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+{
+"cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 13: Nuclear Structure"
+ ]
+ },
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13.11: Radioactive_Dating.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Ex13.11: Pg 490 (2005)\n",
+"clc; clear;\n",
+"T_half = 5370*3.6e+07; // Half life of C-14, s\n",
+"lambda = 0.693/T_half; // // Decay constant for C-14 disintegration, per sec\n",
+"N_C12 = 6.02e+023/12*25; // Number of C-12 nuclei in 25.0 g of carbon\n",
+"N0_C14 = 1.3e-012*N_C12; // Number of C-14 nuclei in 25.0 g of carbon before decay\n",
+"R0 = N0_C14*3.83e-012*60; // Initial activty of the sample, decays/min\n",
+"R = 250; // Present activity of the sample\n",
+"// As R = R0*exp(-lambda*t), solving for t\n",
+"t = -1/lambda*log(R/R0); // Time during which the tree dies, s\n",
+"printf('\nThe lifetime of the tree = %3.1e yr', t/(365*24*60*60));\n",
+"\n",
+"// Result\n",
+"// The lifetime of the tree = 3.6e+03 yr "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13.1: The_Atomic_Mass_Unit.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Ex13.1: Pg 466 (2005)\n",
+"clc; clear;\n",
+"M = 0.012; // Atomic mass of carbon, kg\n",
+"N_A = 6.02e+023; // Avogadro's number\n",
+"m = M/N_A; // Mass of one Carbon-12 atom, kg\n",
+"// As m = 12*u, twelve mass units, solving for u\n",
+"u = m/12; // The atomic mass unit, kg\n",
+"printf('\nThe atomic mass unit = %4.2e kg', u);\n",
+"\n",
+"// Result\n",
+"// The atomic mass unit = 1.66e-27 kg "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13.2: The_Volume_and_Density_of_Nucleus.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Ex13.2: Pg 468 (2005)\n",
+"clc; clear;\n",
+"r0 = 1.2e-015; // Nuclear mean radius, m\n",
+"m = 1.67e-027; // Mass of the nucleon, kg\n",
+"rho_0 = 3*m/(4*%pi*r0^3); // Density of the nucleus, kg per metre cube\n",
+"printf('\nThe mass of the nucleus = Am approx.');\n",
+"printf('\nThe volume of the nucleus = 4/3*pi*r0^3*A');\n",
+"printf('\nThe density of the nucleus = %3.1e kg per metre cube', rho_0);\n",
+"\n",
+"// Result\n",
+"// The mass of the nucleus = Am approx.\n",
+"// The volume of the nucleus = 4/3*pi*r0^3*A\n",
+"// The density of the nucleus = 2.3e+17 kg per metre cube "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13.3: Binding_energy_of_the_Deuteron.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Ex13.3: Pg 473 (2005)\n",
+"clc; clear;\n",
+"M2 = 2.014102; // Atomic mass of deuteron, u\n",
+"M_H = 1.007825; // Atomic mass of hydrogen, u\n",
+"m_n = 1.008665; // Mass of a neutron, u\n",
+"E_b = (M_H + m_n - M2)*931.494; // Binding energy of the deuteron, MeV/u\n",
+"printf('\nThe binding energy of the Deuteron = %5.3f MeV', E_b);\n",
+"\n",
+"// Result\n",
+"// The binding energy of the Deuteron = 2.224 MeV"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13.4: Left_out_sample_during_radioactive_decay.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Ex13.4: Pg 482 (2005)\n",
+"clc; clear;\n",
+"T = 5730; // Half life of the carbon-14 isotope, years\n",
+"N0 = 1000; // Initial number of carbon-14 isotope\n",
+"t = 22920; // Time of decay, years\n",
+"n = t/T; // Total number of half lives\n",
+"N = (1/2)^n*N0; // Sample remains after 22920 years\n",
+"printf('\nNumber of C-14 isotopes remained after %d years = %d', t, N);\n",
+"\n",
+"// Result\n",
+"// Number of C-14 isotopes remained after 22920 years = 62 "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13.5: The_Activity_of_Radium.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Ex13.5: Pg 483 (2005)\n",
+"clc; clear;\n",
+"T_half = 1.6e+03*3.16e+07; // Half life of radioactive nucleus Ra-226, s\n",
+"lambda = 0.693/T_half; // Decay constant of Ra-226, per second\n",
+"N0 = 3.0e+016; // Number of radioactive nuclei at t = 0\n",
+"R0 = lambda*N0; // Activity of sample at t = 0, decays/s\n",
+"t = 2.0e+003*3.16e+07; // Time during which the radioactive disintegration takes place, s\n",
+"R = R0*exp(-1*lambda*t); // Decay rate after 2.0e+003 years, decay/s\n",
+"printf('\nThe decay constant of Ra-226 = %3.1e per second', lambda);\n",
