{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 7: Elecron theory of Solids"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.1, page no-160"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Mobility ofelectrons\n",
"\n",
"import math\n",
"#variable declaration\n",
"rho=1.73*10**-8 # Resistivity of copper\n",
"z=63.5 # atomic weight of copper\n",
"d=8.92*10**3 # density of copper\n",
"avg=6.023*10**26 # Avogadro's number\n",
"e=1.6*10**-19 # charge of an electron\n",
"m=9.11*10**-31 # mass of an electron\n",
"\n",
"#variable declaration\n",
"n=avg*d/z\n",
"sig=1/rho\n",
"tau=sig*m/(n*e**2)\n",
"mu=sig/(n*e)\n",
"\n",
"#Result\n",
"print(\"Mobility of electrons in copper is %.2f *10^-3 m^2/V-s\"%(mu*10**3))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Mobility of electrons in copper is 4.27 *10^-3 m^2/V-s\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.2, page no-161"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Resistivity of copper\n",
"\n",
"import math\n",
"#variable declaration\n",
"r=1.85*10**-10 # radius of the sodium atom\n",
"t=3*10**-14 # mean free time of sodium atom\n",
"m=9.11*10**-31 # mass of electron\n",
"e=1.6*10**-19 # charge of an atom\n",
"n= 2.0 # No of atoms per unit cell\n",
"\n",
"#calculations\n",
"a=r*(4.0/math.sqrt(3.0)) \n",
"a= math.floor(a*10**12)/10**12 \n",
"ne=n/a**3\n",
"ne= math.ceil(ne*10**-26)/10**-26\n",
"rho=m/(ne*t*e**2)\n",
"\n",
"#Result\n",
"print(\"Resistivity of copper is %.3f*10^-8 Ohm-m\"%(rho*10**8))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Resistivity of copper is 4.616*10^-8 Ohm-m\n"
]
}
],
"prompt_number": 23
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.3, page no-161"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Electrical resistivity of sodium\n",
"\n",
"import math\n",
"#variable declaration\n",
"t=3.1*10**14 # mean free time of electron\n",
"m=9.11*10**-31 # mass of an electron\n",
"e=1.6*10**-19 # charge of an electron \n",
"n=25.33*10**27 # no of electrons per unit volume\n",
"\n",
"#calculations\n",
"rho=m/(n*t*e**2)\n",
"\n",
"#Result\n",
"print(\"The electric resistivity of sodium at 0\u00b0C is %.3f*10^-36 Ohm-m\"%(rho*10**36))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The electric resistivity of sodium at 0\u00b0C is 4.532*10^-36 Ohm-m\n"
]
}
],
"prompt_number": 25
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.4, page no-162"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# mobility of the electron\n",
"\n",
"import math\n",
"#variable declaration\n",
"t=3.4*10**-14 # relaxation time of conduction electrons\n",
"m=9.11*10**-31 # mass of electron\n",
"e=1.6*10**-19 # charge of electron\n",
"n=5.8*10**28 # no of force electrons per unit volume\n",
"\n",
"#calculations\n",
"rho=m/(n*t*e**2)\n",
"print(\"\\nThe electric resistivity of material is %.3f*10^-8 Ohm-m\"%(rho*10**8))\n",
"mu=e*t/m\n",
"print(\"\\nThe mobility of the electron in a metal is %.2f*10^-3 m^2/v-s\"%(mu*10**3))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"The electric resistivity of material is 1.805*10^-8 Ohm-m\n",
"\n",
"The mobility of the electron in a metal is 5.97*10^-3 m^2/v-s\n"
]
}
],
"prompt_number": 27
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.5, page no-163"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# drift velocity\n",
"\n",
"import math\n",
