diff options
Diffstat (limited to 'Engineering_Physics_by_D_C_Ghosh')
9 files changed, 5058 insertions, 0 deletions
diff --git a/Engineering_Physics_by_D_C_Ghosh/1-Classical_Mechanics.ipynb b/Engineering_Physics_by_D_C_Ghosh/1-Classical_Mechanics.ipynb new file mode 100644 index 0000000..26940df --- /dev/null +++ b/Engineering_Physics_by_D_C_Ghosh/1-Classical_Mechanics.ipynb @@ -0,0 +1,184 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 1: Classical Mechanics" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.10: Common_velocity_of_a_car_truck_system.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.10: : Page-14 (2008)\n", +"clc; clear;\n", +"m1 = 1200; // Mass of the car, kg\n", +"m2 = 3600; // Mass of the truck, kg\n", +"u1 = 30; // Speed of the car, m/s\n", +"u2 = 20; // Speed of the truck, m/s\n", +"theta = 60; // Direction of motion of the truck w.r.t. that of car, degree\n", +"// As m1*u1 + m2*u2 = (m1 + m2)*v, solving for v along x and y directions\n", +"v_x = (m1*u1 + m2*u2*cosd(theta))/(m1 + m2); // Common speed along x-direction, m/s\n", +"u1 = 0; // The speed of the car after interlocking with the truck, m/s\n", +"v_y = (m1*u1 + m2*u2*sind(theta))/(m1 + m2); // Common speed along y-direction, m/s\n", +"v = sqrt(v_x^2 + v_y^2); // Common speed of the car-truck system, m/s\n", +"theta = atand(v_y/v_x); // Direction of common velocity w.r.t. that of car, degree\n", +"printf('\nThe common speed of the car-truck system = %4.1f m/s', v);\n", +"printf('\nThe direction of common velocity = %4.1f degree north of east', theta);\n", +"// Result \n", +"// The common speed of the car-truck system = 19.8 m/s" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.11: Velocity_of_third_piece_of_the_exploded_object.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.11: Page-14 (2008)\n", +"clc; clear;\n", +"v1 = 20; // Velocity of first piece, m/s\n", +"v2 = 30; // Velocity of second piece, m/s\n", +"// From conservation of momentum, in x-direction \n", +"// m*v1*cosd(0)+m*v2*cosd(45)+m*v3*cosd(theta) = 0, solving for v3*cosd(theta)\n", +"v3_cos_theta = -(v1*cosd(0)+v2*cosd(45)); // x-component of v3 along theta, m/s\n", +"// From conservation of momentum, in y-direction \n", +"// m*v1*sind(0)-m*v2*sind(45)+m*v3*sind(theta) = 0, solving for v3*sind(theta)\n", +"v3_sin_theta = -(v1*sind(0)-v2*sind(45)); // y-component of v3 along theta, m/s\n", +"theta = atand(v3_sin_theta/v3_cos_theta); // Direction of velocity of third piece, degree\n", +"v3 = -(v1*cosd(0)+v2*cosd(45))/cosd(theta+180); // Velocity of third piece, m/s\n", +"printf('\nThe velocity of third piece is %4.1f m/s towards %d degree north of west', v3, ceil(theta+180));\n", +"// Result \n", +"// The velocity of third piece is 46.4 m/s towards 153 degree north of west " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.5: Force_of_contact_between_two_masses.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.5: Page-11 (2008)\n", +"clc; clear;\n", +"m1 = 2; // Mass of first body, kg\n", +"m2 = 1; // Mass of second body, kg\n", +"F = 3; // The horizontal force applied to the mass m1, N\n", +"F_prime = m2/(m1 + m2)*F; // Force of contact between m1 and m2, N\n", +"printf('\nThe force of contact between m1 and m2 = %3.1f N', F_prime);\n", +"F_prime = m1/(m1 + m2)*F; // Force of contact when F is applied to m2, N\n", +"printf('\nThe force of contact when F is applied to m2 = %3.1f N', F_prime);\n", +"// Result \n", +"// The force of contact between m1 and m2 = 1.0 N\n", +"// The force of contact when F is applied to m2 = 2.0 N " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.6: Direction_of_motion_of_a_ball_after_momentum_conservation_during_collision.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.6: Page-12 (2008)\n", +"clc; clear;\n", +"v = 1; // Let the speed of the ball B be unity, unit\n", +"v_prime = v/2; // Speed of the ball after the collision, unit\n", +"theta = atand(v_prime/v); // The direction of motion of the ball A after collision, degree\n", +"printf('\nThe direction of motion of the ball after collision = %2.0f degree', theta);\n", +"// Result \n", +"// The direction of motion of the ball after collision = 27 degree " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.9: Angular_velocity_of_the_combination_of_two_wheels.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.9: Page-14 (2008)\n", +"clc; clear;\n", +"omega1 = 500; // Angular speed of rotating shaft, r.p.m.\n", +"omega2 = 0; // Initial angular speed of the second wheel, r.p.m.\n", +"I = 1; // For simplicity assume moment of ineria of the wheels to be unity\n", +"I1 = I, I2 = I; // Moment of inertia of wheels A and B, kg-Sq.m\n", +"// As I1*omega1 + I2*omega2 = (I1 + I2)*omega, solving for omega\n", +"omega = (I1*omega1 + I2*omega2)/(I1 + I2); // Angular speed of the combination of two wheels, r.p.m.\n", +"printf('\nThe angular speed of the combination of two wheels = %3.0f r.p.m.', omega);\n", +"// Result \n", +"// The angular speed of the combination of two wheels = 250 r.p.m. " + ] + } +], +"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 +} diff --git a/Engineering_Physics_by_D_C_Ghosh/2-Electricity_and_Magnetism.ipynb b/Engineering_Physics_by_D_C_Ghosh/2-Electricity_and_Magnetism.ipynb new file mode 100644 index 0000000..a3cdc5e --- /dev/null +++ b/Engineering_Physics_by_D_C_Ghosh/2-Electricity_and_Magnetism.ipynb @@ -0,0 +1,234 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 2: Electricity and Magnetism" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.12: Work_done_in_moving_a_particle_in_force_field.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.12: Page-80 (2008)\n", +"clc; clear;\n", +"t = poly(0, 't');\n", +"x = t^2 + 1;\n", +"y = 2*t^2;\n", +"z = t^3;\n", +"F = [3*x*y -5*z 10*x]; // Force acting on the particle, N\n", +"t1 = 1; // lower limit\n", +"t2 = 2; // upper limit\n", +"dr = [derivat(x); derivat(y); derivat(z)]; // Infinitesimal displacement, m\n", +"dW = F*dr; // Work done or infinitesimally small displcement, J\n", +"work_exp = sci2exp(dW); // Convert the polynomial to the expression\n", +"W = integrate(work_exp, 't', t1, t2); // Total work done in moving the particle in a force field, J\n", +"printf('\nThe total work done in moving the particle in a force field = %d J', W);\n", +"// Result " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.13: Evaluation_of_force_integral.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.13: Page-80 (2008)\n", +"clc; clear;\n", +"x = poly(0, 'x');\n", +"y = x^2-4;\n", +"F = [x*y (x^2 + y^2)]; // Force acting on the particle, N\n", +"x1 = 2; // lower limit\n", +"x2 = 4; // upper limit\n", +"dr = [derivat(x); derivat(y);]; // Infinitesimal displacement, m\n", +"dW = F*dr; // Work done or infinitesimally small displcement, J\n", +"work_exp = sci2exp(dW); // Convert the polynomial to the expression\n", +"W = integrate(work_exp, 'x', x1, x2); // Total work done in moving the particle in a force field, J\n", +"printf('\nThe total work done in moving the particle in the x-y plane = %d J', W);\n", +"// Result \n", +"// The total work done in moving the particle in the x-y plane = 732 J " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.31: Electric_flux_through_a_surface_area.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.31: Page-93 (2008)\n", +"clc; clear;\n", +"E = [3 4 8]; // Coefficients of i, j and k in the electric field, N/C\n", +"S = [0; 0; 100]; // Coefficients of i, j and k in the area vector, Sq. m\n", +"phi_E = E*S; // Electric flux through the surface, N-Sq.m/C\n", +"printf('\nThe electric flux through the surface = %d N-Sq.m/C', phi_E);\n", +"// Result \n", +"// The electric flux through the surface = 800 N-Sq.m/C " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.32: Electric_flux_through_an_area_in_XY_plane.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.32: Page-93 (2008)\n", +"clc; clear;\n", +"E = [8 4 3]; // Coefficients of i, j and k in the electric field, N/C\n", +"S = [0; 0; 100]; // Coefficients of i, j and k in the area vector, Sq. m\n", +"phi_E = E*S; // Electric flux through the surface, N-Sq.m/C\n", +"printf('\nThe electric flux through the area in XY plane = %d N-Sq.m/C', phi_E);\n", +"// Result \n", +"// The electric flux through the area in XY plane = 300 N-Sq.m/C " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.33: Electric_flux_through_a_surface_in_YZ_plane.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.33: Page-93 (2008)\n", +"clc; clear;\n", +"E = [2 3 4]; // Coefficients of i, j and k in the electric field, N/C\n", +"S = [10; 0; 0]; // Coefficients of i, j and k in the area vector, Sq. m\n", +"phi_E = E*S; // Electric flux through the surface, N-Sq.m/C\n", +"printf('\nThe electric flux through the surface in YZ plane = %d N-Sq.m/C', phi_E);\n", +"// Result \n", +"// The electric flux through the surface in YZ plane = 20 N-Sq.m/C" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.39: Magnetic_field_due_to_a_straight_conductor_carrying_current.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.39: Page-96 (2008)\n", +"clc; clear;\n", +"mu_0 = 4*%pi*1e-007; // Absolute magnetic permeability of free space, N/ampere-square\n", +"I = 15; // Current through the wire, A\n", +"x = 1e-002; // Distance of observation point from the wire, m\n", +"B = mu_0/(4*%pi)*2*I/x; // Magnetic field at 1 cm distance, T\n", +"printf('\nThe magnetic field due to the current carrying wire at %d cm distance = %1.0e tesla', x/1e-002, B);\n", +"x = 5; // Distance of observation point from the infinite straight conductor, m\n", +"I = 100; // Current through the straight conductor, A\n", +"B = mu_0/(4*%pi)*2*I/x; // Magnetic field at 1 cm distance, T\n", +"printf('\nThe magnetic field due to the current carrying infinite straight conductor at %d m distance = %1.0e tesla', x, B);\n", +"// Result \n", +"// The magnetic field due to the current carrying wire at 1 cm distance = 3e-004 tesla\n", +"// The magnetic field due to the current carrying infinite straight conductor at 5 m distance = 4e-006 tesla " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.40: Force_between_two_current_carrying_straight_wires.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.40: Page-96 (2008)\n", +"clc; clear;\n", +"mu_0 = 4*%pi*1e-007; // Absolute magnetic permeability of free space, N/ampere-square\n", +"I1 = 30; // Current through the first wire, A \n", +"I2 = 40; // Current through the second wire, A \n", +"x = 2; // Separation distance between two wires, m\n", +"F = mu_0/(4*%pi)*2*I1*I2/x; // Force between two current carrying straight wires, N\n", +"printf('\nThe force between two current carrying straight wires = %3.1e N', F);\n", +"// Result\n", +"// The force between two current carrying straight wires = 1.2e-004 N " + ] + } +], +"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 +} diff --git a/Engineering_Physics_by_D_C_Ghosh/3-Vibration_Waves_and_Light.ipynb b/Engineering_Physics_by_D_C_Ghosh/3-Vibration_Waves_and_Light.ipynb new file mode 100644 index 0000000..3e3b6a1 --- /dev/null +++ b/Engineering_Physics_by_D_C_Ghosh/3-Vibration_Waves_and_Light.ipynb @@ -0,0 +1,1672 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 3: Vibration Waves and Light" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.a_02: Frequency_of_particle_executing_SHM.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3a.a.2: Page-132 (2008)\n", +"clc; clear;\n", +"m = 10; // Mass of the particle, g\n", +"x = poly(0, 'x');\n", +"V = 50*x^2 + 100; // Potential field surrounding the particle, erg/g\n", +"U = m*V; // Potential energy of the particle field system, erg\n", +"F = -derivat(U); // Force acting on the particle, dyne\n", +"// As F = -m*a = -m*omega^2*x = -m*(2%pi*f)^2*x, solving for f\n", +"f = sqrt(eval(pol2str(-pdiv(F,x)/m)))/(2*%pi); // Frequency of oscillations of the particle executing SHM, Hz\n", +"printf('\nThe frequency of oscillations of the particle executing SHM = %4.2f Hz', f);\n", +"\n", +"// Result\n", +"// The frequency of oscillations of the particle executing SHM = 1.59 Hz " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.a_03: A_body_executing_SHM.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3a.a.3:Page-133 (2008)\n", +"clc; clear;\n", +"v1 = 80; // Velocity of the body at 3 cm displacement, cm/s\n", +"v2 = 60; // Velocity of the body at 4 cm displacement, cm/s\n", +"x1 = 3; // Displacement of the body at velocity of 80 cm/s\n", +"x2 = 4; // Displacement of the body at velocity of 60 cm/s\n", +"// As v = omega*sqrt(a^2 - x^2), solving for a\n", +"a = poly(0, 'a');\n", +"a = roots(v1^2*(a^2-16) - v2^2*(a^2 - 9));\n", +"omega = v1/sqrt(a(1)^2 - x1^2); // Angular ferquency of the oscillations, rad/s\n", +"x = a(1); // Maximum displacement, cm\n", +"// As x = a*sin(omega*t), solving for t\n", +"t_ex = asin(x/a(1))/omega; // Time taken to reach the +ve extremity, s\n", +"d = a(1) - 2.5; // Distance of the point from the mean position, cm\n", +"t = asin(d/a(1))/omega; // Time taken to travel from mean position to positive extremity, s\n", +"printf('\nThe time taken to travel from 2.5 cm from +ve extremity = %5.3f s', t_ex - t); \n", +"\n", +"// Result\n", +"// The time taken to travel from 2.5 cm from +ve extremity = 0.052 s " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.a_04: Time_period_of_a_body_oscillating_in_the_tunnel_across_the_earth.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3a.a.4: Page-134 (2008)\n", +"clc; clear;\n", +"R = 6.4e+006; // Radius of the earth, m\n", +"g = 10; // Acceleration due to gravity, m/sec-square\n", +"T = 2*%pi*sqrt(R/g); // Time period of oscillations of the body, s\n", +"printf('\nThe time period of oscillations of the body = %4.1f min', T/60);\n", +"\n", +"// Result\n", +"// The time period of oscillations of the body = 83.8 min " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.a_05: Resultant_amplitude_and_phase_angle_relative_to_the_first_SHM.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3a.a.5: Page-135 (2008)\n", +"clc; clear;\n", +"phi1 = 0; // Phase of the first SHM, degree\n", +"phi2 = 60; // Phase of the second SHM, degree\n", +"phi3 = 90; // Phase of the third SHM, degree\n", +"a1 = 1.0; // Amplitude of the first SHM, cm\n", +"a2 = 1.5; // Amplitude of the second SHM, cm\n", +"a3 = 2.0; // Amplitude of the third SHM, cm\n", +"A = sqrt((a1 + a2*cosd(phi2)+a3*cosd(phi3))^2 + (a2*sind(phi2)+a3*sind(phi3))^2); // Resultant amplitude relative to the first SHM, cm\n", +"phi = atand((a2*sind(phi2)+a3*sind(phi3))/(a1 + a2*cosd(phi2)+a3*cosd(phi3))); // Resultant phase angle relative to the first SHM, degree\n", +"printf('\nThe resultant amplitude and phase angle relative to the first SHM = %4.2f cm and %2d degrees respectively', A, phi);\n", +"\n", +"// Result\n", +"// The resultant amplitude and phase angle relative to the first SHM are 3.73 cm and 62 degrees respectively" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.a_07: Two_SHMs_acting_in_the_same_direction.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3a.a.7:Page-136 (2008)\n", +"clc; clear;\n", +"phi1 = 0; // Phase of the first SHM, degree\n", +"phi2 = 45; // Phase of the second SHM, degree\n", +"a1 = 0.005; // Amplitude of the first SHM, m\n", +"a2 = 0.002; // Amplitude of the second SHM, m\n", +"A = sqrt((a1 + a2*cosd(phi2))^2 + (a2*sind(phi2))^2); // Resultant amplitude relative to the first SHM, m\n", +"phi = atand(a2*sind(phi2)/(a1 + a2*cosd(phi2))); // Resultant phase angle relative to the first SHM, degree\n", +"printf('\nThe amplitude of the resultant displacement and phase angle relative to the first SHM are %7.5f m and %5.2f degrees respectively', A, phi);\n", +"\n", +"// Result\n", +"// The amplitude of the resultant displacement and phase angle relative to the first SHM are 0.00657 m and 12.43 degrees respectively " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.a_11: A_spring_disc_system_undergoing_damped_oscillation.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3a.b.1: Page-138 (2008)\n", +"clc; clear;\n", +"m = 100; // Mass of the horizontal disc, g\n", +"t = 60; // Time during which the amplitude reduces to half of its undamped value, s\n", +"f = 10; // Frequency of oscillations of the system, Hz\n", +"omega_prime = 2*%pi*f; // Angular frequency of the oscillations, rad/s\n", +"A0 = 1; // Assume the amplitude of undamped oscillations to be unity, cm\n", +"// As A = A0*exp(-k*t), solving for k\n", +"A = A0/2; // Amplitude of damped oscillations after 1 min, cm\n", +"k = log(A0/A)/t; // Resisting force per unit mass per unit velocity, nepers/sec\n", +"r = 2*k*m; // Resistive force constant, sec/cm\n", +"tau = 1/k; // Relaxation time, sec\n", +"Q = m*omega_prime/r; // Quality factor\n", +"s = m*(omega_prime^2 + k^2); // Force constant of the spring, dynes/Sq.cm\n", +"printf('\nThe resistive force constant = %4.2f dyne-sec/cm', r);\n", +"printf('\nThe relaxation time of the system = %4.2f sec', tau);\n", +"printf('\nThe quality factor, Q = %4.2f', Q);\n", +"printf('\nThe force constant of the spring = %4.2e dyne/Sq.cm', s);\n", +"\n", +"// Result\n", +"// The resistive force constant = 2.31 dyne-sec/cm\n", +"// The relaxation time of the system = 86.56 sec\n", +"// The quality factor, Q = 2719.42\n", +"// The force constant of the spring = 3.95e+005 dyne/Sq.cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.a_12: A_mass_executing_damped_oscillations_in_one_dimension.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3a.b.2: Page-139 (2008)\n", +"clc; clear;\n", +"function m = check_motion_type(k, omega0)\n", +" if k > omega0 then\n", +" m = 'aperiodic';\n", +" else if k == omega0 then\n", +" m = 'criticallydamped';\n", +" else if k < omega0 then\n", +" m = 'oscillatory';\n", +" end\n", +" end\n", +" end\n", +"endfunction\n", +"m = 10; // Mass of the body, g\n", +"s = 10; // Restoring force, dyne/cm\n", +"r = 2; // Resistive force constant, dyne.sec/cm\n", +"k = r/(2*m); // Resisting force, nepers/sec\n", +"// As omega0^2 = s/m, solving for omega0\n", +"omega0 = sqrt(s/m); // Angular frequency, rad/s\n", +"motion = check_motion_type(k, omega0); // Check for the type of motion\n", +"r_new = 2*sqrt(m*s); // Resistive force constant, dyne-sec/cm\n", +"m = r^2/(4*s); // Mass for which the given forces makes the motion critically damped, g\n", +"printf('\nThe motion is %s in nature', motion);\n", +"printf('\nThe resistive force constant = %d dyne-sec/cm', r_new);\n", +"printf('\nThe mass for which the given forces makes the motion critically damped = %3.1f g', m);\n", +"\n", +"// Result\n", +"// The motion is oscillatory in nature\n", +"// The resistive force constant = 20 dyne-sec/cm\n", +"// The mass for which the given forces makes the motion critically damped = 0.1 g " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.a_14: A_mass_executing_damped_oscillations_in_one_dimension.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3a.b.4: Page-140 (2008)\n", +"clc; clear;\n", +"m = 1; // Mass of the suspended body, kg\n", +"s = 25; // Stifness constant of the spring, N/m\n", +"r = poly(0, 'r');\n", +"// As f0/f_prime = 2/sqrt(3), solving for r\n", +"r = roots(4*(s/m-r^2/(4*m^2))-3*s/m); // Damping factor, kg/sec\n", +"printf('\nThe damping factor of damped oscillations = %d kg/sec', r(1));\n", +"\n", +"// Result\n", +"// The damping factor of damped oscillations = 5 kg/sec " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.a_15: Resisting_force_for_critically_damped_motion.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"// Scilab Code Ex3a.b.5: Page-141 (2008)\n", +"clc; clear;\n", +"function m = check_motion_type(k, omega0)\n", +" if k > omega0 then\n", +" m = 'aperiodic';\n", +" else if k == omega0 then\n", +" m = 'criticallydamped';\n", +" else if k < omega0 then\n", +" m = 'oscillatory';\n", +" end\n", +" end\n", +" end\n", +"endfunction\n", +"m = 10; // Mass of the oscillating body, g\n", +"r = 2; // Resisting force, dyne-sec/cm\n", +"s = 5; // Restoring force, dyne/cm\n", +"k = r/(2*m); // Resisting force, nepers/sec\n", +"// As omega0^2 = s/m, solving for omega0\n", +"omega0 = sqrt(s/m); // Angular frequency, rad/s\n", +"motion = check_motion_type(k, omega0); // Check for the type of motion\n", +"r = 2*sqrt(m*s); // Resistive force constant for critical damping, dyne-sec/cm\n", +"printf('\nThe motion is %s in nature', motion);\n", +"printf('\nThe resistive force constant for critical damping = %4.1f dyne-sec/cm', r);\n", +"\n", +"// Result\n", +"// The motion is oscillatory in nature\n", +"// The resistive force constant for critical damping = 14.1 dyne-sec/cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.a_16: Damped_oscillatory_motio.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3a.b.6: Page-141 (2008)\n", +"clc; clear;\n", +"m = 0.1; // Mass of the oscillating body, kg\n", +"t = 50; // Time during which the energy of system decays to 1/e of its undamped value, s\n", +"s = 10; // Spring constant, N/m\n", +"E0 = 1; // Assume the energy of undamped oscillations to be unity, erg\n", +"// As E = E0*exp(-k*t) and E/E0 = 1/e, solving for k\n", +"E = E0/%e; // Energy of damped oscillations after 50 sec, erg\n", +"k = log(E0/E)/t; // Resisting force per unit mass per unit velocity, nepers/sec\n", +"p = m*k; // A resistive force constant, N-s/m\n", +"omega0 = sqrt(s/m); // Angular frequency in the absence of damping, rad/sec\n", +"omega_prime = sqrt(omega0^2 - k^2/4); // Angular frequency when damping takes place, rad/sec\n", +"Q = omega_prime/k; // Quality factor\n", +"printf('\nThe resistive force constant, p = %1.0e N-s/m', p);\n", +"printf('\nThe quality factor, Q = %d', ceil(Q));\n", +"\n", +"// Result\n", +"// The resistive force constant, p = 2e-003 N-s/m\n", +"// The quality factor, Q = 500 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.a_17: Damped_simple_harmonic_motion.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3a.b.7: Page-142 (2008)\n", +"clc; clear;\n", +"t = 10; // Time during which the amplitude reduces to 1/10th of its undamped value, s\n", +"f = 200; // Frequency of oscillations of the system, Hz\n", +"omega0 = 2*%pi*f; // Angular frequency of the oscillations, rad/s\n", +"A0 = 1; // Assume the amplitude of undamped oscillations to be unity, cm\n", +"// As A = A0*exp(-k*t), solving for k\n", +"A = A0/10; // Amplitude of damped oscillations after 10 sec, cm\n", +"k = log(A0/A)/t; // Resisting force per unit mass per unit velocity, nepers/sec\n", +"tau = 1/(2*k); // Relaxation time, sec\n", +"Q = omega0*tau; // Quality factor\n", +"E0 = 1; // Assume energy of undamped oscillations to be unity, erg\n", +"E = E0/10; // Energy of damped oscillations after t sec, erg\n", +"// As E = E0*exp(-2*k*t), solving for t\n", +"t = 1/(2*k)*log(E0/E); // Time during which the energy falls to 1/10 of its initial value, sec\n", +"printf('\nThe relaxation time = %4.2f sec', tau);\n", +"printf('\nThe quality factor, Q = %d', Q);\n", +"printf('\nThe time during which the energy falls to 1/10 of its initial value = %d sec', t);\n", +"printf('\nThe damping constant, k = %4.2f', k);\n", +"\n", +"// Result\n", +"// The relaxation time = 2.17 sec\n", +"// The quality factor, Q = 2728\n", +"// The time during which the energy falls to 1/10 of its initial value = 5 sec\n", +"// The damping constant, k = 0.23 \n", +"// The answer for Q is given wrongly in the textbook" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.a_21: Characteristics_of_progressive_waves.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3a.c.1: Page-143 (2008)\n", +"clc; clear;\n", +"// Comparing with the standard progressive wave equation, we have\n", +"a = 0.5; // Amplitude of the wave, m\n", +"lambda = 2*%pi/12.56; // Wavelength of the wave, m\n", +"v = 314/12.56; // Wave velocity, m/s\n", +"nu = v/lambda; // Frequency of the wave, Hz\n", +"printf('\nThe amplitude of the wave = %3.1f m', a);\n", +"printf('\nThe wavelength of the wave = %3.1f m', lambda);\n", +"printf('\nThe velocity of the wave = %d m/s', v);\n", +"printf('\nThe frequency of the wave = %d Hz', ceil(nu));\n", +"\n", +"// Result\n", +"// The amplitude of the wave = 0.5 m\n", +"// The wavelength of the wave = 0.5 m\n", +"// The velocity of the wave = 25 m/s\n", +"// The frequency of the wave = 50 Hz " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.a_22: A_simple_harmonic_wave_travelling_along_X_axis.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3a.c.2: Page-144 (2008)\n", +"clc; clear;\n", +"// Comparing with the standard progressive wave equation, we have\n", +"a = 5; // Amplitude of the wave, m\n", +"nu = 0.2; // Frequency of the wave, Hz\n", +"lambda = 1/0.5; // Wavelength of the wave, m\n", +"v = nu*lambda; // Wave velocity, m/s\n", +"printf('\nThe amplitude of the wave = %3.1f m', a);\n", +"printf('\nThe wavelength of the wave = %3.1f m', lambda);\n", +"printf('\nThe velocity of the wave = %3.1f m/s', v);\n", +"printf('\nThe frequency of the wave = %3.1f Hz', nu);\n", +"\n", +"// Result\n", +"// The amplitude of the wave = 5.0 m\n", +"// The wavelength of the wave = 2.0 m\n", +"// The velocity of the wave = 0.4 m/s\n", +"// The frequency of the wave = 0.2 Hz " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.a_23: Travelling_wave_characteristics_and_phase_difference.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3a.c.3: Page-144 (2008)\n", +"clc; clear;\n", +"// Comparing with the standard progressive wave equation, we have\n", +"a = 8; // Amplitude of the wave, cm\n", +"nu = 4/2; // Frequency of the wave, Hz\n", +"lambda = 2/0.02; // Wavelength of the wave, cm\n", +"v = nu*lambda; // Wave velocity, cm/s\n", +"delta_x = 20; // Path difference between two particles, cm\n", +"delta_phi = delta_x*2*%pi/lambda*180/%pi; // Phase difference between two particles, degree\n", +"printf('\nThe amplitude of the wave = %3.1f cm', a);\n", +"printf('\nThe wavelength of the wave = %3.1f cm', lambda);\n", +"printf('\nThe velocity of the wave = %3.1f cm/s', v);\n", +"printf('\nThe frequency of the wave = %d Hz', nu);\n", +"printf('\nThe phase difference between two particles = %d degree', delta_phi);\n", +"\n", +"// Result\n", +"// The amplitude of the wave = 8.0 cm\n", +"// The wavelength of the wave = 100.0 cm\n", +"// The velocity of the wave = 200.0 cm/s\n", +"// The frequency of the wave = 2 Hz\n", +"// The phase difference between two particles = 72 degree " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.b_101: Brewster_angle_and_angle_of_refraction_for_glass.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3b.1: Page-163 (2008)\n", +"clc; clear;\n", +"mu = 1.5; // Refractive indexof glass\n", +"i_p = atand(mu); // Angle of polarization from Brewster's law, degree\n", +"r = 90 - i_p; // Angale of refraction, degree\n", +"printf('\nThe Brewster angle for glass = %4.1f degree', i_p);\n", +"printf('\nThe angle of refraction for glass = %4.1f degree', r);\n", +"\n", +"// Result\n", +"// The Brewster angle for glass = 56.3 degree\n", +"// The angle of refraction for glass = 33.7 degree " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.b_102: Polarizing_angles_for_various_pair_of_media.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3b.2: Page-163 (2008)\n", +"clc; clear;\n", +"// Function to convert degree to degree-minute\n", +"function [d,m]= deg2deg_min(deg)\n", +" d = int(deg);\n", +" m = (deg - d)*60;\n", +"endfunction\n", +"mu_air = 1; // Refractive index fo air\n", +"mu_glass = 1.54; // Refractive index of glass\n", +"mu_water = 1.33; // Refractive index of water\n", +"// Air to glass incidence\n", +"i_p = atand(mu_glass/mu_air); // Angle of polarization for air to glass incidence, degree\n", +"printf('\nFor air to glass, i_p = %d degree', i_p);\n", +"// glass to air incidence\n", +"i_p = atand(mu_air/mu_glass); // Angle of polarization for glass to air incidence, degree\n", +"printf('\nFor glass to air, i_p = %d degree', ceil(i_p));\n", +"// Water to glass incidence\n", +"i_p = atand(mu_glass/mu_water); // Angle of polarization for water to glass incidence, degree\n", +"[d,m] = deg2deg_min(i_p); // Call function to convert to deg-min\n", +"printf('\nFor water to glass, i_p = %d degree %d min', d, m);\n", +"// Glass to water incidence\n", +"i_p = atand(mu_water/mu_glass); // Angle of polarization for glass to water incidence, degree\n", +"[d,m] = deg2deg_min(i_p); // Call function to convert to deg-min\n", +"printf('\nFor glass to water, i_p = %d degree %d min', d, m);\n", +"// Air to water incidence\n", +"i_p = atand(mu_water/mu_air); // Angle of polarization for air to water incidence, degree\n", +"[d,m] = deg2deg_min(i_p); // Call function to convert to deg-min\n", +"printf('\nFor air to water, i_p = %d degree %d min', d, m);\n", +"// Water to air incidence\n", +"i_p = atand(mu_air/mu_water); // Angle of polarization for water to airincidence, degree\n", +"[d,m] = deg2deg_min(i_p); // Call function to convert to deg-min\n", +"printf('\nFor water to air, i_p = %d degree %d min', d, m);\n", +"\n", +"// Result\n", +"// For air to glass, i_p = 57 degree\n", +"// For glass to air, i_p = 33 degree\n", +"// For water to glass, i_p = 49 degree 11 min\n", +"// For glass to water, i_p = 40 degree 48 min\n", +"// For air to water, i_p = 53 degree 3 min\n", +"// For water to air, i_p = 36 degree 56 min " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.b_103: Polarizing_angle_for_glass.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3b.3: Page-163 (2008)\n", +"clc; clear;\n", +"C = 40; // Critical angle for glass to air\n", +"mu = 1/sind(C); // Refractive index of glass w.r.t. air\n", +"i_p = atand(mu); // Polarizing angle for glass, degree\n", +"printf('\nThe polarizing angle for glass = %4.1f degree', i_p);\n", +"\n", +"// Result\n", +"// The polarizing angle for glass = 57.3 degree " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.b_104: Polarization_by_reflection.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3b.4: Page-164 (2008)\n", +"clc; clear;\n", +"i = 60; // Angle of incidence, degree\n", +"i_p = i; // Angle of polarization, degree\n", +"mu = tand(i_p); // Refractive index of the medium\n", +"r = 90 - i; // Angle of refraction, degree\n", +"printf('\nThe refractive index of transparent medium = %5.3f', mu);\n", +"printf('\nThe angle of refraction, r = %d degree', r);\n", +"printf('\nThe reflected and transmitted components are at right angles to each other.');\n", +"\n", +"// Result\n", +"// The refractive index of transparent medium = 1.732\n", +"// The angle of refraction, r = 30 degree\n", +"// The reflected and transmitted components are at right angles to each other." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.b_105: Intensity_ratio_of_two_beams_through_analyser.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3b.5: Page-164 (2008)\n", +"clc; clear;\n", +"theta_A = 30; // Angle between principal sections of polariser and analyser for beam A, degree\n", +"theta_B = 60; // Angle between principal sections of polariser and analyser for beam B, degree\n", +"// As I_A*cosd(theta_A)^2 = I_B*cosd(theta_B)^2, solving for I ratio\n", +"I_ratio = cosd(theta_B)^2/cosd(theta_A)^2; // The intensity ratio of the two beams\n", +"printf('\nThe intensity ratio of the two beams = %4.2f', I_ratio);\n", +"\n", +"// Result\n", +"// The intensity ratio of the two beams = 0.33" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.b_106: Percentage_reduction_in_the_intensity_of_the_inident_light.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3b.6: Page-165 (2008)\n", +"clc; clear;\n", +"theta = [30 45 60 90]; // Angles between principal sections of polariser and analyser, degree\n", +"for i = 1:1:4\n", +" P_red = (1-cosd(theta(i))^2)*100; // Percentage reduction in intensity of incident light\n", +" printf('\nFor theta = %d degree, percentage reduction = %1.0f percent', theta(i), P_red);\n", +"end\n", +"\n", +"// Result\n", +"// For theta = 30 degree, percentage reduction = 25 percent\n", +"// For theta = 45 degree, percentage reduction = 50 percent\n", +"// For theta = 60 degree, percentage reduction = 75 percent\n", +"// For theta = 90 degree, percentage reduction = 100 percent " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.b_107: Angle_of_rotation_of_polaroid_to_reduce_the_intensity.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3b.7: Page-165 (2008)\n", +"clc; clear;\n", +"// For half reduction in intensity\n", +"I_ratio = 1/2; // Intensity ratio\n", +"theta = acosd(sqrt(I_ratio)); // Angle of rotation of polaroid, degree\n", +"printf('\nFor half reduction in intensity, the angle of rotation = %d degree', theta);\n", +"// For one-fourth reduction in intensity\n", +"I_ratio = 1/4; // Intensity ratio\n", +"theta = acosd(sqrt(I_ratio)); // Angle of rotation of polaroid, degree\n", +"printf('\nFor one-fourth reduction in intensity, the angle of rotation = %d degree', theta);\n", +"\n", +"// Result\n", +"// For half reduction in intensity, the angle of rotation = 45 degree\n", +"// For one-fourth reduction in intensity, the angle of rotation = 60 degree " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.c_202: Ratio_of_maximum_to_minimum_intensity_in_the_interference_fringe_system.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3c.2: Page-184 (2008)\n", +"clc; clear;\n", +"I2 = 1; // Assume intensity of light beam from the second source to be unity\n", +"I1 = 81*I2; // Intensity of light beam from the first source\n", +"a = sqrt(I1); // Width of the first slit, mm\n", +"b = sqrt(I2); // Width of the second slit, mm\n", +"I_max = (1+a/b)^2; // Maximum intensity in the fringe pattern\n", +"I_min = (1-a/b)^2; // Minimum intensity in the fringe pattern\n", +"fact = gcd([I_max,I_min]); // Find l.c.m. of I_max and I_min\n", +"printf('\nThe ratio of maximum to minimum intensity in the fringe system, I_max:I_min = %d:%d', I_max/4, I_min/4);\n", +"\n", +"// Result\n", +"// The ratio of maximum to minimum intensity in the fringe system, I_max:I_min = 25:16 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.c_203: Wavelength_of_light_from_interference_of_fringes.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3c.3: Page-184 (2008)\n", +"clc; clear;\n", +"d = 0.1; // Separation between the two slits, cm\n", +"D = 100; // Distance between the source and the slit, cm\n", +"bita = 0.05; // Fringe width, cm\n", +"lambda = bita*d/D; // Wavelength of light, cm\n", +"printf('\nThe wavelength of light used = %4d angstrom', lambda/1e-008);\n", +"\n", +"// Result\n", +"// The wavelength of light used = 5000 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.c_204: Fringe_width_from_interference_pattern.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3c.4: Page-184 (2008)\n", +"clc; clear;\n", +"d = 0.3; // Separation between the two slits, cm\n", +"D = 60; // Distance between the source and the slit, cm\n", +"lambda = 59e-006; // Wavelength of light, cm\n", +"bita = lambda*D/d; // Fringe width, cm\n", +"printf('\nThe fringe width = %4.2e cm', bita);\n", +"\n", +"// Result\n", +"// The fringe width = 1.18e-002 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.c_205: Distance_between_the_two_coherent_sources.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3c.5: Page-185 (2008)\n", +"clc; clear;\n", +"D = 80; // Distance between the source and the slit, cm\n", +"lambda = 5890e-008; // Wavelength of light, cm\n", +"bita = 9.424e-002; // Fringe width, cm\n", +"d = lambda*D/bita; // Separation between the two slits, cm\n", +"printf('\nThe distance between the two coherent sources = %4.2f cm', d);\n", +"\n", +"// Result\n", +"// The distance between the two coherent sources = 0.05 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.c_206: Distance_between_consecutive_interference_bands.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3c.6: Page-185 (2008)\n", +"clc; clear;\n", +"D = 100; // Distance between the source and the slit, cm\n", +"lambda = 5893e-008; // Wavelength of light, cm\n", +"d1 = 4.05e-001; // Distance between the images of the two slits in one position, cm\n", +"d2 = 2.90e-001; // Distance between the images of the two slits in second position, cm\n", +"d = sqrt(d1*d2); // Separation between the two slits, cm\n", +"bita = lambda*D/d; // Fringe width, cm\n", +"printf('\nThe distance between consecutive interference bands = %6.4f cm', bita);\n", +"\n", +"// Result\n", +"// The distance between consecutive interference bands = 0.0172 cm" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.c_207: Wavelength_of_the_light_used_in_biprism_experiment.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3c.7: Page-185 (2008)\n", +"clc; clear;\n", +"D = 1.2; // Distance between the source and the slit, m\n", +"d = 7.5e-004; // Separation between the two slits, cm\n", +"n = 20; // Number of fringes crossed in the field of view\n", +"bita = 1.888e-002/n; // Fringe width, cm\n", +"lambda = bita*d/D; // Wavelength of light, cm\n", +"printf('\nThe wavelength of the light used in biprism experiment = %4d angstrom', lambda/1e-010);\n", +"\n", +"// Result\n", +"// The wavelength of the light used in biprism experiment = 5900 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.c_208: Number_of_fringes_obtained_with_the_given_wavelength.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3c.8: Page-186 (2008)\n", +"clc; clear;\n", +"lambda1 = 5893; // First wavelength of light, angstrom\n", +"lambda2 = 4358; // Second wavelength of light, angstrom\n", +"n = 40; // Number of fringes obtained with first wavelength\n", +"// As bita1/bita2 = lambda1/lambda2, so\n", +"x = n*lambda1/lambda2; // Number of fringes obtained with the seocond wavelength\n", +"printf('\nThe number of fringes obtained with the given wavelength = %d', x);\n", +"\n", +"// Result\n", +"// The number of fringes obtained with the given wavelength = 54 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.c_209: Wavelength_of_light_from_biprism_interference_pattern.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3c.9: Page-186 (2008)\n", +"clc; clear;\n", +"D = 100; // Distance between the source and the slit, cm\n", +"bita = 0.0135; // Fringe width, cm\n", +"alpha = %pi/360; // Angle of refracting face with the base of biprism, radian\n", +"mu = 1.5; // Refractive index of the material of biprism\n", +"x = 50; // Distance between slit and the biprism, cm\n", +"d = 2*(mu-1)*x*alpha; // Separation between the two virtual slits, cm\n", +"lambda = bita*d/D; // Wavelength of light, cm\n", +"printf('\nThe wavelength of light from biprism interference pattern = %4d angstrom', lambda/1e-008);\n", +"\n", +"// Result\n", +"// The wavelength of light from biprism interference pattern = 5890 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.c_210: Fringe_width_observed_at_one_metre_distance_from_biprism.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3c.10: Page-187 (2008)\n", +"clc; clear;\n", +"mu = 1.5; // Refractive index of the material of biprism\n", +"alpha = %pi/180; // Base angle of biprism, radian\n", +"D = 110; // Distance between the source and the slit, cm\n", +"x = 10; // Distance between slit and the biprism, cm\n", +"d = 2*(mu-1)*x*alpha; // Separation between the two virtual slits, cm\n", +"lambda = 5900e-008; // Wavelength of light, cm\n", +"bita = lambda*D/d; // Fringe width, cm\n", +"printf('\nThe fringe width observed at one metre distance from biprism = %6.4f cm', bita);\n", +"\n", +"// Result\n", +"// The fringe width observed at one metre distance from biprism = 0.0372 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.c_211: Wavelength_of_light_in_Newton_ring_experiment.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3c.11: Page-187 (2008)\n", +"clc; clear;\n", +"D_n = 0.42; // Diameter of nth ring, cm\n", +"D_mplusn = 0.7; // Diameter of (m+n)th ring, cm\n", +"m = 14; // Difference between (m+n)th and nth rings\n", +"R = 100; // Radius of curvature of the plano-convex lens, m\n", +"lambda = (D_mplusn^2 - D_n^2)/(4*m*R); // Wavelength of the light, cm\n", +"printf('\nThe wavelength of the light used = %4d angstrom', lambda/1e-008);\n", +"\n", +"// Result\n", +"// The wavelength of the light used = 5600 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.c_212: Radius_of_plano_convex_lens.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3c.12: Page-187 (2008)\n", +"clc; clear;\n", +"D5 = 0.336; // Diameter of 5th ring, cm\n", +"D10plus5 = 0.590; // Diameter of (10+5)th ring, cm\n", +"m = 10; // Difference between (10+5)th and 5th rings\n", +"lambda = 5890e-008; // Wavelength of the light, cm\n", +"R = (D10plus5^2 - D5^2)/(4*m*lambda); // Radius of curvature of the plano-convex lens, m\n", +"printf('\nThe radius of plano convex lens = %5.2f cm', R);\n", +"\n", +"// Result\n", +"// The radius of plano convex lens = 99.83 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.c_213: Wavelenght_of_light_used_in_obtaining_Newton_rings.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3c.13: Page-187 (2008)\n", +"clc; clear;\n", +"D3 = 0.181; // Diameter of 3rd ring, cm\n", +"D23 = 0.501; // Diameter of 23rd ring, cm\n", +"m = 23-3; // Difference between (m+n)th and nth rings\n", +"R = 50; // Radius of curvature of the plano-convex lens, m\n", +"lambda = (D23^2 - D3^2)/(4*m*R); // Wavelength of the light, cm\n", +"printf('\nThe wavelength of the light used = %4d angstrom', lambda/1e-008);\n", +"\n", +"// Result\n", +"// The wavelength of the light used = 5456 angstrom" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.c_214: Diameter_of_the_20th_dark_ring.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3c.14: Page-188 (2008)\n", +"clc; clear;\n", +"D4 = 0.4; // Diameter of 4th ring, cm\n", +"D12 = 0.7; // Diameter of 12th ring, cm\n", +"m = 12-4; // Difference between (m+n)th and nth rings\n", +"lambda_R = (D12^2 - D4^2)/(4*m); // Wavelength-Radius product, Sq.cm\n", +"D20 = sqrt(80*lambda_R); // Diameter of the 20th dark ring, cm\n", +"printf('\nThe diameter of the 20th dark ring = %5.3f cm', D20);\n", +"\n", +"// Result\n", +"// The diameter of the 20th dark ring = 0.908 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.c_215: Radius_of_curvature_of_the_lens_and_the_thickness_of_the_air_film.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3c.15: Page-188 (2008)\n", +"clc; clear;\n", +"D10 = 0.50; // Diameter of 10th ring, cm\n", +"n = 10; // Number of dark fringe\n", +"lambda = 6250e-008; // Wavelength of light used, cm\n", +"R = D10^2/(4*n*lambda); // Radius of curvature of the lens, cm\n", +"t = D10^2/(8*R); // Thickness of the air film, cm\n", +"printf('\nThe radius of curvature of the lens = %3d cm', R);\n", +"printf('\nThe thickness of the air film = %9.7f cm', t);\n", +"\n", +"// Result\n", +"// The radius of curvature of the lens = 100 cm\n", +"// The thickness of the air film = 0.0003125 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.c_216: Newton_rings_observed_in_reflected_light.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3c.16: Page-188 (2008)\n", +"clc; clear;\n", +"D10 = 5e-003; // Diameter of 10th ring, cm\n", +"n = 10; // Number of dark fringe\n", +"lambda = 5.9e-007; // Wavelength of reflected light, m\n", +"R = D10^2/(4*n*lambda); // Radius of curvature of the lens, cm\n", +"t = D10^2/(8*R); // Thickness of the air film, cm\n", +"printf('\nThe radius of curvature of the lens = %5.3f m', R);\n", +"printf('\nThe thickness of the air film = %4.2e m', t);\n", +"\n", +"// Result\n", +"// The radius of curvature of the lens = 1.059 m\n", +"// The thickness of the air film = 2.95e-006 m " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.c_217: Smallest_thickness_of_the_glass_film_in_which_it_appears_dark.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3c.17: Page-189 (2008)\n", +"clc; clear;\n", +"lambda = 5893e-010; // Wavelength of light used, m\n", +"mu = 1.5; // Refractive index of glass film\n", +"r = 60; // Angle of reflection in the film, degree\n", +"t = lambda/(2*mu*cosd(r)); // Smallest thickness of the \n", +"printf('\nThe smallest thickness of the glass film when it appears dark = %6.1f angstrom', t/1e-010);\n", +"\n", +"// Result\n", +"// The smallest thickness of the glass film when it appears dark = 3928.7 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.d_301: Wavelength_of_light_used_in_diffraction_due_to_narrow_slit.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3d.1: Page-205 (2008)\n", +"clc; clear;\n", +"D = 200; // Distance between the source and the slit, cm\n", +"a = 0.02; // Slit width, cm\n", +"x = 0.5; // Position of first minimum, cm\n", +"n = 1; // Order of diffraction\n", +"lambda = a*x/(D*n); // Wavelength of light used, cm\n", +"printf('\nThe wavelength of light used = %4d angstrom', lambda/1e-008);\n", +"\n", +"// Result\n", +"// The wavelength of light used = 5000 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.d_302: Separation_between_the_second_minima_on_either_side_of_the_central_maximum.