+"printf('\nThe activity of sample at t = 0 = %4.1f micro-Ci', R0/(3.7e+010*1e-006)); \n",
+"printf('\nThe activity of sample after %3.1e years = %3.1e decays/s', t, R); \n",
+"\n",
+"// Result\n",
+"// The decay constant of Ra-226 = 1.4e-11 per second\n",
+"// The activity of sample at t = 0 = 11.1 micro-Ci\n",
+"// The activity of sample after 6.3e+10 years = 1.7e+05 decays/s "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13.6: The_Activity_of_Carbo.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Ex13.6: Pg 483 (2005)\n",
+"clc; clear;\n",
+"M = 11.0; // Atomic mass of C-11 isotope, g\n",
+"NA = 6.02e+023; // Avogadro's number\n",
+"m = 3.50e-06; // Given mass of Cabon-11, g\n",
+"\n",
+"// Part (a)\n",
+"N = m/M*NA; // Number of C-11 atoms in 3.50 micro-g of sample\n",
+"printf('\nThe number of C-11 atoms in %4.2f micro-g of sample = %4.2e nuclei', m/1e-06, N);\n",
+"\n",
+"// Part (b)\n",
+"T_half = 20.4*60; // Half life of radioactive nucleus C-11, s\n",
+"lambda = 0.693/T_half; // Decay constant of C-11, per second\n",
+"R0 = lambda*N; // Activity of sample at t = 0, decays/s\n",
+"t = 8.00*60*60; // Time during which the radioactive disintegration takes place, s\n",
+"R = R0*exp(-1*lambda*t); // Decay rate after 2.0e+003 years, decay/s\n",
+"\n",
+"printf('\nThe activity of C-11 sample at t = 0 is %4.2e decays/s', R0); \n",
+"printf('\nThe activity of sample after %4.2f hours = %4.2e decays/s', t/3600, R); \n",
+"\n",
+"// Result\n",
+"// The number of C-11 atoms in 3.50 micro-g of sample = 1.92e+17 nuclei\n",
+"// The activity of C-11 sample at t = 0 is 1.08e+14 decays/s\n",
+"// The activity of sample after 8.00 hours = 8.99e+06 decays/s "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13.7: The_Radiactive_Isotope_of_Iodine.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Ex13.7: Pg 484 (2005)\n",
+"clc; clear;\n",
+"R0 = 5; // Activity of I-131 isotope at the time of shipment, mCi\n",
+"R = 4.2; // Activity of I-131 isotope at the time of receipt by the medical laboratory, mCi\n",
+"T_half = 8.04; // Half life of radioactive nucleus I-131, days\n",
+"lambda = 0.693/T_half; // Decay constant of C-11, per second\n",
+"// As log(R/R0) = -lambda*t, solving for t\n",
+"t = -1/lambda*log(R/R0); // Time that has elapsed between two measurements, days\n",
+"printf('\nThe time that has elapsed between two measurements = %4.2f days', t);\n",
+"\n",
+"// Result\n",
+"// The time that has elapsed between two measurements = 2.02 days "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13.8: Energy_Liberated_during_Decay_of_Radium.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Ex13.8: Pg 486 (2005)\n",
+"clc; clear;\n",
+"M_X = 226.025406; // Atomic mass of Ra-226, u\n",
+"M_Y = 222.017574; // Atomic mass of Rn-222, u\n",
+"M_alpha = 4.002603; // Mass of alpha particle, u\n",
+"Q = (M_X - M_Y - M_alpha)*931.494; // Q-value for Radium Decay, MeV/u\n",
+"printf('\nThe Q-value for Radium Decay = %4.2f MeV', Q);\n",
+"\n",
+"// Result\n",
+"// The Q-value for Radium Decay = 4.87 MeV "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13.9: Probability_of_Alpha_Decay.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Ex13.9: Pg 487 (2005)\n",
+"clc; clear;\n",
+"Z = 86; // Atomic number of radon\n",
+"A = 222; // Mass number of radon\n",
+"k = 9e+09; // Coulomb constant, N-metre square per C-square\n",
+"e = 1.6e-019; // Charge on an electron, C\n",
+"r0 = 7.25e-015; // Bohr radius for alpha particle, m\n",
+"E0 = k*e^2/(2*r0*1e+06*e); // Rydberg energy, MeV\n",
+"R = 1.2e-015*A^(1/3); // Radius of radon nucleus, fm\n",
+"E = 5; // Disintegration energy during alpha decay, MeV\n",
+"T_E = exp(-4*%pi*Z*sqrt(E0/E)+8*sqrt(Z*R/r0)); // Decay probability for alpha disintegration\n",
+"printf('\nThe decay probability for alpha disintegration at %d MeV energy = %4.2e', E, T_E);\n",
+"\n",
+"// Result\n",
+"// The decay probability for alpha disintegration at 5 MeV energy = 1.29e-34 "
+ ]
+ }
+],
+"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
+}
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