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diff --git a/Engineering_Physics_by_A._Marikani/Chapter_4.ipynb b/Engineering_Physics_by_A._Marikani/Chapter_4.ipynb new file mode 100755 index 00000000..d2b8123c --- /dev/null +++ b/Engineering_Physics_by_A._Marikani/Chapter_4.ipynb @@ -0,0 +1,765 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:e581747b76e15afc0096179446c0fbd68c3566f21f4931be3d8fc722fc1225b8" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Quantum Physics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.1, Page number 133 " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "h=6.63*10**-34; #plancks constant in Js\n", + "m0=9.1*10**-31; #mass of the electron in kg\n", + "c=3*10**8; #velocity of light in m/s\n", + "phi=135; #angle of scattering in degrees\n", + "phi=phi*0.0174532925 #converting degrees to radians \n", + "\n", + "#Calculation\n", + "delta_lamda=(h*(1-math.cos(phi)))/(m0*c);\n", + "\n", + "#Result\n", + "print(\"change in wavelength in metres is\",delta_lamda);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('change in wavelength in metres is', 4.1458307496867315e-12)\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.2, Page number 134 " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "h=6.63*10**-34; #plancks constant in Js\n", + "m0=9.1*10**-31; #mass of the electron in kg\n", + "c=3*10**8; #velocity of light in m/s\n", + "lamda=2; #wavelength in angstrom\n", + "lamdaA=lamda*10**-10; #converting lamda from Angstrom to m\n", + "phi=90; #angle of scattering in degrees\n", + "phi=phi*0.0174532925 #converting degrees to radians \n", + "\n", + "#Calculation\n", + "delta_lamda=(h*(1-math.cos(phi)))/(m0*c);\n", + "delta_lamda=delta_lamda*10**10; #converting delta_lamda from m to Angstrom\n", + "delta_lamda=math.ceil(delta_lamda*10**5)/10**5; #rounding off to 5 decimals\n", + "lamda_dash=delta_lamda+lamda;\n", + "lamdaA_dash=lamda_dash*10**-10; #converting lamda_dash from Angstrom to m\n", + "#energy E=h*new-h*new_dash\n", + "E=h*c*((1/lamdaA)-(1/lamdaA_dash));\n", + "EeV=E/(1.602176565*10**-19); #converting J to eV\n", + "EeV=math.ceil(EeV*10**3)/10**3; #rounding off to 3 decimals\n", + "new=c/lamda;\n", + "new_dash=c/lamda_dash;\n", + "theta=math.atan((h*new*math.sin(phi))/((h*new)-(h*new_dash*math.cos(phi))));\n", + "theta=theta*57.2957795; #converting radians to degrees\n", + "\n", + "#Result\n", + "print(\"change in compton shift in Angstrom is\",delta_lamda);\n", + "print(\"wavelength of scattered photons in Angstrom is\",lamda_dash);\n", + "print(\"energy of recoiling electron in J is\",E);\n", + "print(\"energy of recoiling electron in eV is\",EeV);\n", + "print(\"angle at which recoiling electron appears in degrees is\",int(theta));\n", + "\n", + "#answers given in the book are wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('change in compton shift in Angstrom is', 0.02429)\n", + "('wavelength of scattered photons in Angstrom is', 2.02429)\n", + "('energy of recoiling electron in J is', 1.1933272900621974e-17)\n", + "('energy of recoiling electron in eV is', 74.482)\n", + "('angle at which recoiling electron appears in degrees is', 45)\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.3, Page number 135" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "h=6.626*10**-34; #plancks constant in Js\n", + "m0=9.1*10**-31; #mass of the electron in kg\n", + "c=3*10**8; #velocity of light in m/s\n", + "phi=60; #angle of scattering in degrees\n", + "phi=phi*0.0174532925; #converting degrees to radians\n", + "E=10**6; #energy of photon in eV\n", + "E=E*1.6*10**-19; #converting eV into