{
"metadata": {
"name": "",
"signature": "sha256:9dafdb7acb5e988ab3a5ace98a3f2deebed0e1d539e288cbefca9baaaeda9388"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"10: Quantum Mechanics"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 10.1, Page number 196"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"v=10**7; #speed of electron(m/s)\n",
"h=6.626*10**-34; #plancks constant\n",
"m=9.1*10**-31; #mass of electron(kg)\n",
"\n",
"#Calculation \n",
"lamda=h/(m*v); #de Broglie wavelength(m)\n",
"\n",
"#Result\n",
"print \"The de Broglie wavelength is\",round(lamda*10**11,2),\"*10**-11 m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The de Broglie wavelength is 7.28 *10**-11 m\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 10.2, Page number 196"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"h=6.626*10**-34; #plancks constant\n",
"lamda=0.3; #de Broglie wavelength(nm)\n",
"#For electron\n",
"me=9.1*10**-31; #mass of electron(kg)\n",
"#For proton\n",
"mp=1.672*10**-27; #mass of proton(kg)\n",
"\n",
"#Calculation \n",
"p=h/(lamda*10**-9); #uncertainity in determining momentum(kg m/s)\n",
"K1=p**2/(2*me); #kinetic energy of electron(J)\n",
"K2=p**2/(2*mp); #kinetic energy of proton(J)\n",
"\n",
"#Result\n",
"print \"The kinetic energy of electron is\",round(K1*10**18,1),\"*10**-18 J\"\n",
"print \"The kinetic energy of proton is\",round(K2*10**21,2),\"*10**-21 J\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The kinetic energy of electron is 2.7 *10**-18 J\n",
"The kinetic energy of proton is 1.46 *10**-21 J\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 10.3, Page number 196"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"#K=p^2/(lambda^2*2*m) where K is kinetic energy\n",
"h=6.626*10**-34; #plancks constant\n",
"lamda=10**-14; #de Broglie wavelength(m)\n",
"m=9.1*10**-31; #mass of electron(kg)\n",
"e=1.6*10**-19;\n",
"\n",
"#Calculation \n",
"K=(h**2/((lamda**2)*2*m*e))*10**-9; \n",
"\n",
"#Result\n",
"print \"The kinetic energy is\",int(K),\"GeV\"\n",
"print \"It is not possible to confine the electron to a nucleus.\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The kinetic energy is 15 GeV\n",
"It is not possible to confine the electron to a nucleus.\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 10.4, Page number 197"
]
},
{
"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",
"v=6*10**3; #speed of electron(m/s)\n",
"h=6.626*10**-34; #plancks constant\n",
"a=0.00005; \n",
"\n",
"#Calculation \n",
"p=m*v; #uncertainity in momentum(kg m/s)\n",
"deltap=a*p; #uncertainity in p\n",
"deltax=(h/(4*math.pi*deltap))*10**3 #uncertainity in position(mm)\n",
"\n",
"#Result\n",
"print \"The uncertainity in position is\",round(deltax,3),\"mm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The uncertainity in position is 0.193 mm\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 10.5, Page number 197"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"L=3*10**-5; #diameter of the sphere(nm)\n",
"h=6.626*10**-34; #plancks constant\n",
"m=1.67*10**-27; #mass of the particle(kg)\n",
"n=1;\n",
"e=1.6*10**-19;\n",
"\n",
"#Calculation \n",
"E1=((h**2)*(n**2))/(8*m*(L**2)*e)*10**12 #first energy level(MeV)\n",
"E2=E1*2**2; #second energy level(MeV)\n",
"\n",
"#Result\n",
"print \"The first energy level is\",round(E1,3),\"MeV\"\n",
"print \"The second energy level is\",round(E2,4),\"MeV\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The first energy level is 0.228 MeV\n",
"The second energy level is 0.9128 MeV\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 10.6, Page number 197"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"h=6.626*10**-34; #plancks constant\n",
"a=2*10**12; #angular frequency(rad/s)\n",