"#variable declaration\n",
"rho=1.54*10**-8 # resistivity of silver\n",
"E=100 # electric field along the wire\n",
"n=5.8*10**28 # carrier concentration of electron\n",
"e=1.6*10**-19 # charge on electron\n",
"\n",
"#calculation\n",
"mu=1/(rho*n*e)\n",
"vd=mu*E\n",
"\n",
"#Result\n",
"print(\"\\nMobility of electron in silvetr is %.4f*10^-3 m^2/v-s\\n\\nThe drift velocity of the electron in silver is %.5f m/s \"%(mu*10**3,vd))\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Mobility of electron in silvetr is 6.9973*10^-3 m^2/v-s\n",
"\n",
"The drift velocity of the electron in silver is 0.69973 m/s \n"
]
}
],
"prompt_number": 28
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.6, page no-163"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# mobility ofelectron\n",
"\n",
"import math\n",
"#variable declaration\n",
"d=10.5*10**3 # density of silver\n",
"sig=6.8*10**7 # conductivity of silver\n",
"wt=107.9 # atomic weight of silver\n",
"e=1.609*10**-19 # charge of electron\n",
"avg=6.023*10**26 # avogadro's number\n",
"\n",
"#calculations\n",
"n=avg*d/wt\n",
"mu=sig/(n*e)\n",
"\n",
"#Result\n",
"print(\"The mobility of electron is %.2f *10^-2 m^2.V/s\"%(mu*10**2))\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The mobility of electron is 0.72 *10^-2 m^2.V/s\n"
]
}
],
"prompt_number": 32
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.7, page no-164"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Lorentz number\n",
"\n",
"import math\n",
"#variable declaration\n",
"sig=5.87*10**7 # electrical conductivity of copper\n",
"k=390.0 # thermal conductivity of copper\n",
"T=293.0 # temperature\n",
"\n",
"#calculation\n",
"L=k/(sig*T)\n",
"\n",
"#Result\n",
"print(\"The Lorentz number is %.3f *10^-8 W.Ohm/K^2\"%(L*10**8))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The Lorentz number is 2.268 *10^-8 W.Ohm/K^2\n"
]
}
],
"prompt_number": 33
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.8, page no-164"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Lorentz number\n",
"import math\n",
"\n",
"#variable declaration\n",
"t=1*10**-14 # relaxation time\n",
"T=300 # temperature\n",
"m=9.1*10**-31 # mass of electron\n",
"e=1.6*10**-19 # charge of electron\n",
"n=6*10**28 # electron concentration\n",
"\n",
"#calculations\n",
"sig=(n*t*e**2)/m\n",
"k=1.38*10**-23\n",
"k1=n*math.pi**2*k**2*T*t/(3*m)\n",
"L=k1/(sig*T)\n",
"\n",
"#Result\n",
"print(\"\\nThe electrical conductivity is %.4f * 10^7/ohm-m\"%(sig*10**-7))\n",
"print(\"\\n\\nThermal conductivity is %.2f W/m-k\"%k1)\n",
"print(\"\\n\\nThe Lorentz number is %.4f *10^-8 W.Ohm/k^2\"%(L*10**8))\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"The electrical conductivity is 1.6879 * 10^7/ohm-m\n",
"\n",
"\n",
"Thermal conductivity is 123.93 W/m-k\n",
"\n",
"\n",
"The Lorentz number is 2.4474 *10^-8 W.Ohm/k^2\n"
]
}
],
"prompt_number": 36
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.9, page no-165"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Electrical conductivity\n",
"\n",
"import math\n",
"\n",
"#variable declaration\n",
"d=8900 # Density of copper\n",
"cu=63.5 # Atomic weight of Cu\n",
"t=10**-14 # Relaxation time\n",
"avg=6.022*10**23 # Avogadro's number\n",
"m=9.1*10**-31 # mass of electron\n",
"e=1.6*10**-19 # charge of electron\n",
"\n",
"#Calculations\n",
"n=avg*d*1000/cu\n",
