{
"metadata": {
"name": "",
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 5: Wave Properties of Matter and Quantum Mechanics I"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.1, Page 167"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"N_A = 6.022e+23; # Avogdaro's No., per mole\n",
"n = 1; # Order of diffraction\n",
"M = 58.5; # Molecular mass of NaCl, g/mol\n",
"rho = 2.16; # Density of rock salt, g/cc\n",
"two_theta = 20; # Scattering angle, degree \n",
"theta = two_theta/2; # Diffraction angle, degree\n",
"\n",
"#Calculations\n",
"N = N_A*rho*2/(M*1e-006); # Number of atoms per unit volume, per metre cube \n",
"d = (1/N)**(1./3); # Interplanar spacing of NaCl crystal, m \n",
"lamda = 2*d*math.sin(theta*math.pi/180)/n ; # Wavelength of X-rays using Bragg's law, m\n",
"\n",
"#Result\n",
"print \"The wavelength of the incident X rays = %5.3f nm\"%(lamda/1e-009)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The wavelength of the incident X rays = 0.098 nm\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.2, Page 168"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"h = 6.63e-034; # Planck's constant, Js\n",
"c = 3e+008; # Speed of light, m/s\n",
"\n",
"#Calculations&Results\n",
"# For a moving ball\n",
"m = 0.057; # Mass of the ball, kg\n",
"v = 25; # Velocity of ball, m/s\n",
"p = m*v; # Momentum of the ball, kgm/s\n",
"lamda = h/p; # Lambda is the wavelength of ball, nm\n",
"print \"The wavelength of ball = %3.1e m\"%lamda\n",
"\n",
"# For a moving electron\n",
"m = 0.511e+006; # Rest mass of an electron, eV\n",
"K = 50; # Kinetic energy of the electron, eV\n",
"p = math.sqrt(2*m*K); # Momentum of the electron, kgm/s\n",
"lamda = h*c/(1.602e-019*p*1e-009); # Wavelength of the electron, nm\n",
"print \"The wavelength of the electron = %4.2f nm\"%lamda\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The wavelength of ball = 4.7e-34 m\n",
"The wavelength of the electron = 0.17 nm\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.3, Page 173"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"m = 9.1e-31; # Mass of the electron, kg\n",
"h = 6.63e-34; # Planck's constant, Js\n",
"c = 3e+008; # Speed of light, m/s\n",
"e = 1.6e-19; # Energy equivalent of 1 eV, J/eV\n",
"V0 = 54; # Potential difference between electrodes, V\n",
"\n",
"#Calculations\n",
"lamda = h*c/(math.sqrt(2*m*c**2/e*V0)*e*1e-009); # de Broglie wavelength of the electron, nm\n",
"\n",
"#Result\n",
"print \"The de Broglie wavelength of the electron used by Davisson and Germer = %5.3f nm\"%lamda"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The de Broglie wavelength of the electron used by Davisson and Germer = 0.167 nm\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.4, Page 174"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"h = 6.63e-34; # Planck's constant, Js\n",
"c = 3e+008; # Speed of light, m/s\n",
"e = 1.6e-19; # Energy equivalent of 1 eV, J/eV\n",
"m = 1.67e-27; # Mass of a neutron, kg\n",
"k = 1.38e-23; # Boltzmann constant, J/mol/K\n",
"T = [300, 77]; # Temperatures, K\n",
"\n",
"#Calculations&Results\n",
"lamda = h*c/(math.sqrt(3*m*c**2/e*k/e*T[0])*e); # The wavelength of the neutron at 300 K, nm\n",
"print \"The wavelength of the neutron at %d K = %5.3f nm\"%(T[0], lamda/1e-09)\n",
"lamda = h*c/(math.sqrt(3*m*c**2/e*k/e*T[1])*e); # The wavelength of the neutron at 77 K, nm\n",
"print \"The wavelength of the neutron at %d K = %5.3f nm\"%(T[1], lamda/1e-09)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The wavelength of the neutron at 300 K = 0.146 nm\n",
"The wavelength of the neutron at 77 K = 0.287 nm\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.7, Page 184"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"h = 6.626e-34; # Planck's constant, Js\n",
"c = 3e+008; # Speed of light, m/s\n",
"e = 1.602e-019; # Energy equivalent of 1 eV, J/ev\n",
"d = 2000; # Distance between slit centres, nm\n",
"K = 50e+003; # Kinetic energy of electrons, eV\n",
"l = 350e+006; # Distance of screen from the slits, nm\n",
"\n",
"#Calculations\n",
"lamda = 1.226/math.sqrt(K); # Non-relativistic value of de Broglie wavelength of the electrons, nm\n",
"E0 = 0.511e+006; # Rest energy of the electron, J\n",
"E = K + E0; # Total energy of the electron, J\n",
"p_c = math.sqrt(E**2 - E0**2); # Relativistic mass energy relation, eV\n",
"lambda_r = h*c/(p_c*e*1e-009); # Relativistic value of de Broglie wavelength, nm\n",
"percent_d = (lamda - lambda_r)/lamda*100; # Percentage decrease in relativistic value relative to non-relavistic value\n",
"sin_theta = lambda_r/d; # Bragg's law\n",
"y = l*sin_theta; # The distance of first maximum from the screen, nm\n",
"\n",
"#Results\n",
"print \"The percentage decrease in relativistic value relative to non-relativistic value = %1.0f percent\"%percent_d\n",
"print \"The distance between first two maxima = %3.0f nm\"%y"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The percentage decrease in relativistic value relative to non-relativistic value = 2 percent\n",
"The distance between first two maxima = 938 nm\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.8, Page 187"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"dx = 17.5; # The uncertainty in position, m\n",
"h = 1.05e-034; # Reduced Planck's constant, Js\n",
"\n",
"#Calculations&Results\n",
"dp_x = h/(2*dx); # The uncertainty in momentum, kgm/s\n",
"print \"The uncertainty in momentum of the ball = %1.0e kg-m/s\"%dp_x\n",
"dx = 0.529e-010; # The uncertainty in position, m\n",
"dp_x = h/(2*dx); # The uncertainty in momentum, kgm/s\n",
"print \"The uncertainty in momentum of the electron = %1.0e kg-m/s\"%dp_x"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The uncertainty in momentum of the ball = 3e-36 kg-m/s\n",
"The uncertainty in momentum of the electron = 1e-24 kg-m/s\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.9, Page 188"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"a_0 = 5.29e-11; # Radius of H-atom, m\n",
"l = 2*a_0; # Length, m\n",
"h = 6.63e-34; # Planck's constant, Js\n",
"m = 9.1e-31; # Mass of electron, kg\n",
"\n",
"#Calculations\n",
"K_min = h**2/(8*(math.pi)**2*m*l**2); # Minimum kinetic energy possesed, J\n",
"\n",
"#Result\n",
"print \"The minimum kinetic energy of the electron = %3.1f eV\"%(K_min/1.6e-19)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The minimum kinetic energy of the electron = 3.4 eV\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.10, Page 190"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"dx = 6e-015; # The uncertainty in position of the electron, m\n",
"h_bar = 1.054e-034; # PReduced Planck's constant, Js\n",
"e = 1.602e-019; # Energy equivalnet of 1 eV, J/eV\n",
"c = 3e+008; # Speed of light, m/s\n",
"E0 = 0.511e+006; # Rest mass energy of the electron, J\n",
"\n",
"#Calculations\n",
"dp = h_bar*c/(2*dx*e); # Minimum electron momentum, eV/c\n",
"p = dp; # Momentum of the electron at least equal to the uncertainty in momentum, eV/c\n",
"E = math.sqrt(p**2+E0**2)/1e+006; # Relativistic energy of the electron, MeV \n",
"K = E - E0/1e+006; # Minimum kinetic energy of the electron, MeV\n",
"\n",
"#Result\n",
"print \"The minimum kinetic energy of the electron = %4.1f MeV\"%K"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The minimum kinetic energy of the electron = 15.9 MeV\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.12, Page 191"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"c = 3e+8; # Speed of light, m/s\n",
"dt = 1e-08; # Relaxation time of atom, s\n",
"h = 6.6e-34; # Planck's constant, Js\n",
"dE = h/(4*math.pi*dt); # Energy width of excited state of atom, J\n",
"lamda = 300e-009; # Wavelegth of emitted photon, m\n",
"\n",
"#Calculations&Results\n",
"f = c/lamda; # Frequency of emitted photon, per sec\n",
"print \"The energy width of excited state of the atom = %3.1e eV\"%(dE/1.6e-019)\n",
"df = dE/h; # Uncertainty in frequency, per sec\n",
"print \"The uncertainty ratio of the frequency = %1.0e\"%(df/f)\n",
"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The energy width of excited state of the atom = 3.3e-08 eV\n",
"The uncertainty ratio of the frequency = 8e-09\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.13, Page 195"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"e = 1.6e-019; # Energy equivalent of 1 eV, J/eV\n",
"c = 3e008; # Speed of light, m/s\n",
"h = 6.63e-034; # Planck's constant, Js\n",
"m = 9.1e-031; # Mass of the proton, kg\n",
"l = 0.1; # Length of one-dimensional box, nm\n",
"\n",
"#Calculations&Results\n",
"for n in range(1,4):\n",
" E_n = n**2*(h*c/(e*1e-009))**2/(8*m*c**2/e*l**2); # Energy of nth level, eV\n",
" print \"The first three energy levels are %3.0f eV\"%(E_n)\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The first three energy levels are 38 eV\n",
"The first three energy levels are 151 eV\n",
"The first three energy levels are 340 eV\n"
]
}
],
"prompt_number": 10
}
],
"metadata": {}
}
]
}