J\n", + "\n", + "#Calculation\n", + "delta_lamda=(h*(1-math.cos(phi)))/(m0*c);\n", + "delta_lamda=delta_lamda*10**10; #converting metre to angstrom\n", + "delta_lamda=math.ceil(delta_lamda*10**4)/10**4; #rounding off to 4 decimals\n", + "lamda=(h*c)/E;\n", + "lamdaA=lamda*10**10; #converting metre to angstrom\n", + "lamda_dash=delta_lamda+lamdaA;\n", + "lamda_dash=math.ceil(lamda_dash*10**3)/10**3; #rounding off to 3 decimals\n", + "\n", + "#Result\n", + "print(\"compton shift in angstrom is\",delta_lamda);\n", + "print(\"energy of incident photon in m\",lamda);\n", + "print(\"wavelength of scattered photons in angstrom is\",lamda_dash);\n", + "\n", + "#answer for wavelength of scattered photon given in the book is wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('compton shift in angstrom is', 0.0122)\n", + "('energy of incident photon in m', 1.242375e-12)\n", + "('wavelength of scattered photons in angstrom is', 0.025)\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.4, Page number 135" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "h=6.626*10**-34; #plancks constant in Js\n", + "c=3*10**8; #velocity of light in m/s\n", + "lamda=5893; #wavelength in angstrom\n", + "P=60; #output power in Watt\n", + "\n", + "#Calculation\n", + "lamda=lamda*10**-10; #wavelength in metre\n", + "E=(h*c)/lamda;\n", + "EeV=E/(1.602176565*10**-19); #converting J to eV\n", + "EeV=math.ceil(EeV*10**4)/10**4; #rounding off to 4 decimals\n", + "N=P/E;\n", + "\n", + "#Result\n", + "print(\"energy of photon in J is\",E);\n", + "print(\"energy of photon in eV is\",EeV);\n", + "print(\"number of photons emitted per se cond is\",N);\n", + "\n", + "#answer for energy in eV given in the book is wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('energy of photon in J is', 3.373154590191753e-19)\n", + "('energy of photon in eV is', 2.1054)\n", + "('number of photons emitted per se cond is', 1.7787503773015396e+20)\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.5, Page number 136" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "h=6.626*10**-34; #plancks constant in Js\n", + "c=3*10**8; #velocity of light in m/s\n", + "lamda=10; #wavelength in angstrom\n", + "\n", + "#Calculation\n", + "lamda=lamda*10**-10; #wavelength in metre\n", + "E=(h*c)/lamda;\n", + "EeV=E/(1.602176565*10**-19); #converting J to eV\n", + "EeV=EeV*10**-3; #converting eV to keV\n", + "EeV=math.ceil(EeV*10**3)/10**3; #rounding off to 3 decimals\n", + "P=h/lamda;\n", + "M=h/(lamda*c);\n", + "\n", + "#Result\n", + "print(\"energy of photon in J is\",E);\n", + "print(\"energy of photon in keV is\",EeV);\n", + "print(\"momentum in kg m/sec is\",P);\n", + "print(\"mass of photon in kg is\",M);\n", + "\n", + "#answer for energy of photon in keV given in the book is wrong by 1 decimal" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('energy of photon in J is', 1.9878e-16)\n", + "('energy of photon in keV is', 1.241)\n", + "('momentum in kg m/sec is', 6.626e-25)\n", + "('mass of photon in kg is', 2.2086666666666664e-33)\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.6, Page number 136" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "h=6.626*10**-34; #plancks constant in Js\n", + "m=9.1*10**-31; #mass of the electron in kg\n", + "e=1.602*10**-19;\n", + "V=1.25; #potential difference in kV\n", + "\n", + "#Calculation\n", + "V=V*10**3; #converting kV to V\n", + "lamda=h/math.sqrt(2*m*e*V);\n", + "lamda=lamda*10**10; #converting metre to angstrom\n", + "lamda=math.ceil(lamda*10**4)/10**4; #rounding off to 4 decimals\n", + "\n", + "#Result\n", + "print(\"de Broglie wavelength in angstrom is\",lamda);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('de