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+{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:6f3412539d62c2f676626072f86e8478aa55d9f7f8bd139276fa120f78482f67"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 3: The Quantum Theory of Light"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.1, page no. 69"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ " \n",
+ "\n",
+ "#Variable declaration\n",
+ "Rs=7.0 * (10 ** 8) \t#sun's radius (m)\n",
+ "R = 1.5 *(10 ** 11)\t#earth to sun distance (m)\n",
+ "a = 1 #since sun is considered as a blackbody \n",
+ "k = 5.6 * (10 ** (-8)) #Stefan-Boltzmann constant ( W.m ^-2 .K^-4)\n",
+ "eTotalR = 1400\t#power per unit area (W/m^2)\n",
+ "\n",
+ "#Calculations\n",
+ "T = ((eTotalR * R * R) / (k * Rs * Rs) ) ** .25\n",
+ "\n",
+ "#Results\n",
+ "print '%s %.2f %s' %('the surface temperature of the sun is',T,'K')\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "the surface temperature of the sun is 5820.79 K\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.2, page no. 75"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "\n",
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "h = 6.63 * 10 ** -34 #planck's constant(Js)\n",
+ "c = 3 * 10 ** 8 #speed of light(m/s)\n",
+ "lgreen = 540 * 10 ** -9#wavelength of green light(m)\n",
+ "lred = 700 *10**-9 #wavelength of red light(m)\n",
+ "e = 1.602 * 10 ** -19 #charge of an electron(C)\n",
+ "\n",
+ "#calculation\n",
+ "dEg = h*c /(lgreen* e)\n",
+ "dEr = h*c/(lred * e)\n",
+ "\n",
+ "#results\n",
+ "print '%s %s %s %s %s' %('the minimum energy change for ',lgreen * 10 ** 9,'nm is ',round(dEg,2),'eV')\n",
+ "print '%s %s %s %s %s' %('the minimum energy change for ',lred * 10 ** 9,'nm is ',round(dEr,2),'eV')\n",
+ "\n",
+ "\n",
+ "#Variable declaration\n",
+ "l=1 #length of the pendulum(m)\n",
+ "m = 0.1 # mass of the pendulum(kg)\n",
+ "g = 9.8 #acceleration due to gravity(m.s^-2)\n",
+ "h = 6.63 *10 **-34 #planck's constant(J.s)\n",
+ "theta = 10 # displaced angle\n",
+ "\n",
+ "#Calculations\n",
+ "E = m * g * l *(1 - math.cos(math.pi * theta /180))\n",
+ "f = math.sqrt(g /l) /(2* math.pi)\n",
+ "Edelta = h *f\n",
+ "\n",
+ "#results\n",
+ "print '%s %s %s' %('the pendulum frequency is',round(f,2),'Hz')\n",
+ "print '%s %s %s' %('the total energy of the pendulum is',round(E,3),'J')\n",
+ "print '%s %s %s' %('therefore an energy change of one quantum corresponds to',round(Edelta/10**-34,2),'x 10^-34 J')\n",
+ "print '%s %s %s' %('Therefore the fractional change in energy ^E/E is ',round(Edelta/E/10**-32,2),'x 10^-32 ')"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "the minimum energy change for 540.0 nm is 2.3 eV\n",
+ "the minimum energy change for 700.0 nm is 1.77 eV\n",
+ "the pendulum frequency is 0.5 Hz\n",
+ "the total energy of the pendulum is 0.015 J\n",
+ "therefore an energy change of one quantum corresponds to 3.3 x 10^-34 J\n",
+ "Therefore the fractional change in energy ^E/E is 2.22 x 10^-32 \n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.3, page no. 80"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "\n",
+ "#Variable declaration\n",
+ "\n",
+ "pi = 3.141 \n",
+ "k = 1.381 * 10 **-23 #Boltzmann constant (J/K)\n",
+ "c = 2.998 * 10 ** 8 #Speed of light (m/s)\n",
