{ "metadata": { "name": "", "signature": "sha256:5b9d1e914dbb4b0e0e0650025bfed9ebb154ac3184f6c3eb08f9fb1b53400e59" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 3: The Experimental Basis of Quantum Physics" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.1, Page 87" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#Variable declaration\n", "E = 1.2e+004; # Electric field, V/m\n", "B = 8.8e-004; # Magnetic field, T\n", "l = 0.05; # Length of the deflection plates, m\n", "v0 = E/B; # Initial velocity of the electron, m/s\n", "theta = 30; # Angular deflection of the electron, degrees\n", "\n", "#Calculations\n", "q_ratio_m = E*math.tan(theta*math.pi/180)/(B**2*l); # Specific charge of the electron, C/kg\n", "\n", "#Results\n", "print \"The initial velocity of the electron = %3.1e m/s\"%v0\n", "print \"The specific charge of the electron = %3.1e C/kg\"%q_ratio_m" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The initial velocity of the electron = 1.4e+07 m/s\n", "The specific charge of the electron = 1.8e+11 C/kg\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.3, Page 94" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy\n", "\n", "def check_visible(l):\n", " if l >= 400 and l < 700:\n", " return 1\n", " else:\n", " return 0\n", " \n", "R_H = 1.0968e+007; # Rydberg constanr, per metre\n", "f = numpy.zeros(7)\n", "# Lyman series\n", "print \"\\nFor Lyman series, the wavelengths are:\\n\"\n", "n = 1.; # The lowest level of Lyman series\n", "for k in range(2,4):\n", " l = 1./(R_H*(1./n**2-1./k**2))/1.e-009;\n", " print \"k = %d, %5.1f nm\"%(k, l);\n", " f[k-1] = check_visible(l); \n", " if f[k-1] == 1:\n", " print(\" (Visible) \\n\");\n", " else:\n", " print(\" (Ultraviolet)\\n\");\n", " \n", " \n", "if f[0] == 1 or f[1] == 1 or f[2] == 1:\n", " print(\"Some wavelengths of Lyman series fall in the visible region.\\n\")\n", "else:\n", " print(\"All the wavelengths of Lyman series fall in the UV-region.\\n\")\n", " \n", "\n", "# Balmer series\n", "print(\"\\nFor Balmer series, the wavelengths are:\\n\")\n", "n = 2; # The lowest level of Balmer series\n", "for k in range(3,8):\n", " l = 1./(R_H*(1./n**2.-1./k**2))/1.e-009;\n", " print \"k = %d, %5.1f nm\"%(k, l);\n", " f[k-1] = check_visible(l);\n", " if f[k-1] == 1:\n", " print(\" (Visible) \\n\");\n", " else:\n", " print(\" (Ultraviolet)\\n\");\n", " \n", "# Paschen series\n", "print(\"\\nFor Paschen series, the wavelengths are:\\n\")\n", "n = 3.; # The lowest level of Lyman series\n", "for k in range(4,6):\n", " l = 1./(R_H*(1./n**2-1./k**2))/1e-009;\n", " print \"k = %d, %5.1f nm\"%( k, l);\n", " f[k-1] = check_visible(l); \n", " if f[k-1] == 1:\n", " print(\" (Visible) \\n\");\n", " else:\n", " print(\" (Infrared)\\n\");\n", " \n", "# For limiting member\n", "k = numpy.inf;\n", "l = 1/(R_H*(1/n**2-1/k**2))/1e-009;\n", "print \"k = %f, %5.1f nm\"%(numpy.inf, l);\n", "f[5] = check_visible(l);\n", "if f[5] == 1:\n", " print(\" (Visible) \\n\");\n", "else:\n", " print(\" (Infrared)\\n\");\n", " \n", "if f[3] == 1 or f[4] == 1 or f[5] == 1:\n", " print(\"Some wavelengths of Paschen series fall in the visible region.\")\n", "else:\n", " print(\"All the wavelengths of Paschen series fall in the IR-region.\")\n", " \n", " " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "For Lyman series, the wavelengths are:\n", "\n", "k = 2, 121.6 nm\n", " (Ultraviolet)\n", "\n", "k = 3, 102.6 nm\n", " (Ultraviolet)\n", "\n", "All the wavelengths of Lyman series fall in the UV-region.\n", "\n", "\n", "For Balmer series, the wavelengths are:\n", "\n", "k = 3, 656.5 nm\n", " (Visible) \n", "\n", "k = 4, 486.3 nm\n", " (Visible) \n", "\n", "k = 5, 434.2 nm\n", " (Visible) \n", "\n", "k = 6, 410.3 nm\n", " (Visible) \n", "\n", "k = 7, 397.1 nm\n", " (Ultraviolet)\n", "\n", "\n", "For Paschen series, the wavelengths are:\n", "\n", "k = 4, 1875.6 nm\n", " (Infrared)\n", "\n", "k = 5, 1282.1 nm\n", " (Infrared)\n", "\n", "k = inf, 820.6 nm\n", " (Infrared)\n", "\n", "All the wavelengths of Paschen series fall in the IR-region.\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.4, Page 98" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#Variable declaration\n", "T = 1600 + 273; # Temperature of the furnace, K\n", "b = 2.898e-003; # Wein's constant, m-K\n", "\n", "#Calculation\n", "lamda_max = math.ceil(b/(T*1e-009)); # Maximum wavelength from Wein's Displacement Law, nm\n", "\n", "#Results\n", "print \"The maximum wavelength emitted from the heated furnace = %4d nm\"%lamda_max\n", "print \"This wavelength falls in the IR-region.\"\n", "\n", "#answers differ due to rounding errors" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The maximum wavelength emitted from the heated furnace = 1548 nm\n", "This wavelength falls in the IR-region.\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.5, Page 98" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#Variable declaration\n", "lambda_max = 500e-009; # Maximum intensity wavelength emitted by the sun, m\n", "b = 2.898e-003; # Wein's constant, m-K\n", "sigma = 5.67e-008; # Stefan's constant, W/Sq.m-K^4\n", "r = 6.96e+008; # Radius of the sun, m\n", "r_E = 6.37e+006; # Radius of the earth, m\n", "R_E = 1.49e+011; # Mean-earth sun distance, m\n", "\n", "#Calculations\n", "S = 4*math.pi*r**2; # Surface area of the sun, Sq.m\n", "T_sun = b/lambda_max; # The temperature of the sun's surface, K\n", "R_T = sigma*T_sun**4; # Power per unit area radiated by the sun, W/Sq.m\n", "P_sun = R_T*S; # The total power radiated from the sun's surface, W\n", "F = r_E**2/(4*R_E**2); # Fraction of sun's radiation received by Earth\n", "P_Earth_received = P_sun*F; # The radiation received by the Earth from the sun, W\n", "U_Earth = P_Earth_received*60*60*24; # The radiation received by the Earth from the sun in one day, J\n", "R_Earth = P_Earth_received/(math.pi*r_E**2); # Power received by the Earth per unit of exposed area, W/Sq.m\n", "\n", "#Results\n", "print \"The surface temperature of the sun = %4d K\"%math.ceil(T_sun)\n", "print \"The power per unit area emitted from the surface of the sun = %4.2e W/Sq.m\"%R_T\n", "print \"The energy received by the Earth each day from the radiation of sun = %4.2e J\"%U_Earth\n", "print \"The power received by the Earth per unit of exposed area = %4d W/Sq.m\"%math.ceil(R_Earth)\n", "\n", "#Answers differ due to rounding errors" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The surface temperature of the sun = 5796 K\n", "The power per unit area emitted from the surface of the sun = 6.40e+07 W/Sq.m\n", "The energy received by the Earth each day from the radiation of sun = 1.54e+22 J\n", "The power received by the Earth per unit of exposed area = 1397 W/Sq.m\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.10, Page 106" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Variable declaration\n", "phi = 2.36; # Work function of sodium, eV\n", "N_A = 6.02e+023; # Avogadro's number\n", "e = 1.6e-019; # Energy equivalent of 1 eV, J\n", "I = 1e-008; # Intensity of incident radiation, W/Sq.m\n", "K = 1.00; # Kinetic energy of the ejected photoelectron, eV\n", "rho = 0.97; # Density of Na atoms, g/cc\n", "M = 23; # Gram atomic mass of Na, g/mol\n", "\n", "#Calculations\n", "n = N_A*1e+006/M*rho; # Number of Na atoms per unit volume, atoms/metre-cube\n", "# Assume a cubic structure, then 1/d^3 = n, solving for d\n", "d = (1./n)**(1./3); # Thickness of one layer of sodium atoms, m\n", "N = n*d; # Number of exposed atoms per Sq.m\n", "R = I/(N*e); # Rate of energy received by each atom, eV/s\n", "t = (phi+K)/R; # Time needed to absorb 3.36 eV energy\n", "\n", "#Result\n", "print \"The exposure time of light to produce the photoelectron of %4.2f kinetic energy = %4.1f years\"%(K, t/(60*60*24*365.25))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The exposure time of light to produce the photoelectron of 1.00 kinetic energy = 14.7 years\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.11, Page 109" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Variable declaration\n", "phi = 2.93; # Work function of lithium, eV\n", "lamda = 400e-009; # Wavelength of incident light, m\n", "e = 1.6e-019; # Energy equivalent of 1 eV, J\n", "c = 2.998e+008; # Speed of light in vacuum, m/s\n", "h = 6.626e-034; # Planck's constant, Js\n", "\n", "#Calculations\n", "E = h*c/(lamda*e); # Energy of incident light, eV\n", "V0 = E - phi; # Stopping potential, V\n", "\n", "#Results\n", "print \"The energy of incident photons = %4.2f eV\"%E\n", "print \"The stopping potential = %4.2f V\"%V0" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The energy of incident photons = 3.10 eV\n", "The stopping potential = 0.17 V\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.12, Page 109" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Variable declaration\n", "phi = 2.93; # Work function of lithium, eV\n", "c = 2.998e+008; # Speed of light in vacuum, m/s\n", "K = 3.00; # Kinetic energy of photoelectron, eV\n", "E = phi + K; # Total energy of the incident light, eV\n", "h = 6.626e-034; # Planck's constant, Js\n", "e = 1.6e-019; # Energy equivalent of 1 eV, J\n", "\n", "#Calculations\n", "f = E*e/h; # Frequency of incident light, Hz\n", "lamda = c/f; # Wavelength of the incident light, m\n", "\n", "#Results\n", "print \"The frequency of incident light = %4.2e Hz\"%f\n", "print \"The wavelength of the incident light = %4.2f nm\"%(lamda/1e-009)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The frequency of incident light = 1.43e+15 Hz\n", "The wavelength of the incident light = 209.37 nm\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.13, Page 110" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Variable declaration\n", "lamda = 350; # Wavelength of incident light, nm\n", "e = 1.6e-019; # Energy equivalent of 1 eV, J\n", "E = 1.250e+003/lamda; # Total energy of the incident light, eV\n", "I = 1e-008; # Intensity of incident light, W/Sq.m\n", "\n", "#Calculations\n", "# As Intensity, I = N*E, solving for N\n", "N = I/(E*e); # The number of photons in the light beam\n", "\n", "#Results\n", "print \"The number of photons in the light beam = %3.1e photons/Sq.m/s\"%N" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The number of photons in the light beam = 1.8e+10 photons/Sq.m/s\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.15, Page 113" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Variable declaration\n", "e = 1.6e-019; # Energy equivalent of 1 eV, J\n", "c = 2.998e+008; # Speed of light in vacuum, m/s\n", "h = 6.626e-034; # Planck's constant, Js\n", "V0 = 35e+003; # Electron acceleration voltage, V\n", "\n", "#Calculations\n", "lambda_min = h*c/(e*V0); # Duane-Hunt rule for wavelength, m\n", "\n", "#Result\n", "print \"The minimum wavelength of X-rays = %4.2e m\"%lambda_min" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The minimum wavelength of X-rays = 3.55e-11 m\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.16, Page 116" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#Variable declaration\n", "c = 2.998e+008; # Speed of light in vacuum, m/s\n", "h = 6.626e-034; # Planck's constant, Js\n", "m_e = 9.11e-031; # Rest mass of an electron, kg\n", "lamda = 0.050; # Wavelength of the X-ray, nm\n", "theta = 180; # The angle at which the recoil electron Ke becomes the largest, degree\n", "\n", "#Calculations\n", "E_x_ray = 1.240e+003/lamda; # Energy of the X-ray, eV\n", "lambda_prime = lamda + (1-math.cos(theta*math.pi/180))*h/(m_e*c*1e-009); # The largest wavelength of the scattered photon, nm\n", "E_prime_x_ray = 1.240e+003/lambda_prime; # Energy of the scattered photon, eV\n", "K = (E_x_ray - E_prime_x_ray)/1e+003; # Kinetic energy of the most energetic recoil electron, keV\n", "if (E_prime_x_ray < E_x_ray):\n", " print \"The X-ray is Compton-scattered by the electron.\"\n", "else:\n", " print \"The X-ray is not Compton-scattered by the electron.\"\n", "\n", "#Results\n", "print \"The largest wavelength of the scattered photon = %5.3f nm\"%lambda_prime\n", "print \"The kinetic energy of the most energetic recoil electron = %3.1f keV\"%K\n", "print \"The angle at which the recoil electron energy is the largest = %d degrees\"%theta" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The X-ray is Compton-scattered by the electron.\n", "The largest wavelength of the scattered photon = 0.055 nm\n", "The kinetic energy of the most energetic recoil electron = 2.2 keV\n", "The angle at which the recoil electron energy is the largest = 180 degrees\n" ] } ], "prompt_number": 10 } ], "metadata": {} } ] }