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3d.2: Page-205 (2008)\n", +"clc; clear;\n", +"f = 20; // Focal length of the lens, cm\n", +"a = 0.06; // Slit width, cm\n", +"n = 2; // Order of diffraction\n", +"lambda = 6e-005; // Wavelength of light used, cm\n", +"x = 2*lambda*f/a; // Separation between the second minima on either side of the central maximum, cm\n", +"printf('\nThe separation between the second minimum an central maximum = %4.2f cm', x);\n", +"\n", +"// Result\n", +"// The separation between the second minimum an central maximum = 0.04 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.d_303: Distance_of_the_first_dark_band_from_the_axis.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3d.3: Page-206 (2008)\n", +"clc; clear;\n", +"n = 1; // Order of diffraction\n", +"f = 40; // Focal length of the lens, cm\n", +"a = 0.03; // Slit width, cm\n", +"lambda = 5890e-008; // Wavelength of the light used, cm\n", +"// As a*sind(theta) = n*lambda, solving for theta\n", +"theta = asin(n*lambda/a); // The angle of diffraction corresponding to the first minimum, radian\n", +"x = f*theta; // The distance of the first dark band from the axis, cm \n", +"printf('\nThe distance of the first dark band from the axis = %6.4f cm', x);\n", +"\n", +"// Result\n", +"// The distance of the first dark band from the axis = 0.0785 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.d_304: Angle_of_diffraction_for_the_principal_maxima.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3d.4: Page-206 (2008)\n", +"clc; clear;\n", +"lambda1 = 5890e-008; // Wavelength of D1 line of sodium lamp, cm\n", +"lambda2 = 5896e-008; // Wavelength of D2 line of sodium lamp, cm\n", +"d_lambda = lambda2 - lambda1; // Wavelength difference, cm\n", +"w = 0.5; // Width of the grating, cm\n", +"N = 2500; // Total number of grating lines\n", +"N_prime = N/w; // Number of lines per cm, lines/cm\n", +"a_plus_b = 1/N_prime; // Grating element, cm\n", +"n = 1; // Order of diffraction\n", +"// Case 1\n", +"theta = asind(n*lambda1/a_plus_b); // Angle of diffraction for D1 line, degree\n", +"// Case 2\n", +"theta_prime = asind(n*lambda2/a_plus_b); // Angle of diffraction for D2 line, degree\n", +"printf('\nThe angle of diffraction for D1 and D2 lines of sodium are %5.2f dgree and %5.2f degree respectively.', theta, theta_prime);\n", +"// From the condition for just resolution, lambda/d_lambda = n*N, solving for N\n", +"N_min = lambda1/(d_lambda*n); // Minimum number of lines required on the grating\n", +"if N_min < N then\n", +" printf('\nThe two lines are well resolved.');\n", +"else\n", +" printf('\nThe two lines are not resolved.');\n", +"end\n", +"\n", +"// Result\n", +"// The angle of diffraction for D1 and D2 lines of sodium are 17.13 dgree and 17.15 degree respectively.\n", +"// The two lines are well resolved. " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.d_305: Wavelength_of_the_spectral_line.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3d.5: Page-207 (2008)\n", +"clc; clear;\n", +"N = 4250; // Number of lines per cm of grating, lines/cm\n", +"a_plus_b = 1/N; // Grating element, cm\n", +"n = 2; // Order of diffraction\n", +"theta = 30; // Angle of diffraction, degree\n", +"lambda = sind(theta)*a_plus_b/n; // Wavelength of spectral line from diffraction condition, cm\n", +"printf('\nThe wavelength of spectral line from diffraction condition = %4d angstrom', lambda/1e-008);\n", +"\n", +"// Result\n", +"// The wavelength of spectral line from diffraction condition = 5882 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.d_306: Number_of_lines_in_one_centimeter_of_the_grating_surface.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3d.6: Page-207 (2008)\n", +"clc; clear;\n", +"n = 2; // Order of diffraction\n", +"lambda = 5e-005; // Wavelength of light, cm\n", +"theta = 30; // Angle of diffraction, degree\n", +"N = sind(theta)/(n*lambda); // Number of lines per cm of grating, lines/cm\n", +"printf('\nThe number of lines per cm of grating = %4d per cm', ceil(N));\n", +"\n", +"// Result\n", +"// The number of lines per cm of grating = 5000 per cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.d_307: Highest_order_spectrum_obtainable_with_the_given_diffraction_grating.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3d.7: Page-208 (2008)\n", +"clc; clear;\n", +"N = 5000; // Number of lines per cm ruled on grating, lines/cm\n", +"lambda = 6e-005; // Wavelength of light, m\n", +"a_plus_b = 1/N; // Grating element, m\n", +"theta = 90; // Maximum angle of diffraction, degree\n", +"n = a_plus_b*sind(theta)/lambda; // Order of diffraction\n", +"printf('\nIn highest order spectrum obtainable with the given diffraction grating = %4.2f', n);\n", +"\n", +"// Result\n", +"// In highest order spectrum obtainable with the given diffraction grating = 3.33 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.d_308: Invisible_third_and_higher_order_principal_maxima_in_a_diffraction_grating.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3d.8: Page-208 (2008)\n", +"clc; clear;\n", +"lambda = 5.5e-007; // Wavelength of light, m\n", +"a_plus_b = 1.5e-006; // Grating element, m\n", +"theta = 90; // Maximum angle of diffraction, degree\n", +"n = a_plus_b*sind(theta)/lambda; // Order of diffraction\n", +"printf('\nIn this diffraction grating only %dnd order will be visible while %drd and higher orders are not possible.', n, n+1);\n", +"\n", +"// Result\n", +"// In this diffraction grating only 2nd order will be visible while 3rd and higher orders are not possible. " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.d_309: Number_of_lines_per_cm_on_the_grating.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3d.9: Page-208 (2008)\n", +"clc; clear;\n", +"theta = 30; // Maximum angle of diffraction, degree\n", +"lambda1 = 5400e-010; // Wavelength of light giving certain diffraction order, m\n", +"lambda2 = 4050e-010; // Wavelength of light giving higher diffraction order, m\n", +"n = poly(0, 'n');\n", +"n = roots(lambda1*n-(n+1)*lambda2); // Order of diffraction for first wavelength\n", +"a_plus_b = n*lambda1/sind(theta); // Grating element, m\n", +"N = 1/a_plus_b; // Number of lines per cm ruled on grating, lines/cm\n", +"printf('\nThe number of lines per cm on the diffraction grating = %d lines per cm', N/100);\n", +"\n", +"// Result\n", +"// The number of lines per cm on the diffraction grating = 3086 lines per cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.d_310: Minimum_number_of_lines_on_the_diffraction_grating.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3d.10: Page-209 (2008)\n", +"clc; clear;\n", +"lambda = 5890e-008; // Wavelength of light, cm\n", +"n = 1; // Order of diffraction\n", +"d_lambda = 6e-008; // Difference in wavelengths of D1 and D2 lines, cm\n", +"N = lambda/(n*d_lambda); // Number of lines on grating\n", +"printf('\nThe minimum number of lines on the diffraction grating = %d', ceil(N));\n", +"\n", +"// Result\n", +"// The minimum number of lines on the diffraction grating = 982 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.d_311: Design_of_a_plane_transmission_diffraction_grating.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3d.11: Page-209 (2008)\n", +"clc; clear;\n", +"lambda = 6000e-008; // Wavelength of light, cm\n", +"n = 2; // Order of diffraction\n", +"d_lambda = 6e-008; // Difference in wavelengths of D1 and D2 lines, cm\n", +"N = lambda/(n*d_lambda); // Number of lines on grating\n", +"printf('\nThe minimum number of lines in the required diffraction grating = %d', N);\n", +"\n", +"// Result\n", +"// The minimum number of lines in the required diffraction grating = 500 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.d_312: EX3_d_312.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3d.12: Page-209 (2008)\n", +"clc; clear;\n", +"lambda = 5890e-008; // Wavelength of light, cm\n", +"n = 2; // Order of diffraction\n", +"d_lambda = 6e-008; // Difference in wavelengths of D1 and D2 lines, cm\n", +"w = 2.5; // Width of the grating, cm\n", +"N = lambda/(n*d_lambda); // Number of lines on grating\n", +"printf('\nThe minimum number of lines per cm in the diffraction grating = %5.1f', N/w);\n", +"\n", +"// Result\n", +"// The minimum number of lines per cm in the diffraction grating = 196.3 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.d_313: Maximum_resolving_power_of_a_plane_transmission_grating.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3d.13: Page-210 (2008)\n", +"clc; clear;\n", +"lambda = 5000e-008; // Wavelength of light, cm\n", +"theta = 90; // Angle of diffraction for the maximum resolving power, degree\n", +"N = 40000; // Number of lines on grating\n", +"a_plus_b = 12.5e-005; // Grating element, cm\n", +"n = 2; // Order of diffraction\n", +"n_max = N*a_plus_b*sind(theta)/lambda; // Maximum resolving power\n", +"printf('\nThe maximum resolving power = %d', n_max);\n", +"\n", +"// Result\n", +"// The maximum resolving power = 100000 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.d_314: Maximum_number_of_lines_of_a_grating.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3d.14: Page-209 (2008)\n", +"clc; clear;\n", +"lambda = 5890e-008; // Wavelength of light, cm\n", +"n = 3; // Order of diffraction\n", +"d_lambda = 6e-008; // Difference in wavelengths of D1 and D2 lines, cm\n", +"N = lambda/(n*d_lambda); // Maximum number of lines of a grating\n", +"printf('\nThe maximum number of lines of the grating = %d', N);\n", +"\n", +"// Result\n", +"// The maximum number of lines of the grating = 327 " + ] + } +], +"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 +} diff --git a/Engineering_Physics_by_D_C_Ghosh/4-Special_Theory_of_Relativity.ipynb b/Engineering_Physics_by_D_C_Ghosh/4-Special_Theory_of_Relativity.ipynb new file mode 100644 index 0000000..30894df --- /dev/null +++ b/Engineering_Physics_by_D_C_Ghosh/4-Special_Theory_of_Relativity.ipynb @@ -0,0 +1,372 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 4: Special Theory of Relativity" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.10: Relativisti_variation_of_mass_of_electron_with_velocity.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.10: Page-238 (2008)\n", +"clc; clear;\n", +"c = 3e+008; // Speed of light in vacuum, m/s\n", +"m0 = 9.1e-031; // Rest mass of the electron, kg\n", +"E0 = m0*c^2; // Rest energy of the electron, J\n", +"printf('\nThe rest energy of the electron = %4.2f MeV', E0/1.6e-013);\n", +"E = 1.25*E0; // Total energy of the particle\n", +"v = sqrt(1-(E0/E)^2)*c; // Velocity of the particle from relativistic variation of mass with speed, m/s\n", +"printf('\nThe velocity of the electron when its total energy is 1.25 times its rest energy = %3.1f c = %3.1e cm/s', v/c, v);\n", +"\n", +"// Result\n", +"// The rest energy of the electron = 0.51 MeV\n", +"// The velocity of the electron when its total energy is 1.25 times its rest energy = 0.6 c = 1.8e+008 cm/s" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.11: An_electron_subjected_to_relativistic_motion.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.11: Page-238 (2008)\n", +"clc; clear;\n", +"c = 3e+008; // Speed of light in vacuum, m/s\n", +"v = 0.99*c; // Speed of the electron, m/s\n", +"m0 = 9.1e-031; // Rest mass of the electron, kg\n", +"m = m0/sqrt(1-v^2/c^2); // Moving mass of the electron, kg\n", +"E = m*c^2; // Total energy of the electron, J\n", +"printf('\nThe total energy of the electron = %4.2e J', E);\n", +"KE_ratio = m0/(2*(m-m0))*(v/c)^2; // Ratio of Newtonian kinetic energy to the relativistic kinetic energy\n", +"printf('\nThe ratio of Newtonian kinetic energy to the relativistic kinetic energy = %4.2f', KE_ratio);\n", +"\n", +"// Result\n", +"// The total energy of the electron = 5.81e-013 J\n", +"// The ratio of Newtonian kinetic energy to the relativistic kinetic energy = 0.08 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.1: Fringe_shift_in_the_Michelson_Morley_experiment.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.1: Page-233 (2008)\n", +"clc; clear;\n", +"c = 3e+008; // Speed of light in vacuum, m/s\n", +"v = 3e+004; // Speed of earth, m/s\n", +"d = 7; // Effective length of each path, m\n", +"lambda = 7000e-010; // Wavelength of light used, m\n", +"n = 2*d*v^2/(lambda*c^2); // Fringe shift\n", +"printf('\nThe expected fringe shift = %3.1f', n);\n", +"\n", +"// Result\n", +"// The expected fringe shift = 0.2 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.2: Apparent_length_of_rod_relative_to_the_observer.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.2: Page-233 (2008)\n", +"clc; clear;\n", +"c = 3e+008; // Speed of light in vacuum, m/s\n", +"v = 3e+007; // Speed of metre rod, m/s\n", +"L0 = 1; // Actual length of the rod, m\n", +"L = L0*sqrt(1-v^2/c^2); // Apparent length of rod from Lorentz transformation, m\n", +"printf('\nThe apparent length of rod realtive to the observer = %5.3f m', L);\n", +"\n", +"// Result\n", +"// The apparent length of rod realtive to the observer = 0.995 m " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.3: Apparent_length_of_a_meter_stick_for_different_speeds.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.3: Page-234 (2008)\n", +"clc; clear;\n", +"c = 3e+008; // Speed of light in vacuum, m/s\n", +"v = [c c/sqrt(2) sqrt(3)/2*c c/2 0.8*c]; // Different speeds of metre rod, m/s\n", +"L0 = 100; // Actual length of the rod, cm\n", +"for i = 1:1:5\n", +" L = L0*sqrt(1-v(i)^2/c^2); // Apparent length of rod from Lorentz transformation, m\n", +" printf('\nFor v = %4.2e m/s, L = %4.1f cm', v(i), L);\n", +"end\n", +"\n", +"// Result\n", +"// For v = 3.00e+008 m/s, L = 0.0 cm\n", +"// For v = 2.12e+008 m/s, L = 70.7 cm\n", +"// For v = 2.60e+008 m/s, L = 50.0 cm\n", +"// For v = 1.50e+008 m/s, L = 86.6 cm\n", +"// For v = 2.40e+008 m/s, L = 60.0 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.4: Lorentz_transformations_applied_to_a_rigid_bar.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.4: Page-235-236 (2008)\n", +"clc; clear;\n", +"c = 3e+008; // Speed of light in vacuum, m/s\n", +"// Part (a)\n", +"v = 0.98*c ; // Speed of the rigid bar, m/s\n", +"L2 = 1.5; // Length of the rigid bar in S_prime frame, m\n", +"L1 = L2*sqrt(1-v^2/c^2); // Apparent length of rod from Lorentz transformation, m\n", +"theta2 = 45; // Angle which the bar makes w.r.t. x-aixs in S_prime frame, degree\n", +"theta1 = atand(tand(theta2)/sqrt(1-v^2/c^2)); // Orientation of bar relative to S frame, degree\n", +"printf('\nThe orientation of the %d m bar relative to S frame = %4.1f degree', L2, theta1);\n", +"// Part(b)\n", +"v = 0.6*c ; // Speed of the rigid bar, m/s\n", +"L2 = 5; // Length of the rigid bar in S_prime frame, m\n", +"L1 = L2*sqrt(1-v^2/c^2); // Apparent length of rod from Lorentz transformation, m\n", +"theta2 = 30; // Angle which the bar makes w.r.t. x-aixs in S_prime frame, degree\n", +"theta1 = atand(tand(theta2)/sqrt(1-v^2/c^2)); // Orientation of bar relative to S frame, degree\n", +"printf('\nThe orientation of the %d m bar relative to S frame = %4.1f degree', L2, theta1);\n", +"\n", +"// Result\n", +"// The orientation of the 1 m bar relative to S frame = 78.7 degree\n", +"// The orientation of the 5 m bar relative to S frame = 35.8 degree " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.5: Velocity_of_pi_meso.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.5: Page-236 (2008)\n", +"clc; clear;\n", +"c = 3e+008; // Speed of light in vacuum, m/s\n", +"t0 = 2.5e-008; // Proper life time of pi-meson, s\n", +"t = 2.5e-007; // MEan life time of pi-meson, s\n", +"// As t = t0/(sqrt(1-v^2/c^2)), solving for v\n", +"v = sqrt(1-(t0/t)^2)*c; // Velocity of pi meson, m/s\n", +"printf('\nThe velocity of pi meson = %5.3f c = %4.2e m/s', v/c, v);\n", +"\n", +"// Result\n", +"// The velocity of pi meson = 0.995 c = 2.98e+008 m/s " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.6: Relative_speed_of_the_ships_as_measured_by_an_observer.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.6: Page-237 (2008)\n", +"clc; clear;\n", +"c = 3e+008; // Speed of light in vacuum, m/s\n", +"v = 0.8*c; // Speed of the first spaceship, m/s\n", +"u_prime = 0.9*c; // Speed of the second spaceship, m/s\n", +"u = (u_prime+v)/(1+u_prime*v/c^2); // Relative speed of the ships as measured by the observer on either one from Velocity addition rule, m/s\n", +"printf('\nThe relative speed of the ships as measured by an observer in either one = %5.3f c = %4.2e m/s', u/c, u);\n", +"\n", +"// Result\n", +"// The relative speed of the ships as measured by an observer in either one = 0.988 c = 2.97e+008 m/s " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.7: Velocity_of_one_particle_relative_to_the_other.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.7: Page-237 (2008)\n", +"clc; clear;\n", +"c = 3e+008; // Speed of light in vacuum, m/s\n", +"v = 0.9*c; // Speed of the first particle, m/s\n", +"u_prime = 0.9*c; // Speed of the oppositely moving second particle, m/s\n", +"u = (u_prime+v)/(1+u_prime*v/c^2); // Velocity of one particle relative to the other from Velocity addition rule, m/s\n", +"printf('\nThe velocity of one particle relative to the other = %5.3f c = %4.2e m/s', u/c, u);\n", +"\n", +"// Result\n", +"// The velocity of one particle relative to the other = 0.994 c = 2.98e+008 m/s " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.8: Velocity_of_the_rocket_as_observed_from_the_earth.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.8: Page-237 (2008)\n", +"clc; clear;\n", +"c = 3e+008; // Speed of light in vacuum, m/s\n", +"// Case 1: when velocity of firing is away from the earth\n", +"v = 0.5*c; // Speed of the rocket away from the earth, m/s\n", +"u_prime = 0.8*c; // Speed of the outgoing spaceship relative to earth, m/s\n", +"u = (u_prime+v)/(1+u_prime*v/c^2); // Velocity of rocket moving away relative to the earth, m/s\n", +"printf('\nThe velocity of rocket moving away relative to the earth = %4.2f c = %4.2e m/s', u/c, u);\n", +"// Case 2: when velocity of firing is towards the earth\n", +"v = 0.5*c; // Speed of the rocket moving towards the earth, m/s\n", +"u_prime = -0.8*c; // Speed of the outgoing spaceship relative to earth, m/s\n", +"u = (u_prime+v)/(1+u_prime*v/c^2); // Velocity of approaching rocket relative to the earth, m/s\n", +"printf('\nThe velocity of approaching rocket relative to the earth = %3.1f c = %3.1e m/s', u/c, u);\n", +"\n", +"// Result\n", +"// The velocity of rocket moving away relative to the earth = 0.93 c = 2.79e+008 m/s\n", +"// The velocity of approaching rocket relative to the earth = -0.5 c = -1.5e+008 m/s " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.9: Velocity_of_the_particle_when_its_total_energy_is_thrice_its_rest_energy.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.9: Page-237 (2008)\n", +"clc; clear;\n", +"c = 3e+008; // Speed of light in vacuum, m/s\n", +"E0 = 1; // Assume the rest energy of the particle to be unity\n", +"E = 3*E0; // Total energy of the particle\n", +"v = sqrt(1-(E0/E)^2)*c; // Velocity of the particle from relativistic variation of mass with speed, m/s\n", +"printf('\nThe velocity of the particle when its total energy is thrice its rest energy = %5.3e cm/s', v);\n", +"\n", +"// Result\n", +"// The velocity of the particle when its total energy is thrice its rest energy = 2.828e+008 cm/s " + ] + } +], +"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 +} diff --git a/Engineering_Physics_by_D_C_Ghosh/5-Quantum_Mechanics.ipynb b/Engineering_Physics_by_D_C_Ghosh/5-Quantum_Mechanics.ipynb new file mode 100644 index 0000000..b842eda --- /dev/null +++ b/Engineering_Physics_by_D_C_Ghosh/5-Quantum_Mechanics.ipynb @@ -0,0 +1,841 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 5: Quantum Mechanics" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.10: Planck_constant_and_threshold_wavelength_of_metal.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.10: Page-288 (2008)\n", +"clc; clear;\n", +"c = 3e+008; // Speed of light, m/s\n", +"KE1 = 3.62e-019; // Maximum kinetic energy of photoelectrons with first wavelength, eV\n", +"lambda1 = 3000; // First wavelength of incident radiation, angstrom\n", +"KE2 = 0.972e-019; // Maximum kinetic energy of photoelectrons with second wavelength, eV\n", +"lambda2 = 5000; // Second wavelength of incident radiation, angstrom\n", +"A = [c/lambda1, -1; c/lambda2, -1]; // Declare a square matrix as per Einstein's Photoelectric relation, KE = h*c/lambda - phi\n", +"B = [KE1; KE2]; // Put KEs in a column matrix\n", +"X = inv(A)*B; // Apply inverse multiplication of a matrix to fing h and phi\n", +"lambda0 = X(1)*1e-010*c/X(2); // Threshold wavelength of metal, m\n", +"printf('\nh = %4.2e Js\nphi = %1.0e J', X(1)*1e-010, X(2));\n", +"printf('\nThe threshold wavelength of metal = %d angstrom', ceil(lambda0/1e-010));\n", +"\n", +"// Result\n", +"// h = 6.62e-034 Js\n", +"// phi = 3e-019 J\n", +"// The threshold wavelength of metal = 6620 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.11: Energy_and_wavelength_of_incident_photon.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.11: Page-288 (2008)\n", +"clc; clear;\n", +"c = 3e+008; // Speed of light, m/s\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J\n", +"h = 6.62e-034; // Planck's constant, Js\n", +"m0 = 9.1e-031; // Rest mass of an electron, kg\n", +"alpha = 90; // Scattering angle for X-ray photon, degree\n", +"d_lambda = h/(m0*c)*(1-cosd(alpha)); // Wavelength shift after collision, m\n", +"lambda = d_lambda; // Wavelength of the incident photon according to the condition, m\n", +"E = h*c/(lambda*e*1e+006); // Energy of the incident photon, MeV\n", +"printf('\nThe wavelength of the incident photon = %6.4e m', lambda);\n", +"printf('\nThe energy of the incident photon = %4.2f MeV', E);\n", +"\n", +"// Result\n", +"// The wavelength of the incident photon = 2.4249e-012 m\n", +"// The energy of the incident photon = 0.51 MeV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.12: Energy_lost_by_an_X_ray_photon_in_collsion_with_an_electron.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.12: Page-289 (2008)\n", +"clc; clear;\n", +"c = 3e+008; // Speed of light, m/s\n", +"e = 1.602e-019; // Energy equivalent of 1 eV, J\n", +"h = 6.6e-034; // Planck's constant, Js\n", +"lambda = 0.1; // Wavelength of X ray photon, angstrom\n", +"m0 = 9.1e-031; // Rest mass of an electron, kg\n", +"alpha = 90; // Scattering angle for X-ray photon, degree\n", +"d_lambda = h/(m0*c*1e-010)*(1-cosd(alpha)); // Wavelength shift after collision, angstrom\n", +"lambda_prime = lambda + d_lambda; // Wavelength of the scattered photon, angstrom\n", +"dE = h*c*1e+010/e*(1/lambda - 1/lambda_prime); // Energy lost by the X ray photon by collision, eV\n", +"printf('\nThe energy lost by the X ray photon by collision = %4.1f KeV', dE/1e+003);\n", +"\n", +"// Result\n", +"// The energy lost by the X ray photon by collision = 24.1 KeV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.13: The_Compton_effect_stidied_at_different_scattering_angles.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.13: Page-289 (2008)\n", +"clc; clear;\n", +"c = 3e+008; // Speed of light, m/s\n", +"e = 1.602e-019; // Energy equivalent of 1 eV, J\n", +"h = 6.6e-034; // Planck's constant, Js\n", +"m0 = 9.1e-031; // Rest mass of an electron, kg\n", +"alpha = [90 60 45 180]; // Different scattering angle for X-ray photon, degrees\n", +"d_lambda = zeros(4);\n", +"for i = 1:1:4\n", +" d_lambda(i) = h/(m0*c*1e-010)*(1-cosd(alpha(i))); // Wavelength shift after collision, angstrom\n", +" printf('\nFor alpha = %d degree, d_lambda = %6.4f angstrom', alpha(i), d_lambda(i));\n", +"end\n", +"lambda = 0.2; // Given wavelength of incident X-ray photon, angstrom\n", +"lambda_prime = lambda + d_lambda(3); // Wavelength of the scattered photon at 45 degree, angstrom\n", +"printf('\nThe wavelength of the photon scattered at 45 degree = %5.3f angstrom', lambda_prime);\n", +"lambda_prime = lambda + d_lambda(4); // Maximum wavelength of the photon scattered at 180 degree, angstrom\n", +"KE_max = h*c*1e+010*(1/lambda - 1/lambda_prime); // Maximum kinetic energy of the recoil electron, J\n", +"printf('\nThe maximum kinetic energy of the recoil electron = %4.2e J', KE_max);\n", +"\n", +"// Result\n", +"// For alpha = 90 degree, d_lambda = 0.0242 angstrom\n", +"// For alpha = 60 degree, d_lambda = 0.0121 angstrom\n", +"// For alpha = 45 degree, d_lambda = 0.0071 angstrom\n", +"// For alpha = 180 degree, d_lambda = 0.0484 angstrom\n", +"// The wavelength of the photon scattered at 45 degree = 0.207 angstrom\n", +"// The maximum kinetic energy of the recoil electron = 1.93e-015 J " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.15: de_Broglie_wavelength_associated_with_moving_masses.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.15: Page-292 (2008)\n", +"clc; clear;\n", +"h = 6.6e-034; // Planck's constant, Js\n", +"// For golf ball\n", +"m = 0.046; // Mass of the golf ball, kg\n", +"v = 36; // Velocity of the golf ball, m/s\n", +"lambda = h/(m*v); // de-Broglie wavelength associated with the moving golf ball, m\n", +"printf('\nThe de-Broglie wavelength associated with the moving golf ball = %1.0e m', lambda);\n", +"if lambda/1e-010 > 0.1 then\n", +" printf('\nThe moving golf ball may exhibit wave character.');\n", +"end\n", +"// For an electron\n", +"m = 9.11e-031; // Mass of the electron, kg\n", +"v = 1e+007; // Velocity of the electron, m/s\n", +"lambda = h/(m*v); // de-Broglie wavelength associated with the moving electron, m\n", +"printf('\nThe de-Broglie wavelength associated with the moving electron = %3.1e m', lambda);\n", +"if lambda/1e-010 > 0.1 then\n", +" printf('\nThe moving electron may exhibit wave character.');\n", +"end\n", +"\n", +"// Result\n", +"// The de-Broglie wavelength associated with the moving golf ball = 4e-034 m\n", +"// The de-Broglie wavelength associated with the moving electron = 7.2e-011 m\n", +"// The moving electron may exhibit wave character. " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.16: Voltage_applied_to_the_electron_microscope_to_produce_the_required_wavelength.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.16: Page-292 (2008)\n", +"clc; clear;\n", +"h = 6.62e-034; // Planck's constant, Js\n", +"e = 1.602e-019; // Energy equivalent of 1 eV, J\n", +"lambda = 0.40e-010; // de-Broglie wavelength associated with the moving electron, m\n", +"m = 9.11e-031; // Rest mass of an electron, kg\n", +"V = (h/lambda)^2/(2*m*e); // Voltage applied to the electron microscope to produce the required wavelength, volt\n", +"printf('\nThe voltage applied to the electron microscope to produce the required de-Broglie wavelength = %5.1f volt', V);\n", +"\n", +"// Result\n", +"// The voltage applied to the electron microscope to produce the required de-Broglie wavelength = 938.4 volt " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.18: de_Broglie_wavelength_of_a_neutron_of_given_energy.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.18: Page-293 (2008)\n", +"clc; clear;\n", +"h = 6.62e-034; // Planck's constant, Js\n", +"e = 1.602e-019; // Energy equivalent of 1 eV, J\n", +"E_k = 12.8e+006; // Energy of the moving neutron, eV\n", +"m0 = 1.675e-027; // Rest mass of a neutron, kg\n", +"lambda = h/sqrt(2*m0*E_k*e) // de-Broglie wavelength associated with the moving neutron, m\n", +"printf('\nThe de-Broglie wavelength of the moving neutron = %3.1e angstrom', lambda/1e-010);\n", +"\n", +"// Result\n", +"// The de-Broglie wavelength of the moving neutron = 8.0e-005 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.19: EX5_19.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.19: Page-294 (2008)\n", +"clc; clear;\n", +"h = 6.62e-034; // Planck's constant, Js\n", +"e = 1.602e-019; // Energy equivalent of 1 eV, J\n", +"m = 1.67e-027; // Rest mass of a proton, kg\n", +"r = 5e-015; // Radius of the nucleus, m\n", +"delta_x = 2*r; // Minimum uncertainty in position of the proton, m\n", +"delta_p = h/(2*%pi*delta_x); // Minimum uncertainty in proton's momentum, kg-m/s\n", +"KE = delta_p^2/(2*m); // Minimum kinetic emergy of the proton, J\n", +"printf('\nThe minimum uncertainty in momentum of the proton = %4.2e kg-m/s', delta_p);\n", +"printf('\nThe minimum kinetic emergy of the proton = %5.3f MeV', KE/(e*1e+006));\n", +"\n", +"// Result\n", +"// The minimum uncertainty in momentum of the proton = 1.05e-020 kg-m/s\n", +"// The minimum kinetic emergy of the proton = 0.207 MeV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.20: Minimum_uncertainty_in_the_measurement_of_velocity_of_the_electron.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.20: Page-294 (2008)\n", +"clc; clear;\n", +"h = 6.62e-034; // Planck's constant, Js\n", +"m = 9.11e-031; // Rest mass of a electron, kg\n", +"delta_x = 1e-009; // Minimum uncertainty in position of the electron, m\n", +"delta_p_min = h/delta_x; // Minimum uncertainty in electron's momentum, kg-m/s\n", +"delta_v = delta_p_min/m; // Minimum uncertainty in the measurement of velocity of the electron, m/s\n", +"printf('\nThe minimum uncertainty in the measurement of velocity of the electron = %4.2e m/s', delta_v);\n", +"\n", +"// Result\n", +"// The minimum uncertainty in the measurement of velocity of the electron = 7.27e+005 m/s " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.22: Minimum_uncertainty_in_the_position_of_the_particle.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.22: Page-295 (2008)\n", +"clc; clear;\n", +"h = 6.62e-034; // Planck's constant, Js\n", +"m = 1e-009; // Mass of the particle, kg\n", +"v = 1; // Velocity of the particle, m/s\n", +"delta_v = v*0.01/100; // Minimum uncertainty in the velocity of the particle, m/s\n", +"delta_x = h/(m*delta_v); // Minimum uncertainty in the position of the particle, m \n", +"printf('\nThe minimum uncertainty in the position of the particle = %4.2e m', delta_x);\n", +"\n", +"// Result\n", +"// The minimum uncertainty in the position of the particle = 6.62e-021 m " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.23: Uncertainty_with_which_position_of_the_electron_can_be_located.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.23: Page-295 (2008)\n", +"clc; clear;\n", +"h = 6.62e-034; // Planck's constant, Js\n", +"m = 9.1e-031; // Mass of the electron, kg\n", +"v = 1e+003; // Velocity of the electron, m/s\n", +"delta_v = v*0.05/100; // Minimum uncertainty in the velocity of the electron, m/s\n", +"delta_x = h/(m*delta_v); // Minimum uncertainty in the position of the electron, m \n", +"printf('\nThe minimum uncertainty in the position of the electron = %4.2e m', delta_x);\n", +"\n", +"// Result\n", +"// The minimum uncertainty in the position of the electron = 1.45e-003 m " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.24: Minimum_uncertainty_in_energy_of_the_excited_state_of_an_atom.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.24: Page-295 (2008)\n", +"clc; clear;\n", +"h = 6.62e-034; // Planck's constant, Js\n", +"e = 1.602e-019; // Energy equivalent of 1 eV, J\n", +"delta_t = 1e-008; // Life time of excited state of an atom, s\n", +"delta_E = h/(2*%pi*delta_t); // Minimum uncertainty in the energy of the excited state of the atom, J \n", +"printf('\nThe minimum uncertainty in the energy of the excited state of the atom = %3.1e eV', delta_E/e);\n", +"\n", +"// Result\n", +"// The minimum uncertainty in the energy of the excited state of the atom = 6.6e-008 eV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.25: Probable_uncertainty_in_energy_and_frequency_of_gamma_ray_photon.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.25: Page-296 (2008)\n", +"clc; clear;\n", +"h = 6.62e-034; // Planck's constant, Js\n", +"delta_t = 1e-012; // Life time of a nucleus in the excited state, s\n", +"delta_E = h/(2*%pi*delta_t); // Minimum uncertainty in the energy of the excited state of the nucleus, J \n", +"// As E = h*nu, solving for delta_nu\n", +"delta_nu = delta_E/h; // Minimum uncertainty in the frequency of the excited state of the nucleus, Hz\n", +"printf('\nThe minimum uncertainty in the energy of the excited state of the nucleus = %5.3e J', delta_E);\n", +"printf('\nThe minimum uncertainty in the frequency of the excited state of the nucleus = %4.2e MHz', delta_nu/1e+006);\n", +"\n", +"// Result\n", +"// The minimum uncertainty in the energy of the excited state of the nucleus = 1.054e-022 J\n", +"// The minimum uncertainty in the frequency of the excited state of the nucleus = 1.59e+005 MHz " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.29: Lowest_energy_of_an_electron_in_one_dimensional_force_free_region.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.29: Page-300 (2008)\n", +"clc; clear;\n", +"h = 6.62e-034; // Planck's constant, Js\n", +"e = 1.602e-019; // Energy equivalent of 1 eV, J\n", +"m = 9.11e-031; // Rest mass of the electron, kg\n", +"l = 4e-010; // Length of the force free region, m\n", +"n = 1; // Principal quantum number for lowest energy state\n", +"E1 = n^2*h^2/(8*m*l^2); // Lowest energy of an electron in one dimensional force free region, J\n", +"printf('\nThe lowest energy of an electron in one dimensional force free region = %4.2f eV', E1/e);\n", +"\n", +"// Result\n", +"// The lowest energy of an electron in one dimensional force free region = 2.35 eV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.2: Temperature_of_the_surface_of_su.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.2: Page-284 (2008)\n", +"clc; clear;\n", +"lambda_m = 4753e-010; // Wavelength from the sun at which maximum energy is emitted, m\n", +"b = 2.88e-003; // Wein's constant, m-K\n", +"T = b/lambda_m; // Temperature of the surface of sun\n", +"printf('\nThe temperature of the surface of sun = %d K', ceil(T));\n", +"\n", +"// Result\n", +"// The temperature of the surface of sun = 6060 K " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.30: The_excited_state_energies_of_the_particle_entrapped_in_a_one_dimensional_box.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.30: Page-300 (2008)\n", +"clc; clear;\n", +"e = 1.602e-019; // Energy equivalent of 1 eV, J\n", +"E1 = 3.2e-018/e; // Minimum energy possible for a particle entrapped in a one dimensional box, eV\n", +"n = [1 2 3 4]; // Principal quantum number for K, L, M and N states\n", +"printf('\nThe next three energies which the particle can have are:');\n", +"for i = 2:1:4\n", +" printf('\nE%d = %d eV', i, ceil(i^2*E1));\n", +"end\n", +"\n", +"// Result\n", +"// The next three energies which the particle can have are:\n", +"// E2 = 80 eV\n", +"// E3 = 180 eV\n", +"// E4 = 320 eV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.31: Probability_of_finding_the_particle_within_a_given_interval.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.31: Page-301 (2008)\n", +"clc; clear;\n", +"delta_x = 4; // Interval at the centre of the box at which the probability is to be found out, angstrom\n", +"l = 10; // Width of one dimensional infinite height box, angstrom\n", +"P = 2*delta_x/l; // Probability of finding the particle within 4 angstrom interval\n", +"printf('\nThe probability of finding the particle within the %d angstrom interval at the centre of the box = %3.1f', delta_x, P);\n", +"\n", +"// Result\n", +"// The probability of finding the particle within the 4 angstrom interval at the centre of the box = 0.8 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.32: EX5_32.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.32: Page-301 (2008)\n", +"clc; clear;\n", +"L = 1; // Assume the length of the box to be unity, m\n", +"L1 = 0.4*L; // Lower limit, m\n", +"L2 = 0.6*L; // Upper limit, m\n", +"x = (L1+L2)/2; // Mean position of particle, m\n", +"delta_x = L2 - L1; // Uncertainty in position of the particle, m\n", +"for n = 1:1:3\n", +" P = 2/L*sin(n*%pi*x/L)^2; // Probability density, per m\n", +" printf('\nFor n = %d, the probability, P = %3.1f', n, P*delta_x);\n", +"end\n", +"\n", +"// Result\n", +"// For n = 1, the probability, P = 0.4\n", +"// For n = 2, the probability, P = 0.0\n", +"// For n = 3, the probability, P = 0.4 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.3: Wavelength_of_maximum_intensity_of_radiation.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.3: Page-284 (2008)\n", +"clc; clear;\n", +"b = 2.898e-003; // Wein's constant, m-K\n", +"T = 3000 + 273; // Temperature of the source, K\n", +"lambda_m = b/T; // Wavelength of maximum intensity of radiation emitted from the source, m\n", +"printf('\nThe wavelength of maximum intensity of radiation emitted from the source = %d angstrom', lambda_m/1e-010);\n", +"\n", +"// Result\n", +"// The wavelength of maximum intensity of radiation emitted from the source = 8854 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.4: Kinetic_energy_of_the_ejected_photoelectrons.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.4: Page-285 (2008)\n", +"clc; clear;\n", +"h = 6.62e-034; // Planck's constant, Js\n", +"c = 3e+008; // Speed of light, m/s\n", +"lambda = 2300e-010; // Thereshold wavelength for tungsten, m\n", +"phi = h*c/lambda; // Work function for tungsten, J\n", +"lambda = 1800e-010; // Wavelength of incident radiation, m\n", +"E = h*c/lambda; // Energy of the incidnt radiation, J\n", +"KE = E - phi; // Kinetic energy of the ejected photoelectrons, J\n", +"printf('\nThe kinetic energy of the ejected photoelectrons = %3.1f eV', KE/1.6e-019);\n", +"\n", +"// Result\n", +"// The kinetic energy of the ejected photoelectrons = 1.5 eV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.5: Possibility_of_electron_emission_with_the_given_incident_wavelengths.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.5: Page-285 (2008)\n", +"clc; clear;\n", +"function [] = check_energy(E, L)\n", +"phi = 4.8; // Work function for tungsten, eV\n", +" if E > phi then\n", +" printf('\nThe wavelength %d angstrom will be able to liberate an electron.', ceil(L/1e-010));\n", +" else\n", +" printf('\nThe wavelength %d angstrom will not be able to liberate an electron.', ceil(L/1e-010)); \n", +" end\n", +"endfunction\n", +"h = 6.62e-034; // Planck's constant, Js\n", +"c = 3e+008; // Speed of light, m/s\n", +"// Case 1\n", +"lambda = 2000e-010; // Wavelength of incident radiation, m\n", +"E = h*c/(lambda*1.6e-019); // Energy of the incidnt radiation, eV\n", +"check_energy(E, lambda); // Check for the wavelength\n", +"// Case 2\n", +"lambda = 5000e-010; // Wavelength of incident radiation, m\n", +"E = h*c/(lambda*1.6e-019); // Energy of the incidnt radiation, eV\n", +"check_energy(E, lambda); // Check for the wavelength\n", +"\n", +"// Result\n", +"// The wavelength 2000 angstrom will be able to liberate an electron.\n", +"// The wavelength 5000 angstrom will not be able to liberate an electron. " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.6: Velocity_of_emitted_photoelectrons.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.6: Page-286 (2008)\n", +"clc; clear;\n", +"h = 6.62e-034; // Planck's constant, Js\n", +"c = 3e+008; // Speed of light, m/s\n", +"e = 1.6e-019; // Energy quivalent of 1 eV, J\n", +"phi = 2.28*e; // Work function for material, J\n", +"m = 9.1e-031; // Mass of an electron, kg\n", +"lambda = 3000e-010; // Wavelength of incident radiation, m\n", +"E = h*c/lambda; // Energy of the incidnt radiation, J\n", +"KE = E - phi; // Kinetic energy of the ejected photoelectrons, J\n", +"v = sqrt(2*KE/m); // Velocity of emitted electron, m/s\n", +"printf('\nThe velocity of the emitted electron = %4.2e m/s', v);\n", +"\n", +"// Result\n", +"// The velocity of the emitted electron = 8.08e+005 m/s " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.7: A_photosensitive_material_emitting_photoelectrons.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.7: Page-286 (2008)\n", +"clc; clear;\n", +"h = 6.62e-034; // Planck's constant, Js\n", +"c = 3e+008; // Speed of light, m/s\n", +"e = 1.6e-019; // Energy quivalent of 1 eV, J\n", +"phi = 4.2*e; // Work function for material, J\n", +"lambda = 2000e-010; // Wavelength of incident radiation, m\n", +"E = h*c/lambda; // Energy of the incidnt radiation, J\n", +"KE_fast = (E - phi)/e; // Kinetic energy of the fastest photoelectron, eV\n", +"KE_slow = 0; // Kinetic energy of the slowest photoelectron, eV\n", +"printf('\nThe kinetic energy of the fastest photoelectron = %d eV', KE_fast);\n", +"printf('\nThe kinetic energy of the slowest photoelectron = %d eV', KE_slow);\n", +"V = (E - phi)/e; // Stopping potential, V\n", +"printf('\nThe stopping potential = %d volt', V);\n", +"\n", +"// Result\n", +"// The kinetic energy of the fastest photoelectron = 2 eV\n", +"// The kinetic energy of the slowest photoelectron = 0 eV\n", +"// The stopping potential = 2 volt " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.8: Maximum_wavelength_of_radiation_which_would_start_the_emission_of_photoelectrons.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.8: Page-287 (2008)\n", +"clc; clear;\n", +"h = 6.62e-027; // Planck's constant, erg-s\n", +"c = 3e+010; // Speed of light, cm/s\n", +"phi = 3.31e-012; // Work function for material, erg\n", +"lambda0 = h*c/phi; // Wavelength of incident radiation, cm\n", +"printf('\nThe maximum wavelength of radiation which would start the emission of photoelectrons = %d angstrom', lambda0/1e-008);\n", +"\n", +"// Result\n", +"// The maximum wavelength of radiation which would start the emission of photoelectrons = 6000 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.9: Potassium_surface_exposed_to_UV_radiatio.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.9: Page-287 (2008)\n", +"clc; clear;\n", +"h = 6.62e-034; // Planck's constant, Js\n", +"c = 3e+008; // Speed of light, m/s\n", +"e = 1.6e-019; // Energy quivalent of 1 eV, J\n", +"phi = 2.1*e; // Work function for material, J\n", +"lambda = 3500e-010; // Wavelength of incident UV radiation, m\n", +"E = 1e-004; // Energy incident per sec on 1 Sq. cm of potassium surface, J\n", +"eta = 0.5/100; // Efficiency of potassium surface\n", +"KE = (h*c/lambda-phi)/e; // Maximum kinetic energy of the ejected photoelectrons, eV\n", +"N = eta*E/(KE*e); // Number of photoelectrons emitted per second per Sq. cm of potassium surface\n", +"printf('\nThe maximum kinetic energy of the incidnt radiation = %4.2f eV', KE);\n", +"printf('\nThe number of photoelectrons emitted per second per Sq. cm of potassium surface = %4.2e', N);\n", +"\n", +"// Result\n", +"// The maximum kinetic energy of the incidnt radiation = 1.45 eV\n", +"// The number of photoelectrons emitted per second per Sq. cm of potassium surface = 2.16e+012 " + ] + } +], +"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 +} diff --git a/Engineering_Physics_by_D_C_Ghosh/6-Classical_Statistics_and_Quantum_Statistics.ipynb b/Engineering_Physics_by_D_C_Ghosh/6-Classical_Statistics_and_Quantum_Statistics.ipynb new file mode 100644 index 0000000..682b90d --- /dev/null +++ b/Engineering_Physics_by_D_C_Ghosh/6-Classical_Statistics_and_Quantum_Statistics.ipynb @@ -0,0 +1,292 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 6: Classical Statistics and Quantum Statistics" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.10: Number_of_microstates_formed_by_particles_obeying_Fermi_Dirac_statistics.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex6.10: Page-350 (2008)\n", +"clc; clear;\n", +"g1 = 8, g2 = 10; // Total number of cells in the first and the second compartments respectively\n", +"n1 = 3, n2 = 4; // Given number of cells in the first and the second compartments respectively for given macrostate\n", +"W_34 = factorial(g1)/(factorial(n1)*factorial(g1 - n1))*factorial(g2)/(factorial(n2)*factorial(g2 - n2)); // Total number of microstates in the macrostate (3, 4)\n", +"printf('\nThe total number of microstates in the macrostate (%d, %d) = %d', n1, n2, W_34);\n", +"\n", +"// Result\n", +"// The total number of microstates in the macrostate (3, 4) = 11760 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.11: Fermi_energy_and_internal_energy_for_metallic_silver_at_0_K.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex6.11: Page-351 (2008)\n", +"clc; clear;\n", +"h = 6.6e-034; // Planck's constant, Js\n", +"m = 9.1e-031; // Mass of an electron, kg\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J\n", +"rho = 10.5; // Density of silver, g/cc\n", +"A = 108; // Atomic weight of Ag, g/mole\n", +"N_A = 6.023e+023; // Avogadro's number\n", +"E_F0 = h^2/(8*m)*(3*N_A*rho*1e+006/(%pi*A))^(2/3); // Fermi energy of silver at 0 K, J\n", +"U = 3/5*(N_A*rho*1e+006/A)*E_F0; // Internal energy of the electron gas per unit volume at 0 K, J/metre-cube\n", +"printf('\nThe Fermi energy of silver at 0 K = %3.1f eV', E_F0/e);\n", +"printf('\nThe internal energy of the electron gas per unit volume at 0 K = %4.2e J/cubic-metre', U);\n", +"\n", +"// Result\n", +"// The Fermi energy of silver at 0 K = 5.5 eV\n", +"// The internal energy of the electron gas per unit volume at 0 K = 3.07e+010 J/cubic-metre " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.12: Number_of_conduction_electrons_per_cc_in_silver_at_0_K.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex6.12: Page-351 (2008)\n", +"clc; clear;\n", +"h = 6.6e-034; // Planck's constant, Js\n", +"m = 9.1e-031; // Mass of an electron, kg\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J\n", +"E_F0 = 5.48; // Fermi energy of silver at 0 K, eV\n", +"N_bar = (8*m/h^2)^(3/2)*%pi/3*(E_F0*e)^(3/2); // Number density of conduction electrons in silver at 0 K, per cc\n", +"printf('\nThe number density of conduction electrons in silver at 0 K = %3.1e per cc', N_bar*1e-006);\n", +"\n", +"// Result\n", +"// The number density of conduction electrons in silver at 0 K = 5.9e+022 per cc " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.13: Fermi_energy_of_conduction_electrons_in_cesium.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex6.13: Page-351 (2008)\n", +"clc; clear;\n", +"h = 6.6e-034; // Planck's constant, Js\n", +"m = 9.1e-031; // Mass of an electron, kg\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J\n", +"E_F0_Be = 14.44 // Fermi energy of Be at 0 K, eV\n", +"N_bar_Be = 24.2e+022; // Number density of conduction electrons in Be at 0 K, per cc\n", +"N_bar_Cs = 0.91e+022; // Number density of conduction electrons in Cs at 0 K, per cc\n", +"E_F0_Cs = E_F0_Be*(N_bar_Cs/N_bar_Be)^(2/3); // Fermi energy of conduction electrons in cesium, eV\n", +"printf('\nThe Fermi energy of conduction electrons in cesium = %5.3f eV', E_F0_Cs);\n", +"\n", +"// Result\n", +"// The Fermi energy of conduction electrons in cesium = 1.621 eV \n", +"// The answer is given wrongly in the textbook" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.1: Probability_of_distribution_of_distinguishable_particles.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex6.1: Page-345 (2008)\n", +"clc; clear;\n", +"n = 14; // Total number of particles\n", +"C = 2; // Total number of compartments\n", +"N_micro = C^n; // Total number of microstates\n", +"n1 = [10 7 14]; // Set of number of particles in first compartment\n", +"n2 = [4 7 0]; // Set of number of particles in second compartment\n", +"for i = 1:1:3\n", +" W = factorial(n1(i) + n2(i))/(factorial(n1(i))*factorial(n2(i)));\n", +" P = W/N_micro;\n", +" printf('\nThe probability of microstate (%d, %d) = %8.6f', n1(i), n2(i), P);\n", +"end\n", +"\n", +"// Result\n", +"// The probability of microstate (10, 4) = 0.061096\n", +"// The probability of microstate (7, 7) = 0.209473\n", +"// The probability of microstate (14, 0) = 0.000061 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.6: Most_probable_distribution_for_total_energy.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex6.6: Page-348 (2008)\n", +"clc; clear;\n", +"MAX = 10;\n", +"// Look for all the possible set of values for n1, n2 and n3\n", +"printf('\nThe most probable distribution is for ');\n", +"for i = 0:1:5 \n", +" for j = 0:1:5\n", +" for k = 0:1:5\n", +" // Check for the condition and avoid repetition of set of values\n", +" if ((i + j + k) == 5) & ((j+2*k) == 3) then \n", +" W = factorial(i + j + k)/(factorial(i)*factorial(j)*factorial(k));\n", +" if W > MAX then\n", +" printf('\nn1 = %d, n2 = %d and n3 = %d', i, j, k);\n", +" end\n", +" end\n", +" end\n", +" end\n", +"end\n", +"\n", +"// Result\n", +"// The most probable distribution is for \n", +"// n1 = 3, n2 = 1 and n3 = 1 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.8: Probability_for_a_Maxwell_Boltzmann_system_to_be_in_given_states.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex6.8: Page-349 (2008)\n", +"clc; clear;\n", +"k = 1.38e-016; // Boltzmann constant, erg/K\n", +"T = 100; // Given temperature, K\n", +"E1 = 0; // Energy of the first state, erg\n", +"E2 = 1.38e-014; // Energy of the second state, erg\n", +"E3 = 2.76e-014; // Energy of the third state, erg\n", +"g1 = 2, g2 = 5, g3 = 4; // Different ways of occuring for E1, E2 and E3 states\n", +"P1 = g1*exp(-E1/(k*T)); // Probability of occurence of state E1\n", +"P2 = g2*exp(-E2/(k*T)); // Probability of occurence of state E2\n", +"P3 = g3*exp(-E3/(k*T)); // Probability of occurence of state E3\n", +"PE_3 = P3/(P1+P2+P3); // Probability for the system to be in any one microstates of E3\n", +"P0 = P1/(P1+P2+P3); // Probability for the system to be in ground state\n", +"printf('\nThe probability for the system to be in any one microstates of E3 = %6.4f', PE_3);\n", +"printf('\nThe probability for the system to be in ground state = %5.3f', P0);\n", +"\n", +"// Result\n", +"// The probability for the system to be in any one microstates of E3 = 0.1236\n", +"// The probability for the system to be in ground state = 0.457 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.9: Number_of_microstates_in_the_given_macostate_of_a_Fermi_Dirac_system.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex6.9: Page-350 (2008)\n", +"clc; clear;\n", +"g1 = 6, g2 = 8; // Total number of cells in the first and the second compartments respectively\n", +"n1 = 2, n2 = 3; // Given number of cells in the first and the second compartments respectively for given macrostate\n", +"W_23 = factorial(g1)/(factorial(n1)*factorial(g1 - n1))*factorial(g2)/(factorial(n2)*factorial(g2 - n2)); // Total number of microstates in the macrostate (2, 3)\n", +"printf('\nThe total number of microstates in the macrostate (%d, %d) = %d', n1, n2, W_23);\n", +"\n", +"// Result\n", +"// The total number of microstates in the macrostate (2, 3) = 840 " + ] + } +], +"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 +} 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 +} diff --git a/Engineering_Physics_by_D_C_Ghosh/8-Laser_and_Fibre_Optics.ipynb b/Engineering_Physics_by_D_C_Ghosh/8-Laser_and_Fibre_Optics.ipynb new file mode 100644 index 0000000..3fab81d --- /dev/null +++ b/Engineering_Physics_by_D_C_Ghosh/8-Laser_and_Fibre_Optics.ipynb @@ -0,0 +1,178 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 8: Laser and Fibre Optics" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.1: Image_produced_by_laser_beam.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex8.1: Page-397 (2008)\n", +"clc; clear;\n", +"lambda = 6000e-008; // Wavelength of the lase beam, cm\n", +"P = 10e-003; // Power of the laser beam, W\n", +"theta = 1.5e-004; // Angular spread of laser beam, rad\n", +"f = 10; // Focal length of the lens, cm\n", +"r = f*theta; // Radius of the image, cm\n", +"rho = P/(%pi*r^2*1e+003); // Power density of the image, kW/Sq.cm\n", +"L_w = lambda/(theta/10); // Coherence width, mm\n", +"printf('\nThe radius of the image = %3.1e cm', r);\n", +"printf('\nThe power density of the image = %3.1f kW/Sq.cm', rho);\n", +"printf('\nThe coherence width = %d mm', L_w);\n", +"// Result \n", +"// The radius of the image = 1.5e-03 cm\n", +"// The power density of the image = 1.4 kW/Sq.cm\n", +"// The coherence width = 4 mm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.2: Pumping_energy_required_for_He_Ne_laser_transition.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex8.2: Page-398 (2008)\n", +"clc; clear;\n", +"lambda = 632.8e-009; // Wavelength of the lase beam, cm\n", +"E_2P = 15.2e-019; // Energy of 2P level, J\n", +"h = 6.626e-034; // Planck's constant, Js\n", +"c = 3e+008; // Speed of light, m/s\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"E_Pump = E_2P + h*c/lambda; // The required pumping energy, J\n", +"printf('\nThe pumping energy required for He Ne laser transition = %5.2f eV', E_Pump/e);\n", +"// Result \n", +"// The pumping energy required for He Ne laser transition = 11.46 eV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.3: Wavelength_of_radiation_emitted_at_room_temperature.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex8.3: Page-398 (2008)\n", +"clc; clear;\n", +"h = 6.626e-034; // Planck's constant, Js\n", +"c = 3e+008; // Speed of light, m/s\n", +"T = 27+273; // Room temperature, K\n", +"k = 1.38e-023; // Boltzmann constant, J/mol/K\n", +"lambda = h*c/(k*T); // Wavelength of radiation mitted at room temperature, m\n", +"printf('\nThe wavelength of radiation mitted at room temperature = %3.1e m', lambda);\n", +"// Result \n", +"// The wavelength of radiation mitted at room temperature = 4.8e-05 m" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.4: Refractive_index_of_the_cladding_in_an_optical_fibre.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex8.4: Page-398 (2008)\n", +"clc; clear;\n", +"NA = 0.5; // Numerical aperture of the optical fibre\n", +"n1 = 1.54; // Refractive index of the core material\n", +"n2 = sqrt(n1^2-NA^2); // Refractive index of the cladding in an optical fibre\n", +"printf('\nThe refractive index of the cladding in the optical fibre = %4.2f', n2);\n", +"// Result \n", +"// The refractive index of the cladding in the optical fibre = 1.46 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.5: Numerical_aperture_and_acceptance_angle_of_the_optical_fibre.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex8.5: Page-398 (2008)\n", +"clc; clear;\n", +"n1 = 1.51; // Refractive index of the core material\n", +"n2 = 1.47; // Refractive index of the cladding \n", +"NA = sqrt(n1^2-n2^2); // Numerical aperture of the optical fibre\n", +"n0 = 1; // Refractive index of air\n", +"theta_a = asin(NA/n0); // Acceptance angle of the optical fibre, rad\n", +"printf('\nThe numerical aperture of the optical fibre = %6.4f', NA);\n", +"printf('\nThe acceptance angle of the optical fibre = %4.2f degrees', theta_a*180/3.14);\n", +"// Result \n", +"// The numerical aperture of the optical fibre = 0.3453\n", +"// The acceptance angle of the optical fibre = 20.21 degrees " + ] + } +], +"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 +} diff --git a/Engineering_Physics_by_D_C_Ghosh/9-Nuclear_Physics.ipynb b/Engineering_Physics_by_D_C_Ghosh/9-Nuclear_Physics.ipynb new file mode 100644 index 0000000..4f66f13 --- /dev/null +++ b/Engineering_Physics_by_D_C_Ghosh/9-Nuclear_Physics.ipynb @@ -0,0 +1,691 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 9: Nuclear Physics" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.1_1: Binding_energy_per_nucleon_for_Ni.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex9.1.1:Page-411 (2008)\n", +"clc; clear;\n", +"u = 931.508; // Energy equivalent of 1 amu, MeV\n", +"Z = 28; // Atomic number of ni-64\n", +"A = 64; // Mass number of Ni-64\n", +"m_p = 1.007825; // Mass of a proton, u\n", +"m_n = 1.008665; // Mass of a neutron, u\n", +"M_Ni = 63.9280; // Atomic mass of Ni-64 nucleus, u\n", +"delta_m = Z*m_p + (A-Z)*m_n - M_Ni; // Mass difference, u\n", +"BE = delta_m*u; // Binding energy of Ni-64 nucleus, MeV\n", +"BE_bar = BE/A; // Binding energy per nucleon of Ni-64 nucleus, MeV\n", +"printf('\nThe binding energy per nucleon for Ni-64 nucleus = %4.2f MeV/nucleon', BE_bar);\n", +"// Result \n", +"// The binding energy per nucleon for Ni-64 nucleus = 8.78 MeV/nucleon " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.1_2: Binding_energy_per_nucleon_for_deutron.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex9.1.2:Page-411 (2008)\n", +"clc; clear;\n", +"e = 1.6e-013; // Energy equivalent of 1 MeV, J\n", +"m_p = 1.672e-027; // Mass of a proton, kg\n", +"m_n = 1.675e-027; // Mass of a neutron, kg\n", +"M_D = 3.343e-027; // Mass of a deutron, kg\n", +"c = 3.00e+008; // Speed of light in vacuum, m/s\n", +"delta_m = m_p + m_n - M_D; // Mass defect, kg\n", +"E_B = delta_m*c^2/e; // Binding energy for the deutron, MeV\n", +"BE_bar = E_B/2; // Binding energy per nucleon for the deutron, MeV\n", +"printf('\nThe binding energy per nucleon for the deutron = %5.3f MeV/nucleon', BE_bar);\n", +"// Result \n", +"// The binding energy per nucleon for the deutron = 1.125 MeV/nucleon " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.1_3: Packing_fraction_and_binding_energy_per_nucleon_for_oxygen.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex9.1.3:Page-411 (2008)\n", +"clc; clear;\n", +"u = 931.508; // Energy equivalent of 1 amu, MeV\n", +"Z = 8; // Atomic number of O-16\n", +"A = 16; // Mass number of O-16\n", +"m_p = 1.008142; // Mass of a proton, u\n", +"m_n = 1.008982; // Mass of a neutron, u\n", +"M_O = 15.994915; // Atomic mass of O-16 nucleus, u\n", +"delta_m = Z*m_p + (A-Z)*m_n - M_O; // Mass difference, u\n", +"BE = delta_m*u; // Binding energy of O-16 nucleus, MeV\n", +"BE_bar = BE/A; // Binding energy per nucleon of O-16 nucleus, MeV\n", +"delta_m = abs(M_O - A); // Mass difference, u\n", +"PF = delta_m/A; // Packing fraction for O-16 nucleus, u\n", +"printf('\nThe binding energy per nucleon for O-16 nucleus = %4.2f MeV/nucleon', BE_bar);\n", +"printf('\nThe packing fraction for O-16 nucleus = %5.3e u', PF);\n", +"// Result \n", +"// The binding energy per nucleon for O-16 nucleus = 8.27 MeV/nucleon\n", +"// The packing fraction for O-16 nucleus = 3.178e-004 u " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.1_4: Atomic_mass_of_neon.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex9.1.4: Page-411 (2008)\n", +"clc; clear;\n", +"u = 931.508; // Energy equivalent of 1 amu, MeV\n", +"Z = 10; // Atomic number of Ne-20\n", +"A = 20; // Mass number of Ne-0\n", +"m_p = 1.007825; // Mass of a proton, u\n", +"m_n = 1.008665; // Mass of a neutron, u\n", +"BE = 160.64; // Binding energy of Ne-20 nucleus, MeV\n", +"M = Z*m_p + (A-Z)*m_n + Z*0.51/u - BE/u; // Atomic mass of Ne-20 nucleus, u\n", +"printf('\nThe atomic mass of Ne = %7.4f a.m.u', M);\n", +"// Result \n", +"// The atomic mass of Ne = 19.9979 a.m.u " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.2_11: Q_value_of_nuclear_reaction.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex9.2.11: Page-418(2008)\n", +"clc; clear;\n", +"u = 931.5; // Energy equivalent of 1 amu, MeV\n", +"m_x = 4.002603; // Mass of projectile (alpha-particle), u\n", +"m_y = 1.007825; // Mass of emitted particle (proton), u\n", +"M_X = 14.0031; // Mass of target nucleus (N-14), u\n", +"M_Y = 16.9994; // Mass of daughter nucleus (O-16), u\n", +"Q = ((m_x + M_X) - (m_y + M_Y))*u; // Q-value of the reaction, MeV\n", +"printf('\nThe Q-value of the nuclear reaction = %5.3f MeV', Q);\n", +"// Result \n", +"// The Q-value of the nuclear reaction = -1.418 MeV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.2_12: Threshold_energy_for_the_reactions.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex9.2.12: Page-418(2008)\n", +"clc; clear;\n", +"u = 931.5; // Energy equivalent of 1 amu, MeV\n", +"// First reaction\n", +"m_x = 1.007825; // Mass of projectile (proton), u\n", +"m_y = 2.014102; // Mass of emitted particle (deutron), u\n", +"M_X = 208.980394; // Mass of target nucleus (Bi-209), u\n", +"M_Y = 207.979731; // Mass of daughter nucleus (Bi-208), u\n", +"Q = ((m_x + M_X) - (m_y + M_Y))*u; // Q-value of the reaction, MeV\n", +"Ex_threshold = -Q*(m_x + M_X)/M_X; // The smallest value of the projectile energy, MeV\n", +"printf('\nThe threshhold energy of the reaction Bi(209,83) + p --> Bi(208,83) + d = %4.2f MeV', Ex_threshold);\n", +"// Second reaction\n", +"m_x = 4.002603; // Mass of projectile (alpha-particle), u\n", +"m_y = 1.007825; // Mass of emitted particle (proton), u\n", +"M_X = 27.98210; // Mass of target nucleus (Al-27), u\n", +"M_Y = 30.973765; // Mass of daughter nucleus (P-31), u\n", +"Q = ((m_x + M_X) - (m_y + M_Y))*u; // Q-value of the reaction, MeV\n", +"Ex_threshold = -Q*(m_x + M_X)/M_X; // The smallest value of the projectile energy, MeV\n", +"printf('\nThe threshhold energy of the reaction Al(27,13) + He --> P(31,15) + p = %4.2f MeV', Ex_threshold);\n", +"// Result \n", +"// The threshhold energy of the reaction Bi(209,83) + p --> Bi(208,83) + d = 5.25 MeV\n", +"// The threshhold energy of the reaction Al(27,13) + He --> P(31,15) + p = -3.31 MeV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.2_13: Finding_unknown_particles_in_the_nuclear_reactions.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex9.2.13: Page-418(2008)\n", +"clc; clear;\n", +"function p = Find(Z, A)\n", +" if Z == 2 & A == 4 then\n", +" p = 'alpha';\n", +" end\n", +" if Z == -1 & A == 0 then\n", +" p = 'beta-';\n", +" end\n", +" if Z == 1 & A == 0 then\n", +" p = 'beta+';\n", +" end\n", +"endfunction \n", +"R1 = cell(4,3);\n", +"R2 = cell(4,3);\n", +"// Enter data for first cell (Reaction)\n", +"R1(1,1).entries = 'Li'; // Element\n", +"R1(1,2).entries = 3; // Atomic number\n", +"R1(1,3).entries = 6; // Mass number\n", +"R1(2,1).entries = 'd';\n", +"R1(2,2).entries = 1;\n", +"R1(2,3).entries = 2;\n", +"R1(3,1).entries = 'X';\n", +"R1(3,2).entries = 0;\n", +"R1(3,3).entries = 0;\n", +"R1(4,1).entries = 'He';\n", +"R1(4,2).entries = 2;\n", +"R1(4,3).entries = 4;\n", +"// Enter data for second cell (Reaction)\n", +"R2(1,1).entries = 'Te';\n", +"R2(1,2).entries = 52;\n", +"R2(1,3).entries = 122;\n", +"R2(2,1).entries = 'X';\n", +"R2(2,2).entries = 0;\n", +"R2(2,3).entries = 0;\n", +"R2(3,1).entries = 'I';\n", +"R2(3,2).entries = 53;\n", +"R2(3,3).entries = 124;\n", +"R2(4,1).entries = 'd';\n", +"R2(4,2).entries = 1;\n", +"R2(4,3).entries = 2;\n", +"R1(3,2).entries = R1(1,2).entries+R1(2,2).entries-R1(4,2).entries\n", +"R1(3,3).entries = R1(1,3).entries+R1(2,3).entries-R1(4,3).entries\n", +"particle = Find(R1(3,2).entries, R1(3,3).entries); // Find the unknown particle\n", +"printf('\nFor the reaction\n')\n", +" printf('\t%s(%d) + %s(%d) --> %s + %s(%d)\n X must be an %s particle', R1(1,1).entries, R1(1,3).entries, R1(2,1).entries, R1(2,3).entries, R1(3,1).entries, R1(4,1).entries, R1(4,3).entries, particle);\n", +"R2(2,2).entries = R2(3,2).entries+R2(4,2).entries-R2(1,2).entries\n", +"R2(2,3).entries = R2(3,3).entries+R2(4,3).entries-R2(1,3).entries\n", +"particle = Find(R2(2,2).entries, R2(2,3).entries); // Find the unknown particle\n", +"printf('\n\nFor the reaction\n')\n", +" printf('\t%s(%d) + %s --> %s(%d)+%s(%d)\n X must be an %s particle', R2(1,1).entries, R2(1,3).entries, R2(2,1).entries, R2(3,1).entries, R2(3,3).entries, R2(4,1).entries, R2(4,3).entries, particle);\n", +" \n", +"// Result\n", +"// For the reaction\n", +"// Li(6) + d(2) --> X + He(4)\n", +"// X must be an alpha particle\n", +"// For the reaction\n", +"// Te(122) + X --> I(124)+d(2)\n", +"// X must be an alpha particle " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.2_14: Comptom_scattering.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex9.2.14: Page-419(2008)\n", +"clc; clear;\n", +"h = 6.63e-034; // Planck's constant, Js\n", +"c = 3e+008; // Speed of light, m/s\n", +"lambda = 10e-012; // Wavelength of incident X-rays, m\n", +"lambda_c = 2.426e-012; // Compton wavelength for the electron, m\n", +"phi = 45; // Angle of scattering of X-rays, degree\n", +"lambda_prime = lambda + lambda_c*(1 - cosd(phi)); // Wavelength of scattered X-rays, m\n", +"// For maximum wavelength\n", +"phi = 180; // Angle for maximum scattering, degree\n", +"lambda_prime_max = lambda + lambda_c*(1 - cosd(phi)) ; // Maximum wavelength present in the scattered X-rays, m\n", +"KE_max = h*c*(1/lambda-1/lambda_prime_max); // Maximum kinetic energy of the recoil electrons, J\n", +"printf('\nThe wavelength of scattered X-rays = %5.2e m', lambda_prime);\n", +"printf('\nThe maximum wavelength present in the scattered X-rays = %6.3f pm', lambda_prime_max/1e-012);\n", +"printf('\nThe maximum kinetic energy of the recoil electrons = %5.3e J', KE_max);\n", +"// Result\n", +"// The wavelength of scattered X-rays = 1.07e-011 m\n", +"// The maximum wavelength present in the scattered X-rays = 14.852 pm\n", +"// The maximum kinetic energy of the recoil electrons = 6.498e-015 J " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.2_16: Miller_indices_for_the_lattice_planes.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex9.2.16: Page-420(2008)\n", +"clc; clear;\n", +"m = 3; n = 3; 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 miller indices for planes with set of intercepts (%da, %db, %dc) are (%d %d %d) ', m, n, p, m1, m2, m3);\n", +"m = 1; n = 2; p = %inf; // 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]))); // 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 miller indices for planes with set of intercepts (%da, %db, %dc) are (%d %d %d) ', m, n, p, m1, m2, m3);\n", +"// Result\n", +"// The miller indices for planes with set of intercepts (3a, 3b, 2c) are (2 2 3) \n", +"// The miller indices for planes with set of intercepts (1a, 2b, Infc) are (2 1 0) " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.2_19: Glancing_angles_for_the_second_and_third_order_reflections.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex9.2.19: Page-421(2008)\n", +"clc; clear;\n", +"d = 1; // For simplicity assume interplanar spacing to be unity, m\n", +"theta = 15; // Glancing angle for first order, degree\n", +"n = 1; // Order of reflection\n", +"// From Bragg's law, 2*d*sind(theta) = n*lambda, solving for lambda\n", +"lambda = 2*d*sind(theta)/n; // Wavelength of incident X-ray, angstrom\n", +"// For second order reflection\n", +"n = 2\n", +"theta = asind(n*lambda/(2*d)); // Glancing angle for second order reflection, degree\n", +"printf('\nThe glancing angle for the second order reflection = %4.1f degree', theta);\n", +"// For third order reflection\n", +"n = 3;\n", +"theta = asind(n*lambda/(2*d)); // Glancing angle for third order reflection, degree\n", +"printf('\nThe glancing angle for the third order reflection = %4.1f degree', theta);\n", +"// Result\n", +"// The glancing angle for the second order reflection = 31.2 degree\n", +"// The glancing angle for the third order reflection = 50.9 degree " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.2_1: Average_number_of_photons_pe_cubic_metre_in_a_monochromatic_beam.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex9.2.1: Page-414 (2008)\n", +"clc; clear;\n", +"h = 6.63e-034; // Planck's constant, Js\n", +"c = 3.00e+008; // Speed of light in vacuum, m/s\n", +"I = 1e+004; // Intensity of monochromatic beam, W/Sq.m\n", +"nu = 1e+004; // Frequency of monochromatic beam, Hz\n", +"n = I/(h*nu*c); // Average number of photons per cubic metre, photons/metre-cube\n", +"printf('\nThe average number of photons in the monochromatic beam of radiation = %4.2e photons/metre-cube', n);\n", +"// Result \n", +"// The average number of photons in the monochromatic beam of radiation = 5.03e+024 photons/metre-cube " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.2_2: Average_number_of_photons_pe_cubic_metre_in_a_monochromatic_beam.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex9.2.2: : Page-414 (2008)\n", +"clc; clear;\n", +"h = 6.63e-034; // Planck's constant, Js\n", +"c = 3.00e+008; // Speed of light in vacuum, m/s\n", +"I = 1e+004; // Intensity of monochromatic beam, W/Sq.m\n", +"nu = 1e+004; // Frequency of monochromatic beam, Hz\n", +"n = I/(h*nu*c); // Average number of photons per cubic metre, photons/metre-cube\n", +"printf('\nThe average number of photons in the monochromatic beam of radiation = %4.2e photons/metre-cube', n);\n", +"// Result \n", +"// The average number of photons in the monochromatic beam of radiation = 5.03e+024 photons/metre-cube " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.2_3: Photoelectric_effect_with_silver.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex9.2.3: Page-414 (2008)\n", +"clc; clear;\n", +"h = 6.63e-034; // Planck's constant, Js\n", +"c = 3.00e+008; // Speed of light in vacuum, m/s\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J\n", +"m_e = 9.1e-031; // Rest mass of an electron, kg\n", +"lambda0 = 2762e-010; // Thereshold wavelength of silver, m\n", +"lambda = 2000e-010; // Wavelength of ultraviolet rays, m\n", +"E_max = h*c*(1/lambda - 1/lambda0); // Maximum kinetic energy of the ejected electrons from Einstein's photoelectric equation, J\n", +"// As E_max = 1/2*m_e*v^2, solving for v\n", +"v_max = sqrt(2*E_max/m_e); // Maximum velocity of the photoelectrons, m/s\n", +"V0 = E_max/e; // Stopping potential for the electrons, V\n", +"printf('\nThe maximum kinetic energy of the ejected electrons = %5.3e J', E_max);\n", +"printf('\nThe maximum velocity of the photoelectrons = %4.2e m/s', v_max);\n", +"printf('\nThe stopping potential for the electrons = %5.3f V', V0);\n", +"// Result \n", +"// The maximum kinetic energy of the ejected electrons = 2.744e-019 J\n", +"// The maximum velocity of the photoelectrons = 7.77e+005 m/s\n", +"// The stopping potential for the electrons = 1.715 V " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.2_4: Work_function_of_the_metallic_surface.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex9.2.4: Page-415 (2008)\n", +"clc; clear;\n", +"lambda1 = 3333e-010; // First wavelength of the incident light, m\n", +"lambda2 = 2400e-010; // Second wavelength of the incident light, m\n", +"c = 3e+008; // Speed of light in free space, m/s\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J\n", +"E1 = 0.6; // Kinetic energy of the emitted photoelectrons for the first wavelength, eV\n", +"E2 = 2.04; // Kinetic energy of the emitted photoelectrons for the second wavelength, eV\n", +"h = (E2 - E1)*lambda1*lambda2*e/(c*(lambda1 - lambda2)); // Planck's constant, Js\n", +"W0 = (E2*lambda2 - E1*lambda1)/(lambda1 - lambda2); // Work function of the metal, eV\n", +"printf('\nThe value of Planck constant = %3.1e Js', h);\n", +"printf('\nThe work function of the metal = %3.1f eV', W0);\n", +"// Result \n", +"// The value of Planck constant = 6.6e-034 Js\n", +"// The work function of the metal = 3.1 eV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.2_5: Wavelength_of_the_scattered_photon.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex9.2.5: Page-415 (2008)\n", +"clc; clear;\n", +"c = 3e+008; // Speed of light in free space, m/s\n", +"h = 6.63e-034; // Planck's constant, Js\n", +"m_e = 9.11e-031; // Rest mass of an electron, kg\n", +"lambda = 0.3; // Wavelength of incident X-ray photon, angstrom\n", +"phi = 45; // The angle of scattering, degrees\n", +"lambda_prime = lambda + h/(m_e*c*1e-010)*(1-cosd(phi)); // The wavelength of the scattered photon, angstrom\n", +"printf('\nThe wavelength of the scattered photon = %6.4f angstrom', lambda_prime);\n", +"// Result \n", +"// The wavelength of the scattered photon = 0.3071 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.2_6: de_Broglie_wavelength_of_the_valence_electron_in_metallic_sodium.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex9.2.6: Page-416 (2008)\n", +"clc; clear;\n", +"h = 6.63e-034; // Planck's constant, Js\n", +"m_e = 9.11e-031; // Rest mass of an electron, kg\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J\n", +"K = 3*e; // Kinetic energy of the electron in metllic sodium, J\n", +"lambda = h/sqrt(2*m_e*K)/1e-010; // de Broglie wavelength of the valence electron, angstrom\n", +"printf('\nThe de-Broglie wavelength of the valence electron = %3.1f angstrom', lambda);\n", +"// Result \n", +"// The de-Broglie wavelength of the valence electron = 7.1 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.2_7: de_Broglie_wavelength_of_a_moving_electron.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex9.2.7: Page-416 (2008)\n", +"clc; clear;\n", +"h = 6.63e-034; // Planck's constant, Js\n", +"m = 9.11e-031; // Rest mass of an electron, kg\n", +"c = 3e+008; // Speed of light in vacuum, m/s\n", +"bita = 3/5; // Boost parameter\n", +"v = 3/5*c; // Spped of the electron, m/s\n", +"lambda = h/(m*v)*sqrt(1-bita^2); // de Broglie wavelength of the electron, m\n", +"printf('\nThe de-Broglie wavelength of the moving electron = %6.4f angstrom', lambda/1e-010);\n", +"// Result \n", +"// The de-Broglie wavelength of the moving electron = 0.0323 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.2_8: Uncertainty_in_energy_and_frequency_of_emitted_light.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex9.2.8: Page-416 (2008)\n", +"clc; clear;\n", +"h = 6.63e-034; // Planck's constant, Js\n", +"h_bar = h/(2*%pi); // Reduced Planck's constant, Js\n", +"delta_t = 1e-008; // Time during which the radiation is emitted, s\n", +"delta_E = h_bar/delta_t; // Minimum uncertainty in energy of emitted light, J\n", +"// As delta_E = h*delta_nu from Planck's quantum theory, solving for delta_nu\n", +"delta_nu = delta_E/h; // Minimum uncertainty in frequency of emitted light, Hz\n", +"printf('\nThe minimum uncertainty in energy of emitted light = %5.3e J', delta_E);\n", +"printf('\nThe minimum uncertainty in frequency of emitted light = %4.2e Hz', delta_nu);\n", +"// Result \n", +"// The minimum uncertainty in energy of emitted ligh = 1.055e-026 J\n", +"// The minimum uncertainty in frequency of emitted ligh = 1.59e+007 Hz " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.2_9: Shortest_wavelength_present_in_the_radiation_from_an_X_ray_machine.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex9.2.9: Page-417 (2008)\n", +"clc; clear;\n", +"h = 6.63e-034; // Planck's constant, Js\n", +"c = 3e+008; // Speed of light in free space, m/s\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J\n", +"V = 50000; // Accelerating potential, V\n", +"lambda_min = h*c/(e*V); // The shortest wavelength present in the radiation from an X-ray machine, m\n", +"printf('\nThe shortest wavelength present in the radiation from an X-ray machine = %6.4f nm', lambda_min/1e-009);\n", +"// Result \n", +"// The shortest wavelength present in the radiation from an X-ray machine = 0.0249 nm " + ] + } +], +"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 +} |