=(1-math.cos(45*math.pi/180))/math.cos(45*math.pi/180) #by arrangimg terms we get value of r\n", + "\n", + "print\"critical radius ratio for ligancy 8 =\",round(r,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "critical radius ratio for ligancy 8 = 0.4142\n" + ] + } + ], + "prompt_number": 38 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.5.4,Page number 1-31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#a tetrahedron CAEH can be considered with C as the apex of the tetrahedron.\n", + "\n", + "#the edges AE,AH and EH of the tetrahedron will then be the face of the cube faces ABEF,ADHF,EFHG resp.\n", + "\n", + "#from fig\n", + "\n", + "#AO=ra+rc and AJ=ra\n", + "\n", + "#AE=root(2)*a and AG=root(3)*a\n", + "\n", + "#AO/AJ=AG/AE=(ra+rc)/ra=root(3)*a/root(2)*a\n", + "\n", + "#assume rc/ra=r\n", + "r=(math.sqrt(3)-math.sqrt(2))/math.sqrt(2)\n", + "\n", + "print\"critical radius ratio for ligancy 4 = \",round(r,4)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "critical radius ratio for ligancy 4 = 0.2247\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.5.5,Page number 1-32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#ligancy 8 represents cubic arrangment .8 anions are at the corners and touch along cube edgs.Along the body diagonal the central cation and the corner anion are in contact.\n", + "\n", + "#cube edge=2*ra\n", + "\n", + "#refer diagram from textbook\n", + "\n", + "#and body diagonal=root(3)*cube edge=root(3)[2*(rc+ra)]\n", + "\n", + "#assume rc/ra=r\n", + "\n", + "r=math.sqrt(3)-1.0\n", + "\n", + "print\"critical radius ratio of ligancy 8=\",round(r,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "critical radius ratio of ligancy 8= 0.7321\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.5.6,Page number 1-32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#for an ionic crystal exibiting HCP structure the arrangment of ions refere from textbook\n", + "\n", + "#at centre we have a cation with radius rc=OA\n", + "\n", + "#it is an touch with 6 anions with radius ra=AB\n", + "\n", + "#OB=OC=ra+rc\n", + "\n", + "#intrangle ODB ,m(angle (OBC))=60 degree ,m(angle (ODB))=90 degree\n", + "\n", + "#therefore cos(60)=BD/OB=AB/(OA+OB)=ra/(rc+ra)\n", + "\n", + "#assume rc/ra=r\n", + "\n", + "r=(1.-math.cos(60*math.pi/180))/math.cos(60*math.pi/180) #by arrangimg terms we get value of r\n", + "\n", + "print\"critical radius ratio 0f HCP structure=\",round(r,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "critical radius ratio 0f HCP structure= 1.0\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.6.2,Page number 1-35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#intercept of planeare in proportion a,b/3,2*c\n", + "\n", + "#as a,b and c are basic vectors the proportin of intercepts 1:1/3:2\n", + "\n", + "#therefore reciprocal\n", + "\n", + "r1=1\n", + "\n", + "r2=3\n", + "\n", + "r3=1./2\n", + "\n", + "#taking LCM of 2 and 1 is 2\n", + "\n", + "l=2\n", + "\n", + "m1=(l*r1)\n", + "\n", + "m2=(l*r2)\n", + "\n", + "m3=(l*r3)\n", + "\n", + "print\"miler indices=\",m3,m2,m1\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "miler indices= 1.0 6 2\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.6.4,Page number 1-38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "r=1.414 #atomic radius in amstrong unit\n", + "\n", + "#for FCC structure\n", + "\n", + "a=4*r/math.sqrt(2)\n", + "\n", + "#part 1: plane(2,0,0)\n", + "\n", + "#the interplanar spacing of plane\n", + "\n", + "h1=2\n", + "k1=0\n", + "l1=0\n", + "\n", + "#we know that d=a/sqrt(h**2+k**2+l**2)\n", + "\n", + "d1=a/sqrt(h1**2+k1**2+l1**2)\n", + "\n", + "print\"1)interplanar spacing for (2,0,0) plane=\",round(d1,4),\"amstrong\"\n", + "\n", + "#part 2: plane(1,1,1)\n", + "\n", + "#the interplanar spacing of plane\n", + "\n", + "h2=1\n", + "k2=1\n", + "l2=1\n", + "\n", + "#we know that d=a/sqrt(h**2+k**2+l**2)\n", + "\n", + "d2=a/sqrt(h2**2+k2**2+l2**2)\n", + "\n", + "print\"2)interplanar spacing for(1,1,1) plane=\",round(d2,4),\"amstrong\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)interplanar spacing for (2,0,0) plane= 1.9997 amstrong\n", + "2)interplanar spacing for(1,1,1) plane= 2.3091 amstrong\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.1,Page number 1-58" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=4 #FCC structure\n", + "ro=2180 #density of NaCl\n", + "M=23+35.5 #molecular weight of NaCl\n", + "N=6.023*10**26 #Avogadro's number\n", + "\n", + "a=((n*M)/(N*ro))**(1.0/3)\n", + "\n", + "print\"Lattice constant=\",\"{0:.3e}\".format(a),\"m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Lattice constant= 5.627e-10 m\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.2,Page number 1-58" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=4 #FCC structure\n", + "ro=8.9 #density of Cu atom\n", + "A=63.55 #atomic weight of Cu atom\n", + "N=6.023*10**23 #Avogadro's number\n", + "\n", + "a=((n*A)/(N*ro))**(1./3)\n", + "\n", + "print\"1) Lattice constant=\",\"{0:.3e}\".format(a),\"cm\"\n", + "\n", + "r=math.sqrt(2)*a/4 #radius of Cu atom\n", + "\n", + "d=2*r #diameter of Cu atom\n", + "\n", + "print\"2) Diameter of Cu atom=\",\"{0:.3e}\".format(d),\"cm\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Lattice constant= 3.620e-08 cm\n", + "2) Diameter of Cu atom= 2.559e-08 cm\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.3,Page number 1-59" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=8 #diamond structure\n", + "A=12.01 #atomic wt\n", + "N=6.023*10**23 #Avogadro's number\n", + "a=3.75*10**-8 #lattice constant of diamond\n", + "\n", + "ro=(n*A)/(N*(a**3))\n", + "\n", + "print\"Density of diamond=\",round(ro,4),\"gm/cc\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Density of diamond= 3.025 gm/cc\n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.4,Page number 1-59" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#intercept of planeare in proportion 3a:4b:infinity (plane parallel to z axis)\n", + "\n", + "#as a,b and c are basic vectors the proportin of intercepts 3:4:infinity\n", + "\n", + "#therefore reciprocal\n", + "\n", + "r1=1./3\n", + "r2=1./4\n", + "r3=0\n", + "\n", + "#taking LCM of 3 and 4 i.e. 12\n", + "\n", + "l=12\n", + "\n", + "m1=(l*r1)\n", + "\n", + "m2=(l*r2)\n", + "\n", + "m3=(l*r3)\n", + "\n", + "print\"miler indices=\",(m3,m2,m1)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "miler indices= (0, 3.0, 4.0)\n" + ] + } + ], + "prompt_number": 29 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.5,Page number 1-59" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#intercept of planeare in proportion 3a:-2b:3/2c\n", + "\n", + "#as a,b and c are basic vectors the proportin of intercepts 3:-2:3/2\n", + "\n", + "#therefore reciprocal\n", + "\n", + "r1=1./3\n", + "r2=-1./2\n", + "r3=2./3\n", + "\n", + "#taking LCM of 3, 2 and 3/2 is 6\n", + "\n", + "l=6\n", + "\n", + "m1=(l*r1)\n", + "\n", + "m2=(l*r2)\n", + "\n", + "m3=(l*r3)\n", + "\n", + "print\"miler indices=\",(m3,m2,m1)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "miler indices= (4.0, -3.0, 2.0)\n" + ] + } + ], + "prompt_number": 31 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.6,Page number 1-59" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#if a plane cut at length m,n,p on the three crystal axes,then\n", + "\n", + "#m:n:p=xa:yb:zc\n", + "\n", + "#when primitive vectors of unit cell and numbers x,y,z,are related to miller indices (h,k,l)of the plane by relation\n", + "\n", + "#1/x:1/y:1/z=h:k:l\n", + "\n", + "#since a=b=c (crystal is simple cubic)\n", + "\n", + "#and (h,k,l)=(1,2,3)\n", + "\n", + "#therefore reciprocal\n", + "\n", + "r1=1./1\n", + "r2=1./2\n", + "r3=1./3\n", + "\n", + "#taking LCM of 1 ,2 and 3 is 6\n", + "\n", + "l=6\n", + "\n", + "m=(l*r1)\n", + "\n", + "n=(l*r2)\n", + "\n", + "p=(l*r3)\n", + "\n", + "print\"ratio of intercepts=\",(m,n,p)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "ratio of intercepts= (6.0, 3.0, 2.0)\n" + ] + } + ], + "prompt_number": 35 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.7,Page number 1-60" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#primitive vectors\n", + "\n", + "a=1.2 #in amstrong unit\n", + "b=1.8 #in amstrong unit\n", + "c=2 #in amstrong unit\n", + "\n", + "#miller indices of the plane\n", + "\n", + "h=2\n", + "k=3\n", + "l=1\n", + "\n", + "#therefore intercepts are a/h,b/k,c/l\n", + "\n", + "x=a/h\n", + "y=b/k\n", + "z=c/l\n", + "\n", + "#this gives intercepts along x axis as x amstrong but it is given tthat plane cut x axis at 1.2 amstrong .\n", + "\n", + "t=1.2/x\n", + "\n", + "#this shows that the plane under consideration is another plane which is parallel to it(to keep miller indices same)\n", + "\n", + "n=t*y #Y intercept\n", + "\n", + "p=t*z #Z intercept\n", + "\n", + "print\"1) Y intercept=\",n,\"amstrong\"\n", + "\n", + "print\"2)Z intercept=\",p,\"amstrong\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Y intercept= 1.2 amstrong\n", + "2)Z intercept= 4.0 amstrong\n" + ] + } + ], + "prompt_number": 37 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.8,Page number 1-61" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#the interplanar spacing of plane\n", + "\n", + "h=1\n", + "k=1\n", + "l=0\n", + "d=2 #interpanar spacing in amstrong unit\n", + "\n", + "#we know that d=a/sqrt(h**2+k**2+l**2) therefore\n", + "\n", + "a=d*math.sqrt(h**2+k**2+l**2)\n", + "\n", + "#for FCC structure\n", + "\n", + "r=math.sqrt(2)*a/4\n", + "\n", + "print\"radius r=\",(r),\"amstrong\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "radius r= 1.0 amstrong\n" + ] + } + ], + "prompt_number": 39 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.9,Page number 1-61" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=4 #for FCC structure\n", + "\n", + "#the interplanar spacing of plane\n", + "\n", + "h=1\n", + "k=1\n", + "l=1\n", + "d=2.08*10**-10 #distance\n", + "A=63.54 #atomic weight of Cu\n", + "N=6.023*10**26 #amstrong no\n", + "\n", + "#we know that d=a/sqrt(h**2+k**2+l**2) therefore\n", + "\n", + "a=d*math.sqrt(h**2+k**2+l**2)\n", + "\n", + "#also (a**3*q)=n*A/N\n", + "\n", + "q=n*A/(N*a**3)\n", + "\n", + "print\"1)density=\",round(q,4),\"kg/m^3\"\n", + "\n", + "#for FCC structure\n", + "\n", + "r=math.sqrt(2)*a/4\n", + "\n", + "d=r*2\n", + "\n", + "print\"2)radius r=\",\"{0:.3e}\".format(r),\"m\"\n", + "\n", + "print\"3)diameter d=\",\"{0:.3e}\".format(d),\"m\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)density= 9024.4855 kg/m^3\n", + "2)radius r= 1.274e-10 m\n", + "3)diameter d= 2.547e-10 m\n" + ] + } + ], + "prompt_number": 44 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.10,Page number 1-62" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "A=63.546 #atomic weight of Cu\n", + "N=6.023*10**26 #Avogadro's number\n", + "p=8930 #Density\n", + "n=1.23 #no.of electron per atom\n", + "\n", + "#density=mass/volume\n", + "\n", + "#therfore 1/volume=density/mass\n", + "\n", + "#since