diff options
Diffstat (limited to 'Nuclear_Physics_by_D_C_Tayal/5-Alpha_Particles.ipynb')
| -rw-r--r-- | Nuclear_Physics_by_D_C_Tayal/5-Alpha_Particles.ipynb | 285 |
1 files changed, 285 insertions, 0 deletions
diff --git a/Nuclear_Physics_by_D_C_Tayal/5-Alpha_Particles.ipynb b/Nuclear_Physics_by_D_C_Tayal/5-Alpha_Particles.ipynb new file mode 100644 index 0000000..39a50ec --- /dev/null +++ b/Nuclear_Physics_by_D_C_Tayal/5-Alpha_Particles.ipynb @@ -0,0 +1,285 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 5: Alpha Particles" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.10: Degree_of_hindrance_for_alpha_particle_from_U238.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa5.10 : : Page 206 (2011)\n", +"clc; clear;\n", +"h_kt = 1.05457e-34; // Reduced Planck's constant, joule sec\n", +"e = 1.60218e-19; // Charge of an electron, coulomb\n", +"l = 2; // Orbital angular momentum\n", +"eps_0 = 8.5542e-12; // Absolute permittivity of free space, coulomb square per newton per metre square\n", +"Z_D = 90; // Atomic number of daughter nucleus\n", +"m = 6.644e-27; // Mass of alpha particle, Kg\n", +"R = 8.627e-15; // Radius of daughter nucleus, metre\n", +"T1_by_T0 = exp(2*l*(l+1)*h_kt/e*sqrt(%pi*eps_0/(Z_D*m*R))); // Hindrance factor\n", +"printf('\nThe hindrance factor for alpha particle = %5.3f' ,T1_by_T0);\n", +"\n", +"// Result\n", +"// The hindrance factor for alpha particle = 1.768 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.1: Disintegration_energy_of_alpha_particle.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa5.1 : : Page 203 (2011)\n", +"clc; clear;\n", +"E_a = 8.766; // Energy of the alpha particle, MeV\n", +"A = 212; // Atomic mass of Po-212, amu\n", +"M_a = 4; // Atomic mass of alpha particle, amu\n", +"e = 1.6e-019; // Charge of an electron, coulomb\n", +"Z = 82; // Atomic number of Po-212\n", +"R_0 = 1.4e-015; // Distance of closest approach,metre\n", +"K = 8.99e+09; // Coulomb constant\n", +"E = E_a*A/(A-M_a); // Disintegration energy, mega electron volts\n", +"B_H = 2*Z*e^2*K/(R_0*A^(1/3)*1.6*10^-13); // Barrier height for an alpha particle within the nucleus, MeV\n", +"printf('\nDisintegration energy : %5.3f MeV \nBarrier height for alpha-particle: %5.2f MeV', E,B_H);\n", +"\n", +"// Result\n", +"// Disintegration energy : 8.935 MeV \n", +"// Barrier height for alpha-particle: 28.26 MeV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.2: Calculation_of_the_barrier_height.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa5.2 : : Page 203 (2011)\n", +"// We have to make calculation for alpha particle and for proton\n", +"clc; clear;\n", +"E_a = 8.766; // Energy of the alpha particle, mega electron volts\n", +"A_Bi = 209; // Atomic mass of Bi-209, atomic mass unit\n", +"A_a = 4; // Atomic mass of alpha particle, atomic mass unit\n", +"A_p = 1; // Atomic mass of proton, atomic mass unit\n", +"e = 1.6e-019; // Charge of an electron, coulomb\n", +"Z = 83; // Atomic number of bismuth\n", +"R_0 = 1.4e-015; // Distance of closest approach,metre\n", +"K = 8.99e+09; // Coulomb constant\n", +"B_H_a = 2*Z*e^2*K/(R_0*1.6e-013*(A_Bi^(1/3)+A_a^(1/3))); // Barrier height for an alpha particle, mega electron volts\n", +"B_H_p = 1*Z*e^2*K/(R_0*1.6e-013*(A_Bi^(1/3)+A_p^(1/3))); // Barrier height for proton, mega electron volts\n", +"printf('\nBarrier height for the alpha particle = %5.2f MeV \nBarrier height for the proton = %5.2f MeV', B_H_a,B_H_p);\n", +"\n", +"// Result\n", +"// Barrier height for the alpha particle = 22.67 MeV \n", +"// Barrier height for the proton = 12.30 MeV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.3: Speed_and_BR_value_of_alpha_particles.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa5.3 : : Page 203 (2011)\n", +"// We have also calculate the value of magnetic field in a particular orbit. \n", +"clc; clear;\n", +"C = 3e+08; // Velocity of light, m/S\n", +"M_0 = 6.644e-027*(C)^2/(1.60218e-013); // Rest mass of alpha particle, MeV\n", +"T = 5.998; // Kinetic energy of alpha particle emitted by Po-218\n", +"q = 2*1.60218e-019; // Charge of alpha particle, C\n", +"V = sqrt(C^2*T*(T+2*M_0)/(T+M_0)^2); // Velocity of alpha particle,metre per sec\n", +"B_r = V*M_0*(1.60218e-013)/(C^2*q*sqrt(1-V^2/C^2)); // magnetic field in a particular orbit, Web per mtere\n", +"printf('\nThe velocity of alpha particle : %5.3e m/s\nThe magnetic field in a particular orbit : %6.4f Wb/m', V , B_r);\n", +"\n", +"// Result\n", +"// The velocity of alpha particle : 1.699e+007 m/s\n", +"// The magnetic field in a particular orbit : 0.3528 Wb/m " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.4: Transmission_probability_for_an_alpha_particle_through_a_potential_barrier.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa5.4: : Page 204 (2011)\n", +"clc; clear;\n", +"a = 10^-14; // Width of the potential barrier, m\n", +"E = 5*1.60218e-013; // Energy of the alpha particle, joule\n", +"V = 10*1.60218e-013; // Potential height, joule\n", +"M_0 = 6.644e-027; // Rest mass of the alpha particle, joule\n", +"h_red = 1.05457e-034; // Reduced value of Planck's constant,joule sec \n", +"T = 4*exp(-2*a*sqrt(2*M_0*(V-E)/h_red^2)); // Probability of leakage through through potential barrier\n", +"printf('\nThe probability of leakage of alpha-particle through potential barrier = %5.3e ',T);\n", +"\n", +"// Result\n", +"// The probability of leakage of alpha-particle through potential barrier = 1.271e-008 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.6: Difference_in_life_times_of_Polonium_isotopes.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa5.6: : Page 204 (2011)\n", +"clc; clear; \n", +"Z_D = 82; // Atomic number of Po\n", +"E_Po210 = 5.3; // Alpha-source for Po210, MeV\n", +"E_Po214 = 7.7; // Alpha-source for Po214, MeV\n", +"log_lambda_Po210 = -1*1.72*Z_D*E_Po210^(-1/2); \n", +"log_lambda_Po214 = -1*1.72*Z_D*E_Po214^(-1/2); \n", +"delta_OM_t = log_lambda_Po214 - log_lambda_Po210; // Difference in order of magnitude of life times of Po214 and Po210\n", +"printf('\nThe disintegration constant increases by a factor of some 10^%2d', delta_OM_t);\n", +"\n", +"// Result\n", +"// The disintegration constant increases by a factor of some 10^10 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.8: Half_life_of_plutonium.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa5.8: : Page 205 (2011)\n", +"clc; clear;\n", +"N = 120.1*6.023e+023/239; // Number of Pu nuclei\n", +"P_rel = 0.231; // Power released, watt\n", +"E_rel = 5.323*1.6026e-13; // Energy released, joule\n", +"decay_rate = P_rel/E_rel; // Decay rate of Pu239, per hour\n", +"t_half = N*log(2)/(decay_rate*365*86400); // Half life of Po239, sec\n", +"printf('\nThe half life of Pu = %4.2e yr', t_half);\n", +"\n", +"// Result\n", +"// The half life of Pu = 2.46e+004 yr " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.9: Slope_of_alpha_decay_energy_versus_atomic_number.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa5.9 : : Page 205(2011)\n", +"clc; clear;\n", +"a_v = 14; // Volume energy constant, MeV\n", +"a_s = 13; // Surface energy constant, MeV\n", +"a_c = 0.60; // Coulomb energy constant, MeV\n", +"a_a = 19; // Asymmetric energy constant, MeV\n", +"A = 202; // Mass number\n", +"Z = 82; // Atomic number \n", +"dE_by_dN = -8/9*a_s/A^(4/3)-4/3*a_c*Z/A^(4/3)*(1-4*Z/(3*A))-16*a_a*Z/A^2*(1-2*Z/A); // Slope, mega electron volts per nucleon\n", +"printf('\nThe slope of alpha decay energy versus atomic number = %7.5f MeV/nucleon', dE_by_dN);\n", +"\n", +"// Result\n", +"// The slope of alpha decay energy versus atomic number = -0.15007 MeV/nucleon " + ] + } +], +"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 +} |