"e=1.6*10**-19;\n",
"\n",
"#Calculation \n",
"E0=(0.5*(h/(2*math.pi*e))*a)*10**3; #ground state energy(MeV)\n",
"E1=(1.5*(h/(2*math.pi*e))*a)*10**3; #first excited state energy(MeV)\n",
"\n",
"#Result\n",
"print \"The ground state energy is\",round(E0,3),\"MeV\" \n",
"print \"The first excited state energy is\",round(E1,3),\"MeV\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The ground state energy is 0.659 MeV\n",
"The first excited state energy is 1.977 MeV\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 10.7, Page number 197"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"h=6.626*10**-34; #plancks constant\n",
"E=85; #Energy(keV)\n",
"c=3*10**8; #speed of light(m/s)\n",
"e=1.6*10**-19;\n",
"\n",
"#Calculation \n",
"lamda=(h*c)/(E*10**3*e); #de Broglie wavelength(m)\n",
"m=9.1*10**-31; #mass of electron(kg)\n",
"K=((h**2)/((lamda**2)*2*m*e)); #kinetic energy of electron(keV)\n",
"\n",
"#Result\n",
"print \"The kinetic energy of the electron is\",round(K*10**-3,2),\"keV\"\n",
"print \"answer in the book varies due to rounding off errors\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The kinetic energy of the electron is 7.06 keV\n",
"answer in the book varies due to rounding off errors\n"
]
}
],
"prompt_number": 21
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 10.8, Page number 198"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"lamda=0.08; #de Briglie wavelength(nm)\n",
"m=9.1*10**-31; #mass of electron(kg)\n",
"h=6.626*10**-34; #plancks constant\n",
"\n",
"#Calculation \n",
"v=h/(m*lamda*10**-9); #velocity of the electron(m/s)\n",
"\n",
"#Result\n",
"print \"The velocity of the electron is\",round(v/10**6,1),\"*10**6 m/s\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The velocity of the electron is 9.1 *10**6 m/s\n"
]
}
],
"prompt_number": 28
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 10.9, Page number 198"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"h=6.626*10**-34; #plancks constant\n",
"lamda=589*10**-9; #wavelength(m)\n",
"m=9.1*10**-31; #mass of electron(kg)\n",
"e=1.6*10**-19;\n",
"\n",
"#Calculation \n",
"V=((h**2)/((lamda**2)*2*m*e))*10**6; #potential diference(micro V)\n",
"\n",
"#Result\n",
"print \"The potential difference through which an electron should be accelerated is\",round(V,2),\"micro V\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The potential difference through which an electron should be accelerated is 4.35 micro V\n"
]
}
],
"prompt_number": 31
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 10.10, Page number 198"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"deltax=0.92*10**-9; #uncertainity in position(m)\n",
"m=9.1*10**-31; #mass of electron(kg)\n",
"h=6.626*10**-34; #plancks constant\n",
"\n",
"#Calculation \n",
"deltav=h/(4*math.pi*m*deltax); #uncertainity in velocity(m/s)\n",
"\n",
"#Result\n",
"print \"The uncertainity in velocity is\",round(deltav/10**4,1),\"*10**4 m/s\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The uncertainity in velocity is 6.3 *10**4 m/s\n"
]
}
],
"prompt_number": 33
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 10.11, Page number 198"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"h=6.626*10**-34; #plancks constant\n",
"n=3; #for second excited state\n",
"m=1.67*10**-27; #mass of proton(kg)\n",
"E=0.5; #energy(MeV)\n",
"e=1.6*10**-19;\n",
"\n",
"#Calculation \n",
"L=((h*n)/math.sqrt(8*m*E*10**6*e))*10**15; #length of the box(fm)\n",
"\n",
"#Result\n",
"print \"The length of the box for proton in its second excited state is\",round(L,1),\"fm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The length of the box for proton in its second excited state is 60.8 fm\n"
]
}
],
"prompt_number": 35
}
],
"metadata": {}
}
]
}