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{
"metadata": {
"name": "",
"signature": "sha256:1d13a558dd2cc62e2c7ada350fc7a07d9283efcbc790578d0711fd6c96f50df0"
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"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 10: Statistical Physics"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.1, page no. 340"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\n",
"\n",
"#Variable declaration\n",
"\n",
"n1 = 1 #Ground state\n",
"n2 = 2 #First excited state\n",
"n3 = 3 #second excited state\n",
"T = 300 #room temperature(K)\n",
"kb = 8.617 * 10 **-5 #Boltzmann constant(eV/K)\n",
"\n",
"#Calculation\n",
"\n",
"E1 = -13.6 / n1 ** 2\n",
"g1 = 2 * n1 ** 2\n",
"E2 = -13.6 / n2 ** 2\n",
"g2 = 2 * n2 ** 2\n",
"E3 = -13.6 / n3 ** 2\n",
"g3 = 2 * n3 ** 2\n",
"N3 = g3 * math.exp(-E3/(kb*T))\n",
"N2 = g2 * math.exp(-E2/(kb*T))\n",
"N1 = g1 * math.exp(-E1/(kb*T))\n",
"ratio1 = N2 / N1\n",
"ratio2 = N3 / N1\n",
"\n",
"#results\n",
"\n",
"print \"(a) We can see that n2/n1=\",round(ratio1),\"and n3/n1=\",round(ratio2),\"essentially all atoms are in ground state.\"\n",
"\n",
"\n",
"#Variable Declaration\n",
"\n",
"T = 20000 #Temperature(K)\n",
"\n",
"#Calculation\n",
"\n",
"N3 = g3 * math.exp(-E3/(kb*T))\n",
"N2 = g2 * math.exp(-E2/(kb*T))\n",
"N1 = g1 * math.exp(-E1/(kb*T))\n",
"ratio1 = N2 / N1\n",
"ratio2 = N3 / N1\n",
"\n",
"#result\n",
"\n",
"print \"(b) n2/n1=\",round(ratio1,5),\"and n3/n1=\",round(ratio2,5)\n",
"\n",
"\n",
"ratio3 = N3 / N2\n",
"\n",
"print \"(c) S(3->2)/S(2->1)=\",round(ratio3,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) We can see that n2/n1= 0.0 and n3/n1= 0.0 essentially all atoms are in ground state.\n",
"(b) n2/n1= 0.01076 and n3/n1= 0.00809\n",
"(c) S(3->2)/S(2->1)= 0.75\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.2, page no. 345"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\n",
"\n",
"#Variable Declaration\n",
"\n",
"m = 3.34 * 10 ** -27 #mass of hydrogen(kg)\n",
"kbT = 3.77 * 10 ** -21 #kb * T (eV)\n",
"N = 6.02 * 10 ** 23 #avogadro's number\n",
"V = 22.4 * 10 ** -3 #Volume of H2 gas (m^3)\n",
"h = 1.055 * 10 ** -34 #Planck's constant (J.s)\n",
"\n",
"#Calculation\n",
"\n",
"r = (N/V)* h ** 3 / (8 * (m * kbT)**1.5)\n",
"\n",
"#result\n",
"\n",
"print \"(a) (N/V)h^3/(8*(mkbT)^3/2)=\",round(r/10**-8,2),\"X10^-8 is much less than 1, we conclude that even hydrogen is described by Maxwell-Boltzmann statistics.\"\n",
"\n",
"\n",
"\n",
"#Variable declaration\n",
"\n",
"d = 10.5 #density of silver (g/cm^3)\n",
"mw = 107.9 #Molar weight of silver (g/mol)\n",
"me = 9.109*10**-31 #mass of electron(kg)\n",
"kbT = 4.14 * 10 ** -21 #kb*T (J)\n",
"\n",
"#Calculation\n",
"\n",
"Ns = (d/mw)* N * 10 ** 6\n",
"r = (Ns)* h ** 3 / (8 * (me * kbT)**1.5)\n",
"\n",
"#result\n",
"\n",
"print \"(b) (N/V)h^3/(8*(mkbT)^3/2)=\",round(r/8,2),\"is greater than 1, we conclude that the Maxwell-Boltzmann statistics does not hold for electrons of silver.\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) (N/V)h^3/(8*(mkbT)^3/2)= 8.83 X10^-8 is much less than 1, we conclude that even hydrogen is described by Maxwell-Boltzmann statistics.\n",
"(b) (N/V)h^3/(8*(mkbT)^3/2)= 4.64 is greater than 1, we conclude that the Maxwell-Boltzmann statistics does not hold for electrons of silver.\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.3, page no. 352"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"\n",
"import math\n",
"\n",
"#Variable Declaration\n",
"\n",
"kB = 8.62 * 10 ** -5 #Boltzmann constant(eV/K)\n",
"T1 = 3000 #Cavity walls temperature(K)\n",
"T2 = 3.00 #Cavity walls temperature(K)\n",
"hc = 1.24 * 10 ** -4 #product of planck's constant and speed of light (eV.cm)\n",
"integration = 2.40 #value of integral(z^2/e^z-1,0,+inf)\n",
"\n",
"#Calculation\n",
"\n",
"NbyV_at_3000 = 8* math.pi * (kB * T1/hc)**3 * integration\n",
"NbyV_at_3 = 8* math.pi * (kB * T2/hc)**3 * integration\n",
"\n",
"#result\n",
"\n",
"print \"N/V at 3000K is\",round(NbyV_at_3000/10**11,2),\"X 10^11 photons/cm^3. Likewise N/V at 3.00 K is\",round(NbyV_at_3/10**2,2),\"X 10^2 photons/cm^3\"\n",
"print \"Therefore the photon density decreases by a factor of\",round(NbyV_at_3000/NbyV_at_3/10**9),\" X 10^9 when the temperature drops from 3000K to 3.00K\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"N/V at 3000K is 5.47 X 10^11 photons/cm^3. Likewise N/V at 3.00 K is 5.47 X 10^2 photons/cm^3\n",
"Therefore the photon density decreases by a factor of 1.0 X 10^9 when the temperature drops from 3000K to 3.00K\n"
]
}
],
"prompt_number": 7
}
],
"metadata": {}
}
]
}
|