Broglie wavelength in angstrom is', 0.3471)\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.7, Page number 136" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "E=45; #energy of electron in eV\n", + "E=E*1.6*10**-19; #energy in J\n", + "h=6.626*10**-34; #plancks constant in Js\n", + "m=9.1*10**-31; #mass of the electron in kg\n", + "\n", + "#Calculation\n", + "lamda=h/math.sqrt(2*m*E);\n", + "lamda=lamda*10**10; #converting metres to angstrom\n", + "lamda=math.ceil(lamda*10**4)/10**4; #rounding off to 4 decimals\n", + "\n", + "#Result\n", + "print(\"de Broglie wavelength in angstrom is\",lamda);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('de Broglie wavelength in angstrom is', 1.8305)\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.8, Page number 137" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "v=10**7; #velocity of electron in m/sec\n", + "h=6.626*10**-34; #plancks constant in Js\n", + "m=9.1*10**-31; #mass of the electron in kg\n", + "\n", + "#Calculation\n", + "lamda=h/(m*v);\n", + "lamda=lamda*10**10; #converting metres to angstrom\n", + "lamda=math.ceil(lamda*10**4)/10**4; #rounding off to 4 decimals\n", + "\n", + "#Result\n", + "print(\"de Broglie wavelength in angstrom is\",lamda);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('de Broglie wavelength in angstrom is', 0.7282)\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.9, Page number 137" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "V=1000; #potential difference in V\n", + "h=6.626*10**-34; #plancks constant in Js\n", + "m=1.67*10**-27; #mass of proton in kg\n", + "e=1.6*10**-19; #charge of electron in J\n", + "\n", + "#Calculation\n", + "lamda=h/math.sqrt(2*m*e*V);\n", + "\n", + "#Result\n", + "print(\"de Broglie wavelength of alpha particle in metre is\",lamda);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('de Broglie wavelength of alpha particle in metre is', 9.063964727801313e-13)\n" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.10, Page number 138" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "L=25; #width of potential in armstrong\n", + "delta_x=0.05; #interval in armstrong\n", + "n=1; #particle is in its least energy\n", + "x=L/2; #particle is at the centre\n", + "pi=180; #angle in degrees\n", + "\n", + "#Calculation\n", + "pi=pi*0.0174532925; #angle in radians\n", + "L=L*10**-10; #width in m\n", + "delta_x=delta_x*10**-10; #interval in m\n", + "#probability P = integration of (A**2)*(math.sin(n*pi*x/L))**2*delta_x\n", + "#but A=math.sqrt(2/L)\n", + "#since the particle is in a small interval integration need not be applied\n", + "#therefore P=2*(L**(-1))*(math.sin(n*pi*x/L))**2*delta_x\n", + "P=2*(L**(-1))*((math.sin(n*pi*x/L))**2)*delta_x;\n", + "P=math.ceil(P*10**3)/10**3; #rounding off to 3 decimals\n", + "\n", + "#Result\n", + "print(\"probability of finding the particle is\",P);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('probability of finding the particle is', 0.004)\n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.11, Page number 138" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "n=1;\n", + "h=6.626*10**-34; #plancks constant in Js\n", + "m=9.1*10**-31; #mass of the electron in kg\n", + "L=1; #width of potential well in angstrom\n", + "\n", + "#Calculation\n", + "L=L*10**-10; #converting angstrom into metre\n", + "E=((n**2)*h**2)/(8*m*L**2);\n", + "EeV=E/(1.6*10**-19); #converting J to eV\n", + "EeV=math.ceil(EeV*10**3)/10**3; #rounding off to 3 decimals\n", + "\n", + "#Result\n", + "print(\"lowest energy of electron in J is\",E);\n", + "print(\"lowest energy of electron in eV is\",EeV);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('lowest energy of electron in J is', 6.030752197802197e-18)\n", + "('lowest energy of electron in eV is', 37.693)\n" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.12, Page number 139" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "n=1;\n", + "h=6.626*10**-34; #plancks constant in Js\n", + "m=9.1*10**-31; #mass of the electron in kg\n", + "L=1; #width of potential well in angstrom\n", + "\n", + "#Calculation\n", + "L=L*10**-10; #converting angstrom into metre\n", + "E=(2*(n**2)*h**2)/(8*m*L**2);\n", + "E=E/(1.6*10**-19); #converting J to eV\n", + "E=math.ceil(E*10**3)/10**3; #rounding off to 3 decimals\n", + "\n", + "#Result\n", + "print(\"lowest energy of system in eV is\",E);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('lowest energy of system in eV is', 75.385)\n" + ] + } + ], + "prompt_number": 29 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.13, Page number 139" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "h=6.626*10**-34; #plancks constant in Js\n", + "m=9.1*10**-31; #mass of the electron in kg\n", + "L=1; #width of potential well in angstrom\n", + "\n", + "#Calculation\n", + "L=L*10**-10; #converting angstrom into metre\n", + "#according to pauli's exclusion principle, 1st electron occupies n1=1 and second electron occupies n2=2\n", + "n1=1;\n", + "n2=2;\n", + "E=((2*(n1**2)*h**2)/(8*m*L**2))+(((n2**2)*h**2)/(8*m*L**2));\n", + "E=E/(1.6*10**-19); #converting J to eV\n", + "E=math.ceil(E*10**3)/10**3; #rounding off to 3 decimals\n", + "\n", + "#Result\n", + "print(\"lowest energy of system in eV is\",E);\n", + "print(\"quantum numbers are\");\n", + "print(\"n=1,l=0,mL=0,mS=+1/2\");\n", + "print(\"n=1,l=0,mL=0,mS=-1/2\");\n", + "print(\"n=2,l=0,mL=0,mS=+1/2\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('lowest energy of system in eV is', 226.154)\n", + "quantum numbers are\n", + "n=1,l=0,mL=0,mS=+1/2\n", + "n=1,l=0,mL=0,mS=-1/2\n", + "n=2,l=0,mL=0,mS=+1/2\n" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.14, Page number 140" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "n=1;\n", + "h=6.626*10**-34; #plancks constant in Js\n", + "L=100; #width of potential well in angstrom\n", + "\n", + "#Calculation\n", + "L=L*10**-10; #converting angstrom into metre\n", + "E=0.025; #lowest energy in eV\n", + "E=E*(1.6*10**-19); #converting eV to J\n", + "m=((n**2)*h**2)/(8*E*L**2);\n", + "\n", + "#Result\n", + "print(\"mass of the particle in kg is\",m);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('mass of the particle in kg is', 1.3719961249999998e-31)\n" + ] + } + ], + "prompt_number": 31 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.15, Page number 141" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "k=1.38*10**-23;\n", + "T=6000; #temperature in K\n", + "h=6.626*10**-34; #plancks constant in Js\n", + "c=3*10**8; #velocity of light in m/s\n", + "lamda1=450; #wavelength in nm\n", + "lamda2=460; #wavelength in nm\n", + "\n", + "#Calculation\n", + "lamda1=lamda1*10**-9; #converting nm to metre\n", + "lamda2=lamda2*10**-9; #converting nm to metre\n", + "new1=c/lamda1;\n", + "new2=c/lamda2;\n", + "new=(new1+new2)/2;\n", + "A=math.exp((h*new)/(k*T));\n", + "rho_v=(8*math.pi*h*new**3)/(A*c**3);\n", + "\n", + "#Result\n", + "print(\"energy density of the black body in J/m^3 is\",rho_v);\n", + "\n", + "#answer given in the book is wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('energy density of the black body in J/m^3 is', 9.033622836188887e-16)\n" + ] + } + ], + "prompt_number": 32 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
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