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diff --git a/Engineering_Physics/chapter8.ipynb b/Engineering_Physics/chapter8.ipynb new file mode 100755 index 00000000..106ed7f9 --- /dev/null +++ b/Engineering_Physics/chapter8.ipynb @@ -0,0 +1,620 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:2b8beebd2e19262e31711f6c9b2785f35ddc221da552f5b3fe2ed984a495062e"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter8:X-RAY"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8.1:pg-240"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#to calculate value of planck's constant\n",
+ "e=1.6*10**-19 #in C\n",
+ "V=100*10**3 #voltage in KV\n",
+ "c=3*10**8 #light speed in m/s\n",
+ "lamdamin=12.35*10**-12 #wavelength in m\n",
+ "h=e*V*lamdamin/c\n",
+ "print \"the value of plancks constant is h=\",\"{:.2e}\".format(h),\"J-s\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "the value of plancks constant is h= 6.59e-34 J-s\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8.2:pg-240"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#to calculate maximum frequency\n",
+ "h=6.6*10**-34 #planck's constant in J-s\n",
+ "c=3.0*10**8 #light speed in m/s\n",
+ "Ve=50000 #accelerating potential in V\n",
+ "lamdamin=h*c/Ve #wavelength in m\n",
+ "numax=c/lamdamin\n",
+ "print \"maximum frequency present in the radiation from an X-ray tube is numax=\",\"{:.2e}\".format(numax),\"Hz\"\n",
+ "#answer is given in thec book is incorrect =1.2*10**19 Hz\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "maximum frequency present in the radiation from an X-ray tube is numax= 7.58e+37 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8.3:pg-240"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#to calculate number of electrons \n",
+ "I=2*10**-3 #current in mA\n",
+ "e=1.6*10**-19 \n",
+ "n=I/e\n",
+ "print \"number of electrons striking the target per second is n=\",n,\"unitless\"\n",
+ "#to calculate speed\n",
+ "m=9.1*10**-31 #mass of electron in kg\n",
+ "V=12.4*10**3 #potential difference in V\n",
+ "v=math.sqrt(2*V*e/m)\n",
+ "print \"the speed with which electrons strike the target is v=\",\"{:.1e}\".format(v),\"m/s\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "number of electrons striking the target per second is n= 1.25e+16 unitless\n",
+ "the speed with which electrons strike the target is v= 6.6e+07 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8.4:pg-240"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#to calculate wavelength\n",
+ "n=2 #second order for longest wavelength\n",
+ "d=2.82*10**-10 # spacing in angstrom\n",
+ "sintheta=1 \n",
+ "lamdamax=2*d*sintheta/n\n",
+ "print \"the longest wavelength that can be analysed by a rock salt crystal is lamdamax=\",lamdamax,\"m\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "the longest wavelength that can be analysed by a rock salt crystal is lamdamax= 2.82e-10 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8.5:pg-241"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#to calculate spacing of the crystal\n",
+ "h=6.62*10**-34 #planck's constant in J-s\n",
+ "m=9.1*10**-31 #mass of electron in kg\n",
+ "V=344 #voltage in V\n",
+ "e=1.6*10**-19\n",
+ "lamda=h/math.sqrt(2*m*e*V) #wavelength in m\n",
+ "#according to Bragg's law\n",
+ "n=1\n",
+ "#formula is 2*d*sintheta=n*lamda\n",
+ "d=n*lamda/(2*math.sin(math.pi/6))\n",
+ "print \"the spacing of the crystal is d=\",round(d/1e-10,2),\"angstrom\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "the spacing of the crystal is d= 0.66 angstrom\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8.6:pg-241"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#to calculate wavelength of Kalpha line for an atom\n",
+ "R=1.1*10**5\n",
+ "z=92\n",
+ "#Ka line is emitted when electron jumps from l shell(n2=2) to k shell(n1=1)\n",
+ "#formula is 1/alphaa=R*(z-b)*((1/n1**2)-(1/n2)**2)\n",
+ "alphaa=4/(3*R*(z-1)**2)\n",
