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{
"metadata": {
"name": "Chapter7"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 7:The Hydrogen Atom in Wave Mechanics"
]
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Example 7.2 Page 213"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#initiation of variable\n",
"from math import exp\n",
"import math\n",
"from scipy import integrate\n",
"# calculating radial probability P= (4/ao^3)*integral(r^2 * e^(-2r/ao)) between the limits 0 and ao for r\n",
"\n",
"#calculation\n",
"def integrand(x):\n",
" return ((x**2)*exp(-x))/2.0\n",
"Pr=integrate.quad(integrand,0,2,args=());#simplifying where as x=2*r/a0; hence the limits change between 0 to 2\n",
"\n",
"#result\n",
"print \"Hence the probability of finding the electron nearer to nucleus is\",round(Pr[0],3);\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Hence the probability of finding the electron nearer to nucleus is 0.323\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.3 Page 213"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#initiation of variable\n",
"from math import exp\n",
"import math\n",
"from scipy import integrate\n",
"# employing the formula for probability distribution similarly as done in Exa-7.2 \n",
"#calculation\n",
"def integrand(x):\n",
" return (1.0/8)*((4.0*x**2)-(4.0*x**3)+(x**4))*exp(-x)\n",
"Pr1= integrate.quad(integrand,0,1,args=()) #x=r/ao; similrly limits between 0 and 1.\n",
"\n",
"#result\n",
"print\"The probability for l=0 electron is\",round(Pr1[0],5)\n",
"\n",
"#part2\n",
"def integrand(x):\n",
" return (1.0/24)*(x**4)*(exp(-x))\n",
"Pr2=integrate.quad(integrand,0,1); #x=r/ao; similarly limits between 0 and 1.\n",
"\n",
"#result\n",
"print\"The probability for l=1 electron is\",round(Pr2[0],5)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The probability for l=0 electron is 0.03432\n",
"The probability for l=1 electron is 0.00366\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.4 Page 215"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#initiation of variable\n",
"from math import exp, sqrt\n",
"import math\n",
"from scipy import integrate\n",
"l=1.0; #given value of l\n",
"\n",
"#calculation\n",
"am1=sqrt(l*(l+1)); #angular momentum==sqrt(l(l+1)) h\n",
"l=2.0 #given l\n",
"am2=sqrt(l*(l+1));\n",
"\n",
"#result\n",
"print\"The angular momenta are found out to be\", round(am1,3),\" h and\",round(am2,3),\" h respectively for l=1 and l=2.\";\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The angular momenta are found out to be 1.414 h and 2.449 h respectively for l=1 and l=2.\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.5 Page 216"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#initiation of variable\n",
"from math import sqrt\n",
"print \"The possible values for m are [+2,-2] and hence any of the 5 components [-2h,2h] are possible for the L vector.\";\n",
"print \"Length of the vector as found out previously is %.2f*h.\",round(sqrt(6),4);#angular momentum==sqrt(l(l+1)) h"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The possible values for m are [+2,-2] and hence any of the 5 components [-2h,2h] are possible for the L vector.\n",
"Length of the vector as found out previously is %.2f*h. 2.4495\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.6 Page 223"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#initiation of variable\n",
"uz=9.27*10**-24; t=1.4*10**3; x=3.5*10**-2; #various constants and given values\n",
"m=1.8*10**-25;v=750; # mass and velocity of the particle\n",
"\n",
"#calculation\n",
"d=(uz*t*(x**2))/(m*(v**2)); #net separtion \n",
"\n",
"#result\n",
"print\"The distance of separation in mm is\",round(d*10**3,3);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The distance of separation in mm is 0.157\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.7 Page 227"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#initiation of variable\n",
"n1=1.0;n2=2.0;hc=1240.0; #hc=1240 eV.nm\n",
"E=(-13.6)*((1/n2**2)-(1/n1**2)); #Energy calculation\n",
"\n",
"#calculation\n",
"w=hc/E; #wavelength\n",
"u=9.27*10**-24; B=2; #constants\n",
"delE= u*B/(1.6*10**-19); #change in energy\n",
"delw=((w**2/hc))*delE; #change in wavelength\n",
"\n",
"#result\n",
"print\"The change in wavelength in nm. is\",round(delw,4);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The change in wavelength in nm. is 0.0014\n"
]
}
],
"prompt_number": 12
}
],
"metadata": {}
}
]
}
|
