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{
"metadata": {
"name": "",
"signature": "sha256:a0be5f6d37f6b1696997f58d0cc492cc18c5483e1f769555c228f3249920c51f"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 13: Boltzmann Distribution"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example Problem 13.1, Page Number 309"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import factorial\n",
"\n",
"#Variable Declaration\n",
"\n",
"aH = 40\n",
"N = 100\n",
"\n",
"#Calculations\n",
"aT = 100 - aH\n",
"We = factorial(N)/(factorial(aT)*factorial(aH))\n",
"Wexpected = factorial(N)/(factorial(N/2)*factorial(N/2))\n",
"\n",
"#Results\n",
"print 'The observed weight %5.2e compared to %5.2e'%(We,Wexpected)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The observed weight 1.37e+28 compared to 1.01e+29\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example Problem 13.2, Page Number 310"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example Problem 13.3, Page Number 314"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable Declaration\n",
"p0 = 0.633 #Probabilities of Energy level 1,2,3 \n",
"p1 = 0.233\n",
"p2 = 0.086\n",
"\n",
"#Calculation\n",
"p4 = 1. -(p0+p1+p2)\n",
"\n",
"#Results\n",
"print 'Probability of finding an oscillator at energy level of n>3 is %4.3f i.e.%4.1f percent'%(p4,p4*100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Probability of finding an oscillator at energy level of n>3 is 0.048 i.e. 4.8 percent\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example Problem 13.4, Page Number 315"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable Declaration\n",
"p0 = 0.394 #Probabilities of Energy level 1,2,3 \n",
"p1by2 = 0.239\n",
"p2 = 0.145\n",
"\n",
"#Calculation\n",
"p4 = 1. -(p0+p1by2+p2)\n",
"\n",
"#Results\n",
"print 'Probability of finding an oscillator at energy level of n>3 is %4.3f'%(p4)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Probability of finding an oscillator at energy level of n>3 is 0.222\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example Problem 13.5, Page Number 321"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import exp\n",
"\n",
"#Variable Declaration\n",
"I2 = 208 #Vibrational frequency, cm-1 \n",
"T = 298 #Molecular Temperature, K\n",
"c = 3.00e10 #speed of light, cm/s\n",
"h = 6.626e-34 #Planks constant, J/K\n",
"k = 1.38e-23 #Boltzman constant, J/K\n",
"#Calculation\n",
"q = 1./(1.-exp(-h*c*I2/(k*T)))\n",
"p2 = exp(-2*h*c*I2/(k*T))/q\n",
"\n",
"#Results\n",
"print 'Partition function is %4.3f'%(q)\n",
"print 'Probability of occupying the second vibrational state n=2 is %4.3f'%(p2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Partition function is 1.577\n",
"Probability of occupying the second vibrational state n=2 is 0.085\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example Problem 13.6, Page Number 322"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable Declaration\n",
"B = 1.45 #Magnetic field streangth, Teslas \n",
"T = 298 #Molecular Temperature, K\n",
"c = 3.00e10 #speed of light, cm/s\n",
"h = 6.626e-34 #Planks constant, J/K\n",
"k = 1.38e-23 #Boltzman constant, J/K \n",
"gnbn = 2.82e-26 #J/T\n",
"#Calculation\n",
"ahpbyahm = exp(-gnbn*B/(k*T))\n",
"\n",
"#Results\n",
"print 'Occupation Number is %7.6f'%(ahpbyahm)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Occupation Number is 0.999990\n"
]
}
],
"prompt_number": 18
}
],
"metadata": {}
}
]
}
|