+ "print \"wavelength of Kalpha line for an atom is alphaa=\",\"{:.3e}\".format(alphaa),\"cm\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "wavelength of Kalpha line for an atom is alphaa= 1.464e-09 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8.7:pg-241"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#to calculate thickness\n",
+ "#mass absorption coefficient mum of an absorber is related with linear absorption coefficient mu and density of the material rho is given by\n",
+ "#mu=rho*mum=2.7*0.6=1.62 cm**-1\n",
+ "mu=1.62\n",
+ "#if initial intensity Io of the X-ray beam is reduced to I in traversing a distance x in absorber I=Io*e**-mu*x\n",
+ "#where I/Io=20\n",
+ "#put above values in the below equation , we get\n",
+ "x=(2.3026*(math.log(20)/math.log(10)))/1.62\n",
+ "print \"thickness is x=\",round(x,2),\"cm\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "thickness is x= 1.85 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8.8:pg-242"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#to calculate atomic number of the element\n",
+ "#equation for balmer series in hydrogen spectrum is 1/lamda=R*((1/2**2)-(1/n**2))\n",
+ "#for series limit n=infinity ,R=4/lamdainfinity i.e. R=4/364.6nm\n",
+ "#X-ray wavelength of K series is 1/lamda=R*(z-1)**2*((1/1**2)-(1/n**2))\n",
+ "lamda=0.1*10**-9\n",
+ "R=4/(364.6*10**-9)\n",
+ "#for n=infinity ,minimum wavelength of k series is given by\n",
+ "z=math.sqrt(1/(lamda*R))+1\n",
+ "print \"atomic number is z=\",int(z),\"unitless\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "atomic number is z= 31 unitless\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8.9:pg-242"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#to calculate wavelength\n",
+ "d=1.87*10**-10 #spacing in angstrom\n",
+ "n=2 \n",
+ "#formula is lamda=2*d*sintheta/n\n",
+ "lamda=2*d*math.sin(math.pi/6)/n\n",
+ "print \"the wavelength of X-rays is lamda=\",round(lamda/1e-10,3),\"angstrom\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "the wavelength of X-rays is lamda= 0.935 angstrom\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8.10:pg-242"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#to calculate wavelength of second X-ray beam\n",
+ "#from bragg's law\n",
+ "#lamda=(d*math.sin(math.pi/3))/n eq(1)\n",
+ "#it is given that,theta=60,n=3,lamda=1.97 angstrom\n",
+ "#from eq(1) we get,2*d*sin60degree=3*0.97 eq(2)\n",
+ "#let lamda' be the second X-ray beam \n",
+ "#we get 2*d'*sin theta'=n'*lamda' eq(3)\n",
+ "#from eq(2) and eq(3),we get\n",
+ "lamda1=math.sin(math.pi/6)*3*0.97/math.sin(math.pi/3) #where lamda1=lamda'\n",
+ "print \"wavelength of X-ray is lamda1=\",round(lamda1,2),\"angstrom\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "wavelength of X-ray is lamda1= 1.68 angstrom\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8.11:pg-243"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#to calculate wavelength\n",
+ "d=2.82*10**-10 #spacing in m\n",
+ "n=1 \n",
+ "lamda=2*d*math.sin(10*math.pi/180)/n\n",
+ "print \"wavelength of X-ray is lamda=\",round(lamda/1e-10,3),\"angstrom\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "wavelength of X-ray is lamda= 0.979 angstrom\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8.12:pg-243"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#deduce possible spacing of the set of planes\n",
+ "#for first order , 2*d*sintheta1=1*lamda...eq(1)\n",
+ "#for second order ,2*d*sintheta2=2*lamda..eq(2)\n",
+ "#for third order, 2*d*sintheta3=3*lamda......eq(3)\n",
+ "#for fourth order, 2*d*sintheta4=4*lamda..............eq(4)\n",
+ "#divide eq(2) by eq(1),we get sintheta2=2*sintheta1\n",
+ "#similarly,sintheta3=3*sintheta1,sintheta4=4*sintheta1\n",
+ "lamda=1.32*10**-10\n",
+ "sintheta1=0.1650\n",
+ "d1=lamda/(2*sintheta1)#for first order n=1,d1=d/n\n",
+ "d2=lamda/(2*2*sintheta1) #for second order n=2,d2=d/n\n",
+ "d3=lamda/(2*3*sintheta1) #for third order n=3,d3=d/n\n",
+ "d4=lamda/(2*4*sintheta1) #for fourth order n=4,d4=d/n\n",
+ "print \"d1=\",d1,\"m\"\n",
+ "print \"d2=\",d2,\"m\"\n",
+ "print \"d3=\",round(d3,2),\"m\"\n",
+ "print \"d4=\",d4,\"m\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "d1= 4e-10 m\n",