electron concentration is needed, let us find out no of atoms/volume(x)\n", + "\n", + "x=N*p/A\n", + "\n", + "#now one atom contribute n=1.23 electron\n", + "\n", + "#therefore x atoms contribute y no of free electron\n", + "\n", + "y=x*n\n", + "\n", + "print\"free electron concentration=\",\"{0:.3e}\".format(y),\"electron/m^3\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "free electron concentration= 1.041e+29 electron/m^3\n" + ] + } + ], + "prompt_number": 46 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.11,Page number 1-62" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#primitive vectors\n", + "\n", + "a=1.5 #in amstrong unit\n", + "b=2 #in amstrong unit\n", + "c=4. #in amstrong unit\n", + "\n", + "#miller indices of the plane\n", + "\n", + "h=3\n", + "k=2\n", + "l=6\n", + "\n", + "#therefore intercepts are a/h,b/k,c/l\n", + "\n", + "x=a/h\n", + "y=b/k\n", + "z=c/l\n", + "\n", + "#this gives intercepts along x axis as x amstrong but it is given that plane cut x axis at 1.2 amstrong .\n", + "\n", + "t=1.5/x\n", + "\n", + "#this shows that the plane under consideration is another plane which is parallel to it(to keep miller indices same)\n", + "\n", + "n=t*y #Y intercept\n", + "\n", + "p=t*z #Z intercept\n", + "\n", + "print\"1) Y intercept=\",(n),\"amstrong\"\n", + "\n", + "print\"2)Z intercept=\",(p),\"amstrong\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Y intercept= 3.0 amstrong\n", + "2)Z intercept= 2.0 amstrong\n" + ] + } + ], + "prompt_number": 48 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.12,Page number 1-63" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "ro=7.87 #density of metal\n", + "A=55.85 #atomic wt of metal\n", + "N=6.023*10**23 #Avogadro's number\n", + "a=2.9*10**-8 #lattice constant of metal\n", + "\n", + "n=(N*(a**3)*ro)/A\n", + "\n", + "print\"Number of atom per unit cell of a metal=\",round(n,0)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of atom per unit cell of a metal= 2.0\n" + ] + } + ], + "prompt_number": 52 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.13,Page number 1-63" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=2 #BCC structure\n", + "ro=9.6*10**2 #density of sodium crystal\n", + "A=23 #atomic weight of sodium crystal\n", + "N=6.023*10**26 #Avogadro's number\n", + "\n", + "a=((n*A)/(N*ro))**(1./3)\n", + "\n", + "print\"Lattice constant=\",\"{0:.3e}\".format(a),\"m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Lattice constant= 4.301e-10 m\n" + ] + } + ], + "prompt_number": 50 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.15,Page number 1-64" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "ro=2.7*10**3 #density of metal\n", + "A=27 #atomic wt of metal\n", + "N=6.023*10**26 #Avogadro's number\n", + "a=4.05*10**-10 #lattice constant of metal\n", + "\n", + "n=(N*(a**3)*ro)/A\n", + "\n", + "print\"1) Number of atom per unit cell of a metal=\",round(n,0)\n", + "\n", + "r=math.sqrt(2)*a/4 #radius of metal\n", + "\n", + "print\"2) atomic radius of a metal=\",\"{0:.3e}\".format(r),\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Number of atom per unit cell of a metal= 4.0\n", + "2) atomic radius of a metal= 1.432e-10 m\n" + ] + } + ], + "prompt_number": 56 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.16,Page number 1-64" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=2 #BCC structure\n", + "ro=5.98*10**3 #density of chromium\n", + "A=50 #atomic wt of chromium\n", + "N=6.023*10**26 #Avogadro's number\n", + "\n", + "a=((n*A)/(N*ro))**(1./3)\n", + "\n", + "print\"1) Lattice constant=\",\"{0:.3e}\".format(a),\"m\"\n", + "\n", + "#for BCC\n", + "\n", + "r=math.sqrt(3)*a/4 #radius of chromium\n", + "\n", + "APF=(n*(4./3)*math.pi*(r**3))/(a**3)\n", + "\n", + "print\"2) A.P.F. for chromium=\",round(APF,4)\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Lattice constant= 3.028e-10 m\n", + "2) A.P.F. for chromium= 0.6802\n" + ] + } + ], + "prompt_number": 60 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.17,Page number 1-65" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=4 #FCC structure\n", + "ro=6250 #density\n", + "M=60.2 #molecular weight\n", + "N=6.023*10**26 #Avogadro's number\n", + "\n", + "a=((n*M)/(N*ro))**(1./3)\n", + "\n", + "print\"Lattice constant=\",\"{0:.3e}\".format(a),\"m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Lattice constant= 3.999e-10 m\n" + ] + } + ], + "prompt_number": 62 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.19,Page number 1-66" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "a=2.82*10**-9 #lattice constant\n", + "n=2 #FCC crystal\n", + "t=17.167 #glancing angle in degree\n", + "q=math.pi/180*t #glancing angle in radians\n", + "\n", + "#assuming reflection in (1,0,0) plane\n", + "\n", + "h=1\n", + "k=0\n", + "l=0\n", + "\n", + "d=a/math.sqrt(h**2+k**2+l**2)\n", + "\n", + "#using Bragg's law , 2*d*sin(q)=n*la\n", + "\n", + "la=2*d*sin(q)/n\n", + "\n", + "print\"wavlength of X-ray=\",\"{0:.3e}\".format(la),\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "wavlength of X-ray= 8.323e-10 m\n" + ] + } + ], + "prompt_number": 64 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.20,Page number 1-66" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=8 #Diamond structure\n", + "ro=2.33*10**3 #density of diamond\n", + "M=28.9 #atomic weight of diamond\n", + "N=6.023*10**26 #Avogadro's number\n", + "\n", + "a=((n*M)/(N*ro))**(1./3)\n", + "\n", + "print\"1) Lattice constant=\",\"{0:.3e}\".format(a),\"m\"\n", + "\n", + "r=math.sqrt(3)*a/8 #radius of diamond structure\n", + "\n", + "print\"2) atomic radius of a metal=\",\"{0:.3e}\".format(r),\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Lattice constant= 5.482e-10 m\n", + "2) atomic radius of a metal= 1.187e-10 m\n" + ] + } + ], + "prompt_number": 66 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14.21,Page number 1-66" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=2 #BCC structure\n", + "ro=8.57*10**3 #density of chromium\n", + "d=2.86*10**-10 #nearest atoms distance\n", + "\n", + "#d=sqrt(3)/2*a\n", + "\n", + "a=2*d/math.sqrt(3)\n", + "\n", + "#now use formulae a**3*ro=n*A/N\n", + "\n", + "#therefore a**3*ro/n=mass of unit cell/(no of atoms pre unit cell)=mass of one atom\n", + "\n", + "m=a**3*ro/n\n", + "\n", + "print\"mass of one atom=\",\"{0:.3e}\".format(m),\"kg\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "mass of one atom= 1.543e-25 kg\n" + ] + } + ], + "prompt_number": 68 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.1,Page number 1-68" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "d=4.255*10**-10 #interplaner spacing\n", + "l=1.549*10**-10 #wavelength of x ray\n", + "\n", + "#part 1: for smallest glancing angle(n=1)\n", + "\n", + "n1=1\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "q=math.degrees(math.asin(n1*l/(2*d)))\n", + "\n", + "print\"1)glancing angle=\",round(q,4),\"degree\"\n", + "\n", + "#part 2: for highst order\n", + "\n", + "#for highest order sin(q) not exceed one i.e maximum value is one\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "n2=2*d/l #since sin(q)is one\n", + "\n", + "print\"2)highest order possible =\",math.floor(n2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)glancing angle= 10.4875 degree\n", + "2)highest order possible = 5.0\n" + ] + } + ], + "prompt_number": 70 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.2,Page number 1-69" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "a=2.125*10**-10 #lattice constant\n", + "d=a/2 #interplaner spacing\n", + "n=2 #second order maximum\n", + "l=0.592*10**-10 #wavelength of rock salt crystal\n", + "\n", + "#using Bragg's law\n", + "\n", + "q=math.degrees(math.asin((n*l)/(2*d))) #glancing angle\n", + "\n", + "print\"glancing angle=\",round(q,4),\"degree\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "glancing angle= 33.8608 degree\n" + ] + } + ], + "prompt_number": 72 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.3,Page number 1-69" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n1=1 #for 1st order\n", + "n2=2 #for 2nd order\n", + "t=3.4 #angle where 1st order reflection done\n", + "t1=t*math.pi/180 #convert degree to radian\n", + "\n", + "m=math.sin(t1)\n", + "\n", + "#but from Bragg's law\n", + "\n", + "#n*l=2*d*sin(t)\n", + "\n", + "#for for constant distance(d) and wavelength(l) \n", + "\n", + "#order(n) is directly proportionl to sine of angle i.e (sin(t))\n", + "\n", + "#n1/n2=sin(t1)/sin(t2)\n", + "\n", + "#assume sin(t2)=a\n", + "\n", + "a=n2/n1*m\n", + "\n", + "t2=math.degrees(math.asin(a)) #taking sin inverese in degree\n", + "\n", + "print\"second order reflection take place at an angle=\",round(t2,4),\"degree\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "second order reflection take place at an angle= 6.812 degree\n" + ] + } + ], + "prompt_number": 75 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.4,Page number 1-70" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "V=50*10**3 #operating voltage of x-ray\n", + "M=74.6 #molecular weight\n", + "p=1.99*10**3 #density\n", + "n=4 #no of atoms per unit cell(for FCC structure)\n", + "h=6.63*10**-34 #plank's constant\n", + "c=3*10**8 #velocity \n", + "e=1.6*10**-19 #charge on electron\n", + "N=6.023*10**26 #Avogadro's number\n", + "\n", + "#step 1:clculating shortest wavelength\n", + "\n", + "l=h*c/(e*V)\n", + "\n", + "print\"1)shortest wavelength=\",(l),\"m\"\n", + "\n", + "#step:2 calculating distance(d)\n", + "\n", + "#now a**3*p=n*M/N therefore,\n", + "\n", + "a=(n*M/(N*p))**(1./3)\n", + "\n", + "#since KCl is ionic crystal herefore,\n", + "\n", + "d=a/2\n", + "\n", + "#step 3: calculaing glancing angle\n", + "\n", + "#using Bragg's law\n", + "\n", + "#n*l=2*d*sin(t)\n", + "\n", + "#assume sin(t)=a, wavelength is minimum i.e l and n=1\n", + "\n", + "n=1\n", + "\n", + "a=n*l/(2*d)\n", + "\n", + "t=math.degrees(math.asin(a)) #taking sin inverese in degree\n", + "\n", + "print\"2) glancing angle=\",round(t,4),\"degree\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)shortest wavelength= 2.48625e-11 m\n", + "2) glancing angle= 2.265 degree\n" + ] + } + ], + "prompt_number": 77 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.5,Page number 1-70" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=1.0 #first order maximum\n", + "l=0.82*10**-10 #wavelength of X ray\n", + "qd=7.0 #glancing angle in degree\n", + "qm=51./60 #glancing angle in minute\n", + "qs=48./3600 #glancing angle in second\n", + "\n", + "q=qd+qm+qs #total glancin angle in degree\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "d=n*l/(2*math.sin(q*math.pi/180))\n", + "\n", + "a=3*10**-10 #lattice constant\n", + "\n", + "#we know that d=a/root(h**2+k**2+l**2)\n", + "\n", + "#assume root(h**2+k**2+l**2) =m\n", + "\n", + "#arranging terms we get\n", + "\n", + "m=a/d\n", + "\n", + "print\"square root(h**2+k**2+l**2)=\",round(m,0)\n", + "\n", + "print\"hence possible solutions are (100),(010),(001)\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "square root(h**2+k**2+l**2)= 1.0\n", + "hence possible solutions are (100),(010),(001)\n" + ] + } + ], + "prompt_number": 90 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.6,Page number 1-71" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=1 #first order maximum\n", + "l=1j #wavelength of X ray\n", + "\n", + "#part 1:for(100)\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "q1=5.4 #glancing angle in degree\n", + "\n", + "dl1=n*l/(2*math.sin(q1*math.pi/180))\n", + "\n", + "#part 2:for(110)\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "q2=7.6 #glancing angle in degree\n", + "\n", + "dl2=n*l/(2*math.sin(q2*math.pi/180))\n", + "\n", + "#part 3:for(111)\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "q3=9.4 #glancing angle in degree\n", + "\n", + "dl3=n*l/(2*math.sin(q3*math.pi/180))\n", + "\n", + "#for taking ratio divide all dl by dl1\n", + "\n", + "d1=dl1/dl1\n", + "\n", + "d2=dl2/dl1\n", + "\n", + "d3=dl3/dl1\n", + "\n", + "print\"cubic lattice structure is=\",d1,d2,d3" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " cubic lattice structure is= (1+0j) (0.711559669333+0j) (0.576199350225+0j)\n" + ] + } + ], + "prompt_number": 94 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.7,Page number 1-71" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=1 #first order maximum\n", + "l=1.54*10**-10 #wavelength of rock salt crystal\n", + "q=21.7 #glancing angle in degree\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "d=n*l/(2*math.sin(q*math.pi/180))\n", + "\n", + "print\"lattice constant of crystal=\",\"{0:.3e}\".format(d),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "lattice constant of crystal= 2.083e-10 meter\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.8,Page number 1-72" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "a=2.814*10**-10 #lattice constant\n", + "\n", + "#the interplanar spacing of plane\n", + "\n", + "h=1\n", + "k=0\n", + "l=0\n", + "\n", + "d=a/math.sqrt(h**2+k**2+l**2)\n", + "\n", + "n=2 #first order maximum\n", + "\n", + "l=0.714*10**-10 #wavelength of X-ray crystal\n", + "\n", + "#using Bragg's law\n", + "\n", + "q=math.degrees(math.asin((n*l)/(2*d))) #glancing angle\n", + "\n", + "print\"glancing angle=\",round(q,4),\"degree\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "glancing angle= 14.6984 degree\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.9,Page number 1-72" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "d=2.82*10**-10 #interplaner spacing\n", + "t=10 #glancing angle\n", + "\n", + "#for part 1\n", + "\n", + "n=1 #first order maximum\n", + "\n", + "#using Bragg's law n*l=2*d*sin(t)\n", + "\n", + "l=2*d*math.sin(math.pi*t/180)/n\n", + "\n", + "print\"1)wavelength=\",\"{0:.3e}\".format(l),\"meter\"\n", + "\n", + "#for part 2\n", + "\n", + "n1=2\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "q=math.degrees(math.asin(n1*l/(2*d)))\n", + "\n", + "print\"2)glancing angle=\",round(q,4),\"degree\"\n", + "\n", + "#for part 3\n", + "\n", + "#for highest order sin(q) not exceed one i.e maximum value is one\n", + "\n", + "#using Bragg's law n*l=2*d*sin(q)\n", + "\n", + "n2=2*d/l #since sin(q)is one\n", + "\n", + "print\"3)highest order possible =\",(floor(n2))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)wavelength= 9.794e-11 meter\n", + "2)glancing angle= 20.322 degree\n", + "3)highest order possible = 5.0\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.10,Page number 1-73" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#for line -A\n", + "\n", + "n1=1 #1st order maximum\n", + "q1=30 #glancing angle in degree\n", + "\n", + "#using Bragg's law for line A n1*l1=2*d1*sin(q1)\n", + "\n", + "#d1=n1*l1/(2*sin(q1))\n", + "\n", + "#for line B\n", + "\n", + "l2=0.97 #wavelength in amstrong unit\n", + "n2=3 #1st order maximum\n", + "q2=60 #glancing angle in degree\n", + "\n", + "#using Bragg's law for line B n2*l2=2*d2*sin(q2)\n", + "\n", + "#since for both lines A and B we use same plane of same crystal,therefore\n", + "\n", + "#d1=d2\n", + "\n", + "#therefore equution became n2*l2=2*n1*l1/(2*sin(q1))*sin(q2)\n", + "\n", + "#by arranging terms we get\n", + "\n", + "\n", + "l1=n2*l2*2*math.sin(q1*math.pi/180)/(2*n1*math.sin(q2*math.pi/180))\n", + "\n", + "print\"wavelength of the line A=\",round(l1,4),\"amstrong\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "wavelength of the line A= 1.6801 amstrong\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.11,Page number 1-74" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=1.0 #first order minimum\n", + "d=5.5*10**-11 #atomic spacing\n", + "e=1.6*10**-19 #charge on one electron\n", + "Ee=10*10**3 #energy in eV\n", + "E=e*Ee #energy in Joule\n", + "m=9.1*10**-31 #mass of elelctron\n", + "h=6.63*10**-34 #plank's constant\n", + "\n", + "l=h/math.sqrt(2*m*E) #wavelength\n", + "\n", + "#using Bragg's law\n", + "\n", + "q=math.degrees(math.asin((n*l)/(2*d))) #glancing angle\n", + "\n", + "print\"glancing angle=\",round(q,4),\"degree\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "glancing angle= 6.4129 degree\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15.12,Page number 1-74" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "a=2.814*10**-10 #lattice constant\n", + "\n", + "#for rock salt\n", + "\n", + "d=a/2 #interplaner spacing\n", + "\n", + "n=1 #first order maximum\n", + "\n", + "l=1.541*10**-10 #wavelength of rock salt crystal\n", + "\n", + "#using Bragg's law\n", + "\n", + "q=math.degrees(math.asin((n*l)/(2*d))) #glancing angl\n", + "\n", + "print\"glancing angle=\",round(q,4),\"degree\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "glancing angle= 33.2038 degree\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.16.1,Page number 1-75" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Ev=1.08 #average energy required to creaet a vacancy\n", + "k=1.38*10**-23 #boltzman constant in J/K\n", + "e=1.6*10**-19 #charge on 1 electron\n", + "\n", + "K=k/e #boltzman constant in eV/K\n", + "\n", + "#for a low concentration of vacancies a relation is\n", + "\n", + "#n=Nexp(-Ev/KT)\n", + "\n", + "#since total no atom is 1 hence N=1\n", + "\n", + "#at 1000k\n", + "\n", + "T1=1000 #temperature\n", + "\n", + "n1=math.exp(-Ev/(K*T1))\n", + "\n", + "#at 500k\n", + "\n", + "T2=500 #temperature\n", + "\n", + "n2=math.exp(-Ev/(K*T2))\n", + "\n", + "v=(n1)/(n2) #ratio of vacancies\n", + "\n", + "print\"ratio of vacancies=\",round(v,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "ratio of vacancies= 274234.5745\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.16.2,Page number 1-75" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Ev=1.95 #average energy required to creaet a vacancy\n", + "k=1.38*10**-23 #boltzman constant in J/K\n", + "e=1.6*10**-19 #charge on 1 electron\n", + "K=k/e #boltzman constant in eV/K\n", + "T=500 #temperature\n", + "\n", + "#for a low concentration of vacancies a relation is\n", + "\n", + "#n=Nexp(-Ev/KT)\n", + "\n", + "m=math.exp(-Ev/(K*T)) #ratio of no of vacancies to no of atoms n/N\n", + "\n", + "print\"ratio of no of vacancies to no of atoms=\",\"{0:.3e}\".format(m)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "ratio of no of vacancies to no of atoms= 2.303e-20\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.16.3,Page number 1-76" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Ev=1.8 #average energy required to creaet a vacancy\n", + "k=1.38*10**-23 #boltzman constant in J/K\n", + "e=1.6*10**-19 #charge on 1 electron\n", + "K=k/e #boltzman constant in eV/K\n", + "\n", + "#for a low concentration of vacancies a relation is\n", + "\n", + "#n=Nexp(-Ev/KT)\n", + "\n", + "#ratio of vacancy is n/N assume be r=exp(-Ev/KT)\n", + "\n", + "#since total no atom is 1 hence N=1\n", + "\n", + "#at 1000k\n", + "\n", + "t1=-119 #temperature in degree\n", + "T1=t1+273 #temperature in kelvine\n", + "r1=math.exp(-Ev/(K*T1))\n", + "\n", + "print\"1)ratio of vacancies at -119 degree=\",\"{0:.3e}\".format(r1)\n", + "\n", + "#at 500k\n", + "\n", + "t2=80 #temperature in degree\n", + "\n", + "T2=t2+273 #temperature in kelvine\n", + "\n", + "r2=exp(-Ev/(K*T2))\n", + "\n", + "v=(r1)/(r2) #ratio of vacancies\n", + "\n", + "print\"2)ratio of vacancies at 80 degree=\",\"{0:.3e}\".format(r2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)ratio of vacancies at -119 degree= 1.399e-59\n", + "2)ratio of vacancies at 80 degree= 2.110e-26\n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.16.4,Page number 1-76" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Ev=1.5 #energy of formaton of frankel defect\n", + "k=1.38*10**-23 #boltzman constant in J/K\n", + "e=1.6*10**-19 #charge on 1 electron\n", + "K=k/e #boltzman constant in eV/K\n", + "T=700 #temperature\n", + "N=6.023*10**26 #avogadro's no\n", + "\n", + "#for a low concentration of vacancies a relation is\n", + "\n", + "#n=Nexp(-Ev/KT)\n", + "\n", + "m=math.exp(-Ev/(2*K*T)) #ratio of no of vacancies to no of atoms n/N\n", + "\n", + "qs=5.56 #specific density\n", + "q=5.56*10**3 #real density ke/m**3\n", + "M=0.143 #molecular weight in kg/m**3\n", + "ma=M/N #mass of one molecule\n", + "v=ma/q #vol of one molecule\n", + "\n", + "#v volume containe 1 molecule\n", + "\n", + "#therefore 1 m**3 containe x molecule\n", + "\n", + "x=1./v\n", + "d=m*x #defect per m**3\n", + "dm=d*10**-9 #defect per mm**3\n", + "\n", + "print\"number of frankel defects per mm^3=\",\"{0:.3e}\".format(dm)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "number of frankel defects per mm^3= 9.432e+16\n" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Applied_Physics-I_by_I_A_Shaikh/chapter_2.ipynb b/Applied_Physics-I_by_I_A_Shaikh/chapter_2.ipynb new file mode 100644 index 00000000..17fcfe26 --- /dev/null +++ b/Applied_Physics-I_by_I_A_Shaikh/chapter_2.ipynb @@ -0,0 +1,851 @@ +{ + "metadata": { + "celltoolbar": "Raw Cell Format", + "name": "", + "signature": "sha256:48c8e92f460a56975ab73a5ede03395bfb2a33fc5326e02cbff674697a4f07d0" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 2: Semiconductor Physics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21.1,Page number 2-47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "ro=1.72*10**-8 #resistivity of Cu\n", + "s=1/ro #conductivity of Cu\n", + "n=10.41*10**28 #no of electron per unit volume\n", + "e=1.6*10**-19 #charge on electron\n", + "\n", + "u=s/(n*e)\n", + "\n", + "print\"mobility of electron in Cu =\",\"{0:.3e}\".format(u),\"m^2/volt-sec\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "mobility of electron in Cu = 3.491e-03 m^2/volt-sec\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21.2,Page number 2-47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "m=63.5 #atomic weight\n", + "u=43.3 #mobility of electron\n", + "e=1.6*10**-19 #charge on electron\n", + "N=6.02*10**23 #Avogadro's number\n", + "d=8.96 #density\n", + "\n", + "Ad=N*d/m #Atomic density\n", + "\n", + "n=1*Ad\n", + "\n", + "ro=1/(n*e*u)\n", + "\n", + "print\"Resistivity of Cu =\",\"{0:.3e}\".format(ro),\"ohm-cm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Resistivity of Cu = 1.699e-06 ohm-cm\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21.3,Page number 2-47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "e=1.6*10**-19 #charge on electron\n", + "ne=2.5*10**19 #density of carriers\n", + "nh=ne #for intrinsic semiconductor\n", + "ue=0.39 #mobility of electron\n", + "uh=0.19 #mobility of hole\n", + "\n", + "s=ne*e*ue+nh*e*uh #conductivity of Ge\n", + "\n", + "ro=1.0/s #resistivity of Ge\n", + "\n", + "print\"Resistivity of Ge =\",round(ro,4),\"ohm-m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Resistivity of Ge = 0.431 ohm-m\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21.5,Page number 2-48" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Eg=1.2 #energy gap\n", + "T1=600 #temperature\n", + "T2=300 #temperature\n", + "\n", + "#since ue>>uh for intrinsic semiconductor\n", + "\n", + "#s=ni*e*ue\n", + "\n", + "K=8.62*10**-5 #Boltzman constant\n", + "\n", + "s=1l\n", + "\n", + "s1=s*exp((-Eg)/(2*K*T1))\n", + "\n", + "s2=s*exp((-Eg)/(2*K*T2))\n", + "\n", + "m=(s1/s2)\n", + "\n", + "print'Ratio between conductivity =',\"{0:.3e}\".format(m)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Ratio between conductivity = 1.092e+05\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21.6,Page number 2-49" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "c=5*10**28 #concentration of Si atoms\n", + "e=1.6*10**-19 #charge on electron\n", + "u=0.048 #mobility of hole\n", + "s=4.4*10**-4 #conductivity of Si\n", + "\n", + "#since millionth Si atom is replaced by an indium atom\n", + "\n", + "n=c*10**-6\n", + "\n", + "sp=u*e*n #conductivity of resultant\n", + "\n", + "print\"conductivity =\",(sp),\"mho/m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "conductivity = 384.0 mho/m\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21.7,Page number 2-49" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "m=28.1 #atomic weight of Si\n", + "e=1.6*10**-19 #charge on electron\n", + "N=6.02*10**26 #Avogadro's number\n", + "d=2.4*10**3 #density of Si\n", + "p=0.25 #resistivity\n", + "\n", + "#no. of Si atom/m**3\n", + "\n", + "Ad=N*d/m #Atomic density\n", + "\n", + "#impurity level is 0.01 ppm i.e. 1 atom in every 10**8 atoms of Si\n", + "\n", + "n=Ad/10**8 #no of impurity atoms\n", + "\n", + "#since each impurity produce 1 hole\n", + "\n", + "nh=n\n", + "\n", + "print\"1) hole concentration =\",round(n,4),\"holes/m^3\"\n", + "\n", + "up=1/(e*p*nh)\n", + "\n", + "print\"2) mobility =\",round(up,4),\"m^2/volt.sec\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) hole concentration = 5.14163701068e+20 holes/m^3\n", + "2) mobility = 0.0486 m^2/volt.sec\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.22.1,Page number 2-50" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "t=27 #temp in degree \n", + "T=t+273 #temp in kelvin\n", + "K=8.62*10**-5 #Boltzman constant in eV\n", + "Eg=1.12 #Energy band gap\n", + "\n", + "#For intrensic semiconductor (Ec-Ev)=Eg/2\n", + "\n", + "#let (Ec-Ev)=m\n", + "\n", + "m=Eg/2\n", + "\n", + "a=(m/(K*T))\n", + "\n", + "#probability f(Ec)=1/(1+exp((Ec-Ev)/(K*T))\n", + "\n", + "p=1/(1+exp(a))\n", + "\n", + "\n", + "print\"probability of an electron being thermally excited to conduction band=\",\"{0:.3e}\".format(p)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "probability of an electron being thermally excited to conduction band= 3.938e-10\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.22.2,Page number 2-50" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "T=300 #temp in kelvin\n", + "K=8.62*10**-5 #Boltzman constant in eV\n", + "m=0.012 #energy level(Ef-E)\n", + "\n", + "a=(m/(K*T))\n", + "\n", + "#probability f(Ec)=1/(1+exp((Ec-Ev)/(K*T))\n", + "\n", + "p=1.0/(1+exp(a))\n", + "\n", + "p1=1-p\n", + "\n", + "print\"probability of an energy level not being occupied by an electron=\",round(p1,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "probability of an energy level not being occupied by an electron= 0.614\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.22.3,Page number 2-51" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "t=20 #temp in degree \n", + "T=t+273 #temp in kelvin\n", + "K=8.62*10**-5 #Boltzman constant in eV\n", + "Eg=1.12 #Energy band gap\n", + "\n", + "#For intrensic semiconductor (Ec-Ev)=Eg/2\n", + "\n", + "#let (Ec-Ev)=m\n", + "\n", + "m=Eg/2\n", + "\n", + "a=(m/(K*T))\n", + "\n", + "#probability f(Ec)=1/(1+exp((Ec-Ev)/(K*T))\n", + "\n", + "p=1.0/(1+exp(a))\n", + "\n", + "\n", + "print\"probability of an electron being thermally excited to conduction band=\",\"{0:.3e}\".format(p)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "probability of an electron being thermally excited to conduction band= 2.348e-10\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.22.4,Page number 2-51" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "T=300 #temp in kelvin\n", + "K=8.62*10**-5 #Boltzman constant in eV\n", + "Eg=2.1 #Energy band gap\n", + "\n", + "#probability f(Ec)=1/(1+exp((Ec-Ev)/(K*T))\n", + "\n", + "m=K*T\n", + "\n", + "#for f(E)=0.99\n", + "\n", + "p1=0.99\n", + "\n", + "b=abs(1.0-(1.0/p1))\n", + "\n", + "a=math.log(b) #a=(E-2.1)/m\n", + "\n", + "E=2.1+m*a\n", + "\n", + "print\"1) Energy for which probability is 0.99=\",round(E,4),\"eV\"\n", + "\n", + "#for f(E)=0.01\n", + "\n", + "p2=0.01\n", + "\n", + "b2=abs(1-1.0/p2)\n", + "\n", + "a1=math.log(b2) #a=(E-2.1)/m\n", + "\n", + "E1=2.1+m*a1\n", + "\n", + "print\"2)Energy for which probability is 0.01=\",round(E1,4),\"eV\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Energy for which probability is 0.99= 1.9812 eV\n", + "2)Energy for which probability is 0.01= 2.2188 eV\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.1,Page number 2-52" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "ni=2.4*10**19 #density of intrensic semiconductor\n", + "n=4.4*10**28 #no atom in Ge crystal\n", + "Nd=n/10**6 #density\n", + "Na=Nd\n", + "e=1.6*10**-19 #charge on electron\n", + "T=300 #temerature at N.T.P.\n", + "K=1.38*10**-23 #Boltzman constant\n", + "\n", + "Vo=(K*T/e)*log(Na*Nd/(ni**2))\n", + "\n", + "print\"Potential barrier for Ge =\",round(Vo,4),\"Volts\"\n", + "\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Potential barrier for Ge = 0.3888 Volts\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.2,Page number 2-52" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "B=0.6 #magnetic field\n", + "d=5*10**-3 #distancebetween surface\n", + "J=500 #current density\n", + "Nd=10**21 #density\n", + "e=1.6*10**-19 #charge on electron\n", + "\n", + "Vh=(B*J*d)/(Nd*e) #due to Hall effect\n", + "\n", + "print\"Hall voltage =\",\"{0:.3e}\".format(Vh),\"Volts\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Hall voltage = 9.375e-03 Volts\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.3,Page number 2-53" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Rh=6*10**-7 #Hall coefficient\n", + "B=1.5 #magnetic field\n", + "I=200 #current in strip\n", + "W=1*10**-3 #thickness of strip\n", + "\n", + "Vh=Rh*(B*I)/W #due to Hall effect\n", + "\n", + "print\"Hall voltage =\",(Vh),\"Volt\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Hall voltage = 0.18 Volt\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.4,Page number 2-53" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Rh=2.25*10**-5 #Hall coefficient\n", + "u=0.025 #mobility of hole\n", + "\n", + "r=Rh/u\n", + "\n", + "print\"Resistivity of P type silicon =\",\"{0:.3e}\".format(r),\"ohm-m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Resistivity of P type silicon = 9.000e-04 ohm-m\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.5,Page number 2-53" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "B=0.55 #magnetic field\n", + "d=4.5*10**-3 #distancebetween surface\n", + "J=500 #current density\n", + "n=10**20 #density\n", + "e=1.6*10**-19 #charge on electron\n", + "Rh=1/(n*e) #Hall coefficient\n", + "\n", + "Vh=Rh*B*J*d #Hall voltage\n", + "\n", + "print\"1) Hall voltage =\",round(Vh,4),\"Volts\"\n", + "\n", + "print\"2) Hall coefficient =\",(Rh),\"m^3/C\"\n", + "\n", + "u=0.17 #mobility of electrom\n", + "\n", + "m=math.atan(u*B)\n", + "\n", + "a=m*180/math.pi #conversion randian into degree\n", + "\n", + "print\"3) Hall angle =\",round(a,4),\"degree\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Hall voltage = 0.0773 Volts\n", + "2) Hall coefficient = 0.0625 m^3/C\n", + "3) Hall angle = 5.3416 degree\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.6,Page number 2-54" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Rh=3.66*10**-4 #Hall coefficient\n", + "r=8.93*10**-3 #resistivity \n", + "e=1.6*10**-19 #charge on electron\n", + "\n", + "#Hall coefficient Rh=1/(n*e)\n", + "\n", + "n=1/(Rh*e) #density\n", + "\n", + "print\"1) density(n) =\",round(n,4),\"/m^3\"\n", + "\n", + "u=Rh/r #mobility of electron\n", + "\n", + "print\"2) mobility (u) =\",round(u,4),\"m^2/v-s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) density(n) = 1.70765027322e+22 /m^3\n", + "2) mobility (u) = 0.041 m^2/v-s\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.7,Page number 2-55" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "B=0.2 #magnetic field\n", + "e=1.6*10**-19 #charge on electron\n", + "ue=0.39 #mobility of electron\n", + "l=0.01 #length\n", + "A=0.001*0.001 #cross section area of bar\n", + "V=1*10**-3 #Applied voltage\n", + "d=0.001 #sample of width \n", + "\n", + "r=1/(ue*e) #resistivity\n", + "R=r*l/A #resistance of Ge bar\n", + "\n", + "#using ohm's law\n", + "\n", + "I=V/R\n", + "Rh=r*ue #hall coefficient\n", + "\n", + "#using formulae for hall effect\n", + "\n", + "J=I/A #current density\n", + "Vh=Rh*B*J*d\n", + "\n", + "print\"Hall voltage =\",(Vh)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Hall voltage = 7.8e-06\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.24.1,Page number 2-55" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "x1=0.4 #difference between fermi level and conduction band(Ec-Ef)\n", + "T=300 #temp in kelvin\n", + "K=8.62*10**-5 #Boltzman constant in eV\n", + "\n", + "#ne=N*e**(-(Ec-Ef)/(K*T))\n", + "#ne is no of electron in conduction band\n", + "#since concentration of donor electron is doubled\n", + "\n", + "a=2 #ratio of no of electron\n", + "\n", + "#let x2 be the difference between new fermi level and conduction band(Ec-Ef')\n", + "\n", + "x2=-math.log(a)*(K*T)+x1 #arranging equation ne=N*e**(-(Ec-Ef)/(K*T))\n", + "\n", + "print\"Fermi level will be shifted towards conduction band by\",round(x2,4),\"eV\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Fermi level will be shifted towards conduction band by 0.3821 eV\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
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