"sig=(n*t*e**2)/m\n",
"print(\"The electrical conductivity is %.3f *10^7 /Ohm-m\"%(sig*10**-7))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The electrical conductivity is 2.374 *10^7 /Ohm-m\n"
]
}
],
"prompt_number": 38
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.10, page no-166"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Drift velocity of electrons\n",
"import math\n",
"\n",
"#variable declaration\n",
"rho=1.6*10**-8 # resistivity of the silver piece\n",
"e=1.603*10**-19 # charge of an electron\n",
"fe=5.5*e # energy of the silver\n",
"avg=6.023*10**23 # avogadro's number\n",
"d=1.05*10**4 # density of silver\n",
"wt=107.9*10**-3 # atomic weight of silver\n",
"m=9.1*10**-31 # mass of electron\n",
"c=3*10**8 # speed of light\n",
"\n",
"#calculations\n",
"sig=1/rho\n",
"n=avg*d/wt\n",
"t=sig*m/(n*e**2)\n",
"lam=c*t\n",
"vd=sig*100/(n*e)\n",
"\n",
"#Result\n",
"print(\"\\nThe conductivity of silver piece is %.2f*10^7 per Ohm-m\\n\\nThe relaxation time is %.2f*10^-14 s\"%(sig*10**-7,t*10**14))\n",
"print(\"\\nThe drift velocity of electrons in the silver piece is %.2f m/s\"%(math.floor(vd*100)/100))\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"The conductivity of silver piece is 6.25*10^7 per Ohm-m\n",
"\n",
"The relaxation time is 3.78*10^-14 s\n",
"\n",
"The drift velocity of electrons in the silver piece is 0.66 m/s\n"
]
}
],
"prompt_number": 51
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.11, page no-167"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# resistivityy of the copper\n",
"\n",
"import math\n",
"#variable declaration\n",
"r1=1.7*10**-8 # resistivity of copper at T1\n",
"t2=300.0 # temperature(T1)\n",
"t1=700.0+273 # temperature(T2)\n",
"\n",
"#calculation\n",
"r2=r1*math.sqrt((t1/t2))\n",
"print(\"The resistivityy of the copper wire is %.4f*10^-8 Ohm-m\"%(r2*10**8))\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The resistivityy of the copper wire is 3.0616*10^-8 Ohm-m\n"
]
}
],
"prompt_number": 52
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.12, page no-168"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Relaxation time, Drift velocity, Fermi velocity, mean free path\n",
"\n",
"import math\n",
"#variable declarations\n",
"rho=1.54*10**-8 # Resistivity \n",
"e=1.6*10**-19 # charge of electron\n",
"ef=5.5*e # Fermi energy\n",
"n=5.8*10**28 # concentration of electrons\n",
"m=9.1*10**-31 # mass of electron \n",
"\n",
"#(i)\n",
"t=m/(rho*n*e**2)\n",
"mu=e*t/m\n",
"print(\"\\n(i)\\nThe relaxation time is %.2f*10^-14 s\\nThe mobility of the electrons is %.4f *10^-3 m^2/V-s\"%(t*10**14,mu*10**3))\n",
"\n",
"#(ii)\n",
"vd=e*t*100/m\n",
"print(\"\\n\\n(ii)\\nthe drift velocity of elctron is %.5f m/s\"%vd)\n",
"\n",
"#(iii)\n",
"vf=math.sqrt(2*ef/m)\n",
"print(\"\\n\\n(iii)\\nFermi velocity is %.2f*10^6 m/s\"%(vf*10**-6))\n",
"\n",
"#(iv)\n",
"lam=vf*t\n",
"print(\"\\n\\n(iv)\\nThe mean free path is %.3f*10^-8 m\"%(lam*10**8))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"(i)\n",
"The relaxation time is 3.98*10^-14 s\n",
"The mobility of the electrons is 6.9973 *10^-3 m^2/V-s\n",
"\n",
"\n",
"(ii)\n",
"the drift velocity of elctron is 0.69973 m/s\n",
"\n",
"\n",
"(iii)\n",
"Fermi velocity is 1.39*10^6 m/s\n",
"\n",
"\n",
"(iv)\n",
"The mean free path is 5.535*10^-8 m\n"
]
}
],
"prompt_number": 55
}
],
"metadata": {}
}
]
}