+ "d2= 2e-10 m\n",
+ "d3= 0.0 m\n",
+ "d4= 1e-10 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8.13:pg-248"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#to calculate compton shift and wavelength\n",
+ "h=6.63*10**-34 #planck's constant in J-s\n",
+ "m0=9.11*10**-31 #mass of electron\n",
+ "c=3*10**8 #light speed in m/s\n",
+ "dellamda=h*(1-(1/math.sqrt(2)))/(m0*c)\n",
+ "lamda0=2*10**-10\n",
+ "lamda=dellamda+lamda0\n",
+ "print \"compton shift is dellamda=\",round(dellamda/1e-10,4),\"angstrom\"\n",
+ "print \"wavelength of the scattered X-rays is lamda=\",round(lamda/1e-10,4),\"angstrom\"\n",
+ "#to calculate fraction of energy lost by the photon in the collision\n",
+ "#energy lost =E0-E/E0=(hc/lamda0)-(hc/lamda)/(ha/lamda0)\n",
+ "#we get,\n",
+ "energylost=dellamda/lamda\n",
+ "print \"energylost =\",round(energylost,5),\"unitless\" \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "compton shift is dellamda= 0.0071 angstrom\n",
+ "wavelength of the scattered X-rays is lamda= 2.0071 angstrom\n",
+ "energylost = 0.00354 unitless\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8.14:pg-249"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#to calculate wavelength and energy\n",
+ "#formula is lamda'-lamda=h*(1-cos phi)/(m0*c),where phi=90 degree, lamda'=2lamda ---------------eq(1)\n",
+ "#dellamda=2lamda-lamda=lamda ----------------------------eq(2)\n",
+ "h=6.62*10**-34 #planck's constant\n",
+ "c=3*10**8 #light speed in m.s\n",
+ "m0=9*10**-31 #mass of electron in kg\n",
+ "#from eq(1) and eq(2) ,we get\n",
+ "lamda=h/(m0*c)\n",
+ "print \"wavelength is lamda=\",round(lamda/1e-10,4),\"angstrom\"\n",
+ "E=h*c/lamda\n",
+ "print \"energy of the incident photon is E=\",E,\"J\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "wavelength is lamda= 0.0245 angstrom\n",
+ "energy of the incident photon is E= 8.1e-14 J\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8.15:pg-249"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#to calculate wavelength of radiation and direction of emission\n",
+ "h=6.6*10**-34 #planck's constant in J-s\n",
+ "c=3*10**8 #speed of light in m/s\n",
+ "energy=510*10**3 #energy of photon in eV\n",
+ "lamda=h*c/(energy*1.6*10**-19)\n",
+ "mo=9.1*10**-31 #mass of electron in Kg\n",
+ "lamda1=lamda+h*(1-math.cos(math.pi/2))/(mo*c)\n",
+ "print \"wavelength of radiation is lamda1=\",\"{:.2e}\".format(lamda1),\"m\"\n",
+ "theta=math.degrees(math.atan(lamda*math.sin(math.pi/2)/(lamda1-lamda*math.cos(math.pi/2))))\n",
+ "print\"direction of emission of electron is theta=\",round(theta,2),\"degree\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "wavelength of radiation is lamda1= 4.84e-12 m\n",
+ "direction of emission of electron is theta= 26.61 degree\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8.16:pg-249"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#to calculate wavelength of two X-rays\n",
+ "h=6.6*10**-34 #planck's constant in J-s\n",
+ "c=3.0*10.0**8 #light speed in m/s\n",
+ "mo=9.1*10**-31 #mass of electron in kg\n",
+ "lamda=10.0*10**-12 #wavelength in pm\n",
+ "lamda1=lamda+((h/(mo*c))*(1-(1/math.sqrt(2))))\n",
+ "print \"wavelength of two X-rays is lamda1=\",round(lamda1*(1e12),1),\"picometer\"\n",
+ "#to calculate maximum wavelength\n",
+ "lamda2=lamda+((2*h)/(mo*c))\n",
+ "print \"maximum wavelength present in the scattered X-rays is lamda2=\",round(lamda2*(1e12),2),\"picometer\"\n",
+ "#to calculate maximum kinetic energy \n",
+ "Kmax=(h*c)*((1/lamda)-(1/lamda2))/(1.6*10**-19)\n",
+ "print \"maximum kinetic energy of the recoil electrons is Kmax=\",round(Kmax/1000.0,1),\"KeV\"\n",
+ "\n",
+ "# the answer is slightly different due to approximation\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "wavelength of two X-rays is lamda1= 10.7 picometer\n",
+ "maximum wavelength present in the scattered X-rays is lamda2= 14.84 picometer\n",
+ "maximum kinetic energy of the recoil electrons is Kmax= 40.3 KeV\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |