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author | Prashant S | 2020-04-14 10:25:32 +0530 |
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committer | GitHub | 2020-04-14 10:25:32 +0530 |
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tree | 2b1df110e24ff0174830d7f825f43ff1c134d1af /Engineering_Physics_by_D_C_Ghosh/7-Classical_Statistics_and_Quantum_Statistics.ipynb | |
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diff --git a/Engineering_Physics_by_D_C_Ghosh/7-Classical_Statistics_and_Quantum_Statistics.ipynb b/Engineering_Physics_by_D_C_Ghosh/7-Classical_Statistics_and_Quantum_Statistics.ipynb new file mode 100644 index 0000000..30b7e25 --- /dev/null +++ b/Engineering_Physics_by_D_C_Ghosh/7-Classical_Statistics_and_Quantum_Statistics.ipynb @@ -0,0 +1,594 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 7: Classical Statistics and Quantum Statistics" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.10: Interplanar_spacing_for_a_set_of_planes_in_a_cubic_lattice.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.10: Page-380 (2008)\n", +"clc; clear;\n", +"h = 3; k = 2; l = 1; // Miller Indices for planes in a cubic crystal\n", +"a = 4.21D-10; // Interatomic spacing, m\n", +"d = a/(h^2+k^2+l^2)^(1/2); // The interplanar spacing for cubic crystals, m\n", +"printf('\nThe interplanar spacing between consecutive (321) planes = %3.1e m', d);\n", +"\n", +"// Result\n", +"// The interplanar spacing between consecutive (321) planes = 1.1e-010 m " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.11: Determining_Planck_constant_from_given_set_of_X_ray_data.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.11: Page-380 (2008)\n", +"clc; clear;\n", +"e = 1.6e-019; // The energy equivalent of 1 eV, J\n", +"c = 3e+008; // Speed of light in vacuum, m/s\n", +"V = [30 44 50 200]; // Operating voltages of X ray, kV\n", +"lambda_min = [0.414 0.284 0.248 0.062]; // Minimum wavelengths of emitted continuous X rays, angstrom\n", +"for i = 1:1:4\n", +" h = e*V(i)*1e+003*lambda_min(i)*1e-010/c; // Planck's constant, Js\n", +" printf('\nFor V = %d kV and lambda_min = %5.3f angstrom, h = %4.2e Js', V(i), lambda_min(i), h);\n", +"end\n", +" \n", +"// Result\n", +"// For V = 30 kV and lambda_min = 0.414 angstrom, h = 6.62e-034 Js\n", +"// For V = 44 kV and lambda_min = 0.284 angstrom, h = 6.66e-034 Js\n", +"// For V = 50 kV and lambda_min = 0.248 angstrom, h = 6.61e-034 Js\n", +"// For V = 200 kV and lambda_min = 0.062 angstrom, h = 6.61e-034 Js " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.12: Maximum_speed_of_striking_electron_and_the_shortest_wavelength_of_X_ray_produced.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.12: Page-381 (2008)\n", +"clc; clear;\n", +"e = 1.6e-019; // The energy equivalent of 1 eV, J\n", +"m = 9.11e-031; // Rest mass of an electron, kg\n", +"h = 6.62e-034; // Planck's constant, Js\n", +"c = 3e+008; // Speed of light in vacuum, m/s\n", +"V = [20 100]; // Operating voltages of X ray, kV\n", +"for i = 1:1:2\n", +" v = sqrt(2*e*V(i)*1e+003/m); // Maximum striking speed of the electron, m/s\n", +" lambda_min = c*h/(e*V(i)*1e+003*1e-010); // Minimum wavelength of emitted continuous X rays, angstrom\n", +" printf('\nFor V = %d kV:', V(i));\n", +" printf('\nThe maximum striking speed of the electron = %5.2e m/s', v);\n", +" printf('\nThe minimum wavelength of emitted continuous X rays = %5.3f angstrom\n', lambda_min);\n", +"end\n", +" \n", +"// Result\n", +"// For V = 20 kV:\n", +"// The maximum striking speed of the electron = 8.38e+007 m/s\n", +"// The minimum wavelength of emitted continuous X rays = 0.621 angstrom\n", +"//\n", +"// For V = 100 kV:\n", +"// The maximum striking speed of the electron = 1.87e+008 m/s\n", +"// The minimum wavelength of emitted continuous X rays = 0.124 angstrom\n", +"// There are small variation in the answers as approximations are used in the text\n", +" " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.13: Interatomic_spacing_using_Bragg_relation.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.13: Page-381 (2008)\n", +"clc; clear;\n", +"n = 1; // Order of diffraction\n", +"lambda = 1.75e-010; // Wavelength of X rays, m\n", +"h = 1, k = 1, l = 1; // Miller indices for the set of planes\n", +"theta = 30; // Bragg's angle, degree\n", +"// As from Bragg's law, 2*d*sind(theta) = n*lambda and d = a/sqrt(h^2+k^2+l^2). solving for a we have\n", +"a = sqrt(h^2+k^2+l^2)*n*lambda/(2*sind(theta)*1e-010); // Interatomic spacing of the crystal, angstrom\n", +"printf('\nThe interatomic spacing of the crystal = %5.3f angstrom', a);\n", +"\n", +"// Result\n", +"// The interatomic spacing of the crystal = 3.031 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.14: Value_of_Planck_constant_from_Bragg_relation.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.14: Page-382 (2008)\n", +"clc; clear;\n", +"e = 1.6e-019; // The energy equivalent of 1 eV, J\n", +"c = 3e+008; // Speed of light in vacuum, m/s\n", +"n = 1; // Order of diffraction\n", +"d = 2.82e-010; // Interplanar spacing, m\n", +"V = 9.1e+003; // Operating voltage of X rays\n", +"theta = 14; // Bragg's angle, degree\n", +"lambda = 2*d*sind(theta)/n; // Wavelength of X rays, m\n", +"nu = c/lambda; // Frequency of X rays, Hz\n", +"h = e*V/nu; // Planck's constant, Js\n", +"printf('\nThe value of Planck constant, h = %4.2e Js', h);\n", +"\n", +"// Result\n", +"// The value of Planck constant, h = 6.62e-034 Js " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.15: Diffraction_of_X_rays_from_a_crystal.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.15: Page-382 (2008)\n", +"clc; clear;\n", +"e = 1.6e-019; // The energy equivalent of 1 eV, J\n", +"c = 3e+008; // Speed of light in vacuum, m/s\n", +"lambda = 0.5e-010; // Wavelength of X rays, m\n", +"theta = 5; // Bragg's angle, degree\n", +"n = 1; // Order of diffraction\n", +"d = n*lambda/(2*sind(theta)*1e-010); // Interplanar spacing, angstrom\n", +"n = 2; // Ordr of diffraction\n", +"theta1 = asind(n*lambda/(2*d*1e-010)); // Angle at which the second maximum occur, degree\n", +"printf('\nThe spacing between adjacent planes of the crystal = %4.2f angstrom', d);\n", +"printf('\nThe angle at which the second maximum occur = %5.2f degree', theta1);\n", +"\n", +"// Result\n", +"// The spacing between adjacent planes of the crystal = 2.87 angstrom\n", +"// The angle at which the second maximum occur = 10.04 degree " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.16: Wavelength_of_X_rays_from_grating_space_of_the_rock_salt.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.16: Page-383 (2008)\n", +"clc; clear;\n", +"M = 58.5 // Gram atomic mass of NaCl, kg/mole\n", +"N = 6.023e+026; // Avogadro's number per kmol\n", +"rho = 2.17e+003; // Density of NaCl, kg/metre-cube\n", +"m = M/N; // Mass of each NaCl molecule, g\n", +"V = m/rho; // Volume of each NaCl molecule, metre-cube\n", +"d = (V/2)^(1/3)/1e-010; // Atomic apacing in the NaCl crystal, angstrom\n", +"theta = 26; // Bragg's angle, degree\n", +"n = 2; // Order of diffraction\n", +"lambda = 2*d*sind(theta)/n; // Wavelength of X rays, m\n", +"printf('\nThe grating spacing of rock salt = %4.2f angstrom', d);\n", +"printf('\nThe wavelength of X rays = %4.2f angstrom', lambda);\n", +"\n", +"// Result\n", +"// The grating spacing of rock salt = 2.82 angstrom\n", +"// The wavelength of X rays = 1.24 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.17: Diffraction_of_X_rays_by_the_calcite_crystal.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.17: Page-383 (2008)\n", +"clc; clear;\n", +"d = 3.02945e-010; // Atomic apacing in the calcite crystal, m\n", +"lambda_alpha = 0.563e-010; // Wavelength of the K-alpha line of Ag, m\n", +"n = 1; // Order of diffraction\n", +"theta = asind(n*lambda_alpha/(2*d)); // Angle of reflection for the first order, degree\n", +"theta_max = 90; // Angle of reflection for the highest order, degree\n", +"n = 2*d*sind(theta_max)/lambda_alpha; // The highest order for which the line may be observed\n", +"printf('\nThe angle of reflection for the first order = %4.2f degree', theta);\n", +"printf('\nThe highest order for which the line may be observed = %d', n);\n", +"\n", +"// Result\n", +"// The angle of reflection for the first order = 5.33 degree\n", +"// The highest order for which the line may be observed = 10 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.18: Interatomic_spacing_for_given_crystal_planes.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.18: Page-384 (2008)\n", +"clc; clear;\n", +"lambda = 1.8e-010; // Wavelength of the X rays, m\n", +"n = 1; // Order of diffraction\n", +"theta = 60; // Angle of diffraction for the first order, degree\n", +"d = n*lambda/(2*sind(theta)); // Interplanar spacing, m\n", +"// Since for a simple cubic lattice, d_111 = d = a/sqrt(3), solving for a\n", +"a = sqrt(3)*d; // The interatomic spacing for the given crystal planes, m\n", +"printf('\nThe interatomic spacing for the given crystal planes, a = %3.1f angstrom', a/1e-010);\n", +"\n", +"// Result\n", +"// The interatomic spacing for the given crystal planes, a = 1.8 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.19: Smallest_angle_between_the_crystal_plane_and_the_X_ray_beam.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.19: Page-384 (2008)\n", +"clc; clear;\n", +"function [d, m] = deg2degmin(theta)\n", +" d = int(theta);\n", +" m = (theta-d)*60;\n", +"endfunction\n", +"h = 6.626e-034; // Planck's constant, Js\n", +"e = 1.6e-019; // The energy equivalent of 1 eV, J\n", +"c = 3e+008; // Speed of light in vacuum, m/s\n", +"V = 50e+003; // Operating voltage of X ray, V\n", +"lambda_min = h*c/(e*V); // Minimum wavelength of emitted continuous X rays, angstrom\n", +"n = 1; // Order of diffraction\n", +"d = 3.02945e-010; // Interplanar spacing, m\n", +"theta = asind(n*lambda_min/(2*d)); // The smallest angle between the crystal plane and the X ray beam, degree\n", +"[deg , m] = deg2degmin(theta);\n", +"printf('\nThe smallest angle between the crystal plane and the X ray beam = %d degree %d min', deg, m);\n", +"\n", +"// Result\n", +"// The smallest angle between the crystal plane and the X ray beam = 2 degree 21 min " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.1: Atomic_packing_fractions_of_SC_FCC_and_BCC_unit_cells.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.1: Page-376 (2008)\n", +"clc; clear;\n", +"a = poly(0, 'a'); // Lattice parameter for a cubic unit cell, m\n", +"// For simple cubic cell\n", +"n = 1; // Number of atoms per simple cubic unit cell\n", +"r = a/2; // Atomic radius for a simple cubic cell, m\n", +"f = pol2str(int(numer(n*4/3*%pi*r^3/a^3)*100)); // Atomic packing fraction for a simple cubic cell\n", +"printf('\nFor simple cubic cell, f = %s percent', f);\n", +"// For face centered cubic cell\n", +"n = 2; // Number of atoms per face centered cubic unit cell\n", +"r = sqrt(3)/4*a; // Atomic radius for a face centered cubic cell, m\n", +"f = pol2str(int(numer(n*4/3*%pi*r^3/a^3)*100)); // Atomic packing fraction for a face centered cubic cell\n", +"printf('\nFor face centered cubic cell, f = %s percent', f);\n", +"// For body centered cubic cell\n", +"n = 4; // Number of atoms per body centered cubic unit cell\n", +"r = a/(2*sqrt(2)); // Atomic radius for a body centered cubic cell, m\n", +"f = pol2str(int(numer(n*4/3*%pi*r^3/a^3)*100)); // Atomic packing fraction for a body centered cubic cell\n", +"printf('\nFor body centered cubic cell, f = %s percent', f);\n", +"\n", +"// Result\n", +"// For simple cubic cell, f = 52 percent\n", +"// For face centered cubic cell, f = 68 percent\n", +"// For body centered cubic cell, f = 74 percent " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.3: Distance_between_two_adjacent_atoms_in_the_NaCl.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.3: Page-377 (2008)\n", +"clc; clear;\n", +"M = 58.46; // Gram atomic mass of NaCl, g/mole\n", +"N = 6.023e+023; // Avogadro's number\n", +"rho = 2.17; // Density of NaCl, g/cc\n", +"m = M/N; // Mass of each NaCl molecule, g\n", +"n = rho/m; // Number of NaCl molecules per unit volume, molecules/cc\n", +"N = 2*n; // Number of atoms per unit volume, atoms/cc\n", +"a = (1/N)^(1/3); // Distance between two adjacent atoms in the NaCl, cm\n", +"printf('\nThe distance between two adjacent atoms in the NaCl = %4.2f angstrom', a/1e-008);\n", +"\n", +"// Result\n", +"// The distance between two adjacent atoms in the NaCl = 2.82 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.4: Type_of_unit_cell_of_Cs.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.4: Page-377 (2008)\n", +"clc; clear;\n", +"function p = find_cell_type(x)\n", +" if x == 1 then\n", +" p = 'simple cubic';\n", +" end \n", +" if x == 2 then\n", +" p = 'body centered';\n", +" end \n", +" if x == 4 then \n", +" p = 'face centered'; \n", +" end\n", +"endfunction\n", +"M = 130; // Gram atomic weight of Cs, g/mole\n", +"N = 6.023e+023; // Avogadro's number\n", +"rho = 2; // Density of Cs, g/cc\n", +"a = 6e-008; // Distance between two adjacent atoms in the Cs, cm\n", +"m = M/N; // Mass of each Cs atom, g\n", +"x = rho*a^3*N/M; // Number of Cs atoms in cubic unit cell\n", +"c_type = find_cell_type(int(x)); // Call function to determine the type of cell\n", +"printf('\nThe cubic unit cell of Cs is %s.', c_type);\n", +"\n", +"// Result\n", +"// The cubic unit cell of Cs is body centered. " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.5: Miller_indices_of_given_planes.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.5: Page-378 (2008)\n", +"clc; clear;\n", +"m = 2; n = 3; p = 6; // Coefficients of intercepts along three axes\n", +"m_inv = 1/m; // Reciprocate the first coefficient\n", +"n_inv = 1/n; // Reciprocate the second coefficient\n", +"p_inv = 1/p; // Reciprocate the third coefficient\n", +"mul_fact = double(lcm(int32([m,n,p]))); // Find l.c.m. of m,n and p\n", +"m1 = m_inv*mul_fact; // Clear the first fraction\n", +"m2 = n_inv*mul_fact; // Clear the second fraction\n", +"m3 = p_inv*mul_fact; // Clear the third fraction\n", +"printf('\nThe required miller indices are : (%d %d %d) ', m1,m2,m3);\n", +"\n", +"// Result\n", +"// The required miller indices are : (3 2 1) " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.6: Meaning_of_hkl_notation_of_planes.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.6: Page-378 (2008)\n", +"clc; clear;\n", +"// For first set (3, 2, 2)\n", +"m = 3; n = 2; p = 2; // Coefficients of intercepts along three axes\n", +"m_inv = 1/m; // Reciprocate the first coefficient\n", +"n_inv = 1/n; // Reciprocate the second coefficient\n", +"p_inv = 1/p; // Reciprocate the third coefficient\n", +"mul_fact = double(lcm(int32([m,n,p]))); // Find l.c.m. of m,n and p\n", +"m1 = m_inv*mul_fact; // Clear the first fraction\n", +"m2 = n_inv*mul_fact; // Clear the second fraction\n", +"m3 = p_inv*mul_fact; // Clear the third fraction\n", +"printf('\nThe plane (%d %d %d) has intercepts %da, %db and %dc on the three axes.', m, n, p, m1, m2, m3);\n", +"// For second set (1 1 1)\n", +"m = 1; n = 1; p = 1; // Coefficients of intercepts along three axes\n", +"m_inv = 1/m; // Reciprocate the first coefficient\n", +"n_inv = 1/n; // Reciprocate the second coefficient\n", +"p_inv = 1/p; // Reciprocate the third coefficient\n", +"mul_fact = double(lcm(int32([m,n,p]))); // Find l.c.m. of m,n and p\n", +"m1 = m_inv*mul_fact; // Clear the first fraction\n", +"m2 = n_inv*mul_fact; // Clear the second fraction\n", +"m3 = p_inv*mul_fact; // Clear the third fraction\n", +"printf('\nThe plane (%d %d %d) has intercepts a, b and c on the three axes.', m, n, p);\n", +"\n", +"// Result\n", +"// The plane (3 2 2) has intercepts 2a, 3b and 3c on the three axes.\n", +"// The plane (1 1 1) has intercepts a, b and c on the three axes. " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.9: Lengths_of_intercepts_along_y_and_z_axis.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.9: Page-379 (2008)\n", +"clc; clear;\n", +"h = 2; k = 3; l = 1; // Miller indices of the set of planes\n", +"p = 1/h; // Reciprocate h\n", +"q = 1/k; // Reciprocate k\n", +"r = 1/l; // Reciprocate l\n", +"lx = 1.2; // Intercept cut by plane along x-axis, angstrom\n", +"a = 1.2, b = 1.8, c = 2; // Primitives of the crystal, angstrom\n", +"mul_fact = double(lcm(int32([h, k, l]))); // Find l.c.m. of h, k and l\n", +"pa = mul_fact*p*a; \n", +"qb = mul_fact*q*b;\n", +"rc = mul_fact*r*c;\n", +"ly = lx*qb/pa; // Length of intercept along y-axis\n", +"lz = lx*rc/pa; // Length of intercept along z-axis\n", +"printf('\nThe length of intercept along y-axis = %3.1f angstrom', ly);\n", +"printf('\nThe length of intercept along z-axis = %3.1f angstrom', lz);\n", +"\n", +"// Result\n", +"// The length of intercept along y-axis = 1.2 angstrom\n", +"// The length of intercept along z-axis = 4.0 angstrom " + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |