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{
"metadata": {
"name": "",
"signature": "sha256:ea49c9c54a7abfea63e3838cff940d23d5976ae6af1b86c7e497f10ce35239cd"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"14: Waves and Particles"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 14.1, Page number 17"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"V=150; #potential difference(V)\n",
"e=1.6*10**-19; #charge of electron(c)\n",
"m=9.1*10**-31; #mass of electron(kg)\n",
"h=6.626*10**-34; #planck's constant\n",
"\n",
"#Calculation\n",
"lamda=h/math.sqrt(2*m*e*V); #de broglie wavelength of electron(m)\n",
"\n",
"#Result\n",
"print \"de broglie wavelength of electron is\",round(lamda*10**10,5),\"*10**-10 m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"de broglie wavelength of electron is 1.00256 *10**-10 m\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 14.2, Page number 17"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"E=0.025; #energy of electron(MeV)\n",
"e=1.6*10**-19; #charge of electron(c)\n",
"m=9.1*10**-31; #mass of electron(kg)\n",
"h=6.626*10**-34; #planck's constant\n",
"\n",
"#Calculation\n",
"E=E*10**6*e; #energy of electron(J)\n",
"v=math.sqrt(2*E/m); #velocity of electron(m/s)\n",
"lamda=h/(m*v); #de broglie wavelength(m)\n",
"\n",
"#Result\n",
"print \"de broglie wavelength is\",round(lamda*10**10,5),\"angstrom\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"de broglie wavelength is 0.07766 angstrom\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 14.3, Page number 18"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"E=1; #kinetic energy of electron(MeV)\n",
"e=1.6*10**-19; #charge of electron(c)\n",
"m=9.1*10**-31; #mass of electron(kg)\n",
"h=6.626*10**-34; #planck's constant\n",
"\n",
"#Calculation\n",
"E=E*10**6*e; #energy of electron(J)\n",
"v=math.sqrt(2*E/m); #velocity of electron(m/s)\n",
"lamda=h/(m*v); #de broglie wavelength of electron(m)\n",
"\n",
"#Result\n",
"print \"de broglie wavelength of electron is\",round(lamda*10**10,5),\"angstrom\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"de broglie wavelength of electron is 0.01228 angstrom\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 14.4, Page number 18"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"V=100; #potential difference(V)\n",
"e=1.6*10**-19; #charge of electron(c)\n",
"m=9.1*10**-31; #mass of electron(kg)\n",
"h=6.626*10**-34; #planck's constant\n",
"c=3*10**8; #velocity of light(m/s)\n",
"\n",
"#Calculation\n",
"v=math.sqrt(2*e*V/m); #velocity of electron(m/s)\n",
"u=c**2/v; #phase velocity of electron(m/s)\n",
"lamda=h/(m*v); #de broglie wavelength of electron(m)\n",
"p=m*v; #momentum of electron(kg m/s)\n",
"vbar=1/lamda; #wave number of electron wave(per m)\n",
"\n",
"#Result\n",
"print \"velocity of electron is\",round(v/10**6,5),\"*10**6 m/s\"\n",
"print \"phase velocity of electron is\",round(u/10**10,4),\"*10**10 m/s\"\n",
"print \"de broglie wavelength of electron is\",round(lamda*10**10,3),\"angstrom\"\n",
"print \"momentum of electron is\",round(p*10**24,3),\"*10**-24 kg m/s\"\n",
"print \"wave number of electron wave is\",round(vbar/10**9,3),\"*10**9 per m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"velocity of electron is 5.92999 *10**6 m/s\n",
"phase velocity of electron is 1.5177 *10**10 m/s\n",
"de broglie wavelength of electron is 1.228 angstrom\n",
"momentum of electron is 5.396 *10**-24 kg m/s\n",
"wave number of electron wave is 8.144 *10**9 per m\n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 14.5, Page number 19"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"deltax=10**-14; #radius of nucleus(m)\n",
"m=1.67*10**-27; #mass of proton(kg)\n",
"h=6.626*10**-34; #planck's constant\n",
"e=1.6*10**-19; #charge of electron(c)\n",
"\n",
"#Calculation\n",
"deltap=h/(2*math.pi*deltax); #uncertainity in momentum of proton(kg m/s)\n",
"KE=deltap**2/(2*m); #minimum kinetic energy of proton(J)\n",
"KE=KE/(e*10**6); #minimum kinetic energy of proton(MeV)\n",
"\n",
"#Result\n",
"print \"uncertainity in momentum of proton is\",round(deltap*10**20,4),\"*10**-20 kg m/s\"\n",
"print \"minimum kinetic energy of proton is\",round(KE,3),\"MeV\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"uncertainity in momentum of proton is 1.0546 *10**-20 kg m/s\n",
"minimum kinetic energy of proton is 0.208 MeV\n"
]
}
],
"prompt_number": 19
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 14.6, Page number 20"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"deltax=0.1*10**-10; #uncertainity in position of electron(m)\n",
"h=6.626*10**-34; #planck's constant\n",
"\n",
"#Calculation\n",
"deltap=h/(2*math.pi*deltax); #uncertainity in momentum of electron(kg m/s)\n",
"\n",
"#Result\n",
"print \"uncertainity in momentum of electron is\",round(deltap*10**23,4),\"*10**-23 kg m/s\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"uncertainity in momentum of electron is 1.0546 *10**-23 kg m/s\n"
]
}
],
"prompt_number": 21
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 14.7, Page number 20"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"m=9.1*10**-31; #mass of electron(kg)\n",
"h=6.626*10**-34; #planck's constant\n",
"a=1*10**-10; #width of potential wall(m)\n",
"n1=1; \n",
"n2=2;\n",
"n3=3;\n",
"e=6.24*10**18; #conversion factor from J to eV\n",
"\n",
"#Calculation\n",
"En=(h**2)/(8*m*(a**2)); #energy of electron(J)\n",
"E1=En*n1**2; #energy of 1st excited state(J)\n",
"E1=E1*e; #energy of 1st excited state(eV)\n",
"E2=En*n2**2; #energy of 2nd excited state(J)\n",
"E2=E2*e; #energy of 2nd excited state(eV)\n",
"E3=En*n3**2; #energy of 3rd excited state(J)\n",
"E3=E3*e; #energy of 3rd excited state(eV)\n",
"\n",
"#Result\n",
"print \"first 3 permitted energy levels of electron are\",round(E1,2),\"eV\",round(E2,2),\"eV and\",round(E3,2),\"eV\"\n",
"print \"answers given in the book vary due to rounding off errors\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"first 3 permitted energy levels of electron are 37.63 eV 150.53 eV and 338.69 eV\n",
"answers given in the book vary due to rounding off errors\n"
]
}
],
"prompt_number": 30
}
],
"metadata": {}
}
]
}
|