+ "h = 6.626 * 10 ** -34 #Planck's constant (J.s)\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "sigma = 2 * pi**5 * k**4 / (15 * c**2 * h**3)\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print \"e_total=sigma * T^4 where sigma=\",round(sigma/10**-8,2),\"X 10^-8 W.m^-2.K^-4\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "e_total=sigma * T^4 where sigma= 5.67 X 10^-8 W.m^-2.K^-4\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.4, page no. 83"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "e= 1.68 * 10 **-19 #electron charge(C)\n",
+ "O = 2.28 * e #work function of sodium\n",
+ "I = 10 ** -10 #power per unit area(W/cm^2)\n",
+ "\n",
+ "#calculation\n",
+ "A = math.pi * 10 ** -16\n",
+ "t= O / (I * A)\n",
+ "\n",
+ "#result\n",
+ "print '%s %s %s' %('the time lag is given by',round(t/(60*60*24)),'days which is approximated to 130 days in the text book')"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "the time lag is given by 141.0 days which is approximated to 130 days in the text book\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.5, page no. 85"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "Vs = 4.3 #Stopping voltage(V)\n",
+ "e = 1.6 * 10 **-19 #electron charge(C)\n",
+ "Me = 9.1 *10**-31 #mass of electron(kg)\n",
+ "\n",
+ "#calculation\n",
+ "vmax = math.sqrt( 2* e* Vs /Me)\n",
+ "Kmax = e *Vs\n",
+ "\n",
+ "#result\n",
+ "print '%s %s %s' %('the Kmax of these electrons are', Kmax ,'J')\n",
+ "print '%s %s %s' %('vmax of these electrons are',round(vmax/10**6,2),' x 10^6 m/s')"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "the Kmax of these electrons are 6.88e-19 J\n",
+ "vmax of these electrons are 1.23 x 10^6 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.6, page no. 85"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "#variable declaration\n",
+ "I0 = 1 * 10 ** -6 #intensity of light falling W/cm^2\n",
+ "\n",
+ "#calculation\n",
+ "I = .03 * .04 * I0\n",
+ "\n",
+ "#result\n",
+ "print '%s %s %s' %('The actual intensity available is',I,'W/cm^2')\n",
+ "\n",
+ "#variable declaration\n",
+ "lamda = 250 *10 ** -9 #wavelength of violet light(m)\n",
+ "c= 3*10**8 #speed of light(m/s)\n",
+ "h = 6.63 *10 **-34 #planck's constant(J.s)\n",
+ "\n",
+ "#calculation\n",
+ "Ne = I *lamda / (h * c)\n",
+ "\n",
+ "#result\n",
+ "print '%s %s %s' %('number of electrons is',round(Ne/10**9,1),'x 10^9')\n",
+ "\n",
+ "\n",
+ "#variable declaration\n",
+ "e = 1.6 * 10 **-19 #electron charge(c)\n",
+ "\n",
+ "#calculation\n",
+ "i = e * Ne\n",
+ "\n",
+ "#result\n",
+ "print '%s %s %s' %('current in the phototube is ',round(i/10**-10,1),'x 10^-10 A')\n",
+ "\n",
+ "\n",
+ "#variable declaration\n",
+ "f0 = 1.1 *10**15 #cutoff frequency (Hz)\n",
+ "\n",
+ "#calculation\n",
+ "O = h *f0 / e \n",
+ "\n",
+ "#result\n",
+ "print '%s %s %s' %('the work function is ',round(O,1),'eV')\n",
+ "\n",
+ "\n",
+ "\n",
+ "#variable declaration\n",
+ "lamda = 250 * 10 ** -9 #wavelength(m)\n",
+ "\n",
+ "#calculation\n",
+ "Vs = ((h*c )/(lamda * e )) - O\n",
+ "\n",
+ "#result\n",
+ "print '%s %s %s' %('stopping voltage for iron is ',round(Vs,2),'V')"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The actual intensity available is 1.2e-09 W/cm^2\n",
+ "number of electrons is 1.5 x 10^9\n",
+ "current in the phototube is 2.4 x 10^-10 A\n",
+ "the work function is 4.6 eV\n",
+ "stopping voltage for iron is 0.41 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.7, page no. 93"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "\n",
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "lamda = .2 * 10 ** -9 #wavelength(m)\n",
+ "theta = 45 #observed angle(degrees)\n",
+ "h = 6.63 * 10 ** -34 #planck's constant(J.s)\n",
+ "Me = 9.1 * 10 ** -31 #electron mass(kg)\n",
+ "c = 3* 10 ** 8 #speed of light(m/s)\n",
+ "\n",
+ "#calculation\n",
+ "dl= h *(1 - math.cos(math.pi * theta /180)) /(Me * c)\n",
+ "\n",
+ "#result\n",
+ "print '%s %s %s' %('the wavelength off the scattered x-ray at this angle is',dl+lamda,'m')"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "the wavelength off the scattered x-ray at this angle is 2.00711312103e-10 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.8, page no. 93"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "lamdaG = 0.0106 #wavelenght(m)\n",
+ "\n",
+ "#calculation\n",
+ "dl = 0.0243 * (1-math.cos(math.pi/2))\n",
+ "f= dl/ lamdaG\n",
+ "\n",
+ "#result\n",
+ "print \"the compton shift is \",dl,\"A'\"\n",
+ "print \"the fractional change in wavelength of gamma rays is\",round(f,4)\n",
+ "\n",
+ "#(2)X-rays from molybdenum, lamda = 0.712 x 10 ^-10 m,\n",
+ "\n",
+ "#variable declaration\n",
+ "lamdaX = 0.712 #wavelenght(m)\n",
+ "\n",
+ "#calculation\n",
+ "f= dl/ lamdaX\n",
+ "\n",
+ "#result\n",
+ "print \"the fractional change in wavelength of X rays is\",round(f,4)\n",
+ "\n",
+ "#(3)green light from a mercury lamp, lamda = 5461 *10 ^ -10 \n",
+ "\n",
+ "#variable declaration\n",
+ "lamdaGr = 5461\n",
+ "\n",
+ "#calculation\n",
+ "f= dl/ lamdaGr\n",
+ "\n",
+ "#result\n",
+ "print \"the fractional change in wavelength of green rays is\",round(f/10**-6,3),\"x 10^-6\"\n",
+ "\n",
+ "\n",
+ "#variable declaration\n",
+ "h = 6.63 * 10 ** -34 #planck's constant(J.s)\n",
+ "c = 3* 10 ** 8 #speed of light(m/s)\n",
+ "lamda = 0.712 * 10 **-10\n",
+ "e = 1.6 * 10 **-19 #electron charge(c)\n",
+ "\n",
+ "#calculation\n",
+ "E = h*c/(lamda * e)\n",
+ "\n",
+ "#result\n",
+ "print \"the energy of incident x-ray is\",round(E,2),\"ev. It is large when compared to binding energy of 4eV\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "the compton shift is 0.0243 A'\n",
+ "the fractional change in wavelength of gamma rays is 2.2925\n",
+ "the fractional change in wavelength of X rays is 0.0341\n",
+ "the fractional change in wavelength of green rays is 4.45 x 10^-6\n",
+ "the energy of incident x-ray is 17459.62 ev. It is large when compared to binding energy of 4eV\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.9, page no. 96"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "#variable declaration\n",
+ "M = 1.99 * 10 ** 30 #mass of sun(kg)\n",
+ "lamda = 300 *10**-9 #wavelength(m)\n",
+ "Rs = 6.37 * 10 ** 6 #radius of earth(m)\n",
+ "G = 6.67 * 10 ** -11 #gravitational constant(N.m^2.kg^-2)\n",
+ "c = 3 * 10 ** 8 #speed of light(m/s)\n",
+ "\n",
+ "#calculation\n",
+ "fraction = G * M / (Rs * c *c)\n",
+ "\n",
+ "#result\n",
+ "print '%s %s %s'%(\"the shift in wavelength\",round(lamda * fraction *10**9,4),'nm')"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "the shift in wavelength 0.0695 nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+} \ No newline at end of file
generated by cgit (git 2.34.1) at 2024-12-20 13:51:15 +0000