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{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Statistical Physics"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.2 Page 307"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#initiation of variable\n",
"from math import sqrt\n",
"#The solution is purely theoretical and involves a lot of approximations.\n",
"print\"The value of shift in frequency was found out to be delf=7.14*fo*10^-7*sqrt(T) for a star composing of hydrogen atoms at a temperature T.\";\n",
"T=6000.0; #temperature for sun\n",
"delf=7.14*10**-7*sqrt(T);#change in frequency\n",
"\n",
"#result\n",
"print\"The value of frequency shift for sun(at 6000 deg. temperature) comprsing of hydrogen atoms is\",delf,\" times the frequency of the light.\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The value of shift in frequency was found out to be delf=7.14*fo*10^-7*sqrt(T) for a star composing of hydrogen atoms at a temperature T.\n",
"The value of frequency shift for sun(at 6000 deg. temperature) comprsing of hydrogen atoms is 5.53062021838e-05 times the frequency of the light.\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.3 Page 309"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#initiation of variable\n",
"from math import sqrt,pi, exp, log\n",
"kT=0.0252;E=10.2 # at room temperature, kT=0.0252 standard value and given value of E\n",
"\n",
"#calculation\n",
"n2=2;n1=1; g2=2*(n2**2);g1=2*(n1**2); #values for ground and excited states\n",
"t=(g2/g1)*exp(-E/kT); #fraction of atoms\n",
"\n",
"#result\n",
"print\"The number of hydrogen atoms required is %.1e\" %(1.0/t),\" which weighs %.1e\" %((1/t)*(1.67*10**-27)),\"Kg\"\n",
"\n",
"#partb\n",
"t=0.1/0.9;k=8.65*10**-5 #fracion of atoms in case-2 is given\n",
"T=-E/(log(t/(g2/g1))*k); #temperature\n",
"\n",
"#result\n",
"print\"The value of temperature at which 1/10 atoms are in excited state in K is %.1e\" %round(T,3);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The number of hydrogen atoms required is 1.5e+175 which weighs 2.5e+148 Kg\n",
"The value of temperature at which 1/10 atoms are in excited state in K is 3.3e+04\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.4 Page 311"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#initiation of variable\n",
"from math import log\n",
"#theoritical part a\n",
"print'The energy of interaction with magnetic field is given by uB and the degeneracy of the states are +-1/2 which are identical.\\nThe ratio is therefore pE2/pE1 which gives e^(-2*u*B/k*T)';\n",
"#partb\n",
"uB=5.79*10**-4; #for a typical atom\n",
"t=1.1;k=8.65*10**-5; #ratio and constant k\n",
"\n",
"#calculation\n",
"T=2*uB/(log(t)*k); #temperature\n",
"\n",
"#result\n",
"print\"The value of temperature ar which the given ratio exists in K is\",round(T,3);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The energy of interaction with magnetic field is given by uB and the degeneracy of the states are +-1/2 which are identical.\n",
"The ratio is therefore pE2/pE1 which gives e^(-2*u*B/k*T)\n",
"The value of temperature ar which the given ratio exists in K is 140.46\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.5 Page 313"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#initiation of variable\n",
"from math import pi\n",
"p=0.971; A=6.023*10**23; m=23.0; # various given values and constants\n",
"\n",
"#calculation\n",
"c= (p*A/m)*10**6; # atoms per unit volume\n",
"hc=1240.0; mc2=0.511*10**6; # hc=1240 eV.nm\n",
"E= ((hc**2)/(2*mc2))*(((3/(8*pi))*c)**(2.0/3)); #value of fermi energy\n",
"\n",
"#result\n",
"print\"The fermi energy for sodium is\",round(E*10**-18,4),\"eV\";#multiply by 10^-18 to convert metres^2 term to nm^2"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The fermi energy for sodium is 3.1539 eV\n"
]
}
],
"prompt_number": 12
}
],
"metadata": {}
}
]
}
|
