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+{
+"cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 1: General Properties of Atomic Nucleus"
+ ]
+ },
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.10: Calculation_of_energy_released_during_nuclear_fusion_reaction.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Ex1.10 : : Page 55 (2011)\n",
+"clc; clear;\n",
+"M_Li = 7.0116004; // Mass of lithium nucleus, u\n",
+"M_Be = 7.016929; // Mass of beryllium nucleus, u\n",
+"m_e = 0.511; // Mass of an electron, MeV\n",
+"if (M_Li-M_Be)*931.48 < 2*m_e then\n",
+" printf('\nThe Li-7 is not a beta emitter');\n",
+"else\n",
+" printf('\nThe Li-7 is a beta emitter'); \n",
+"end\n",
+"if (M_Be-M_Li)*931.48 > 2*m_e then\n",
+" printf('\nThe Be-7 is a beta emitter');\n",
+"else\n",
+" printf('\nThe Be-7 is not a beta emitter'); \n",
+"end\n",
+"\n",
+"// Result\n",
+"// The Li-7 is not a beta emitter\n",
+"// The Be-7 is a beta emitter "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.11: Binding_energies_calculation.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Ex1.11 : : Page 55 (2011)\n",
+"clc; clear;\n",
+"M_n = 1.008665; // Mass of neutron, amu\n",
+"M_p = 1.007825; // Mass of proton, amu\n",
+"N_Ni = 36; // Number of neutron in Ni-64\n",
+"Z_Ni = 28; // Atomic number of Ni-64\n",
+"N_Cu = 35; // Number of neutron in Cu-64\n",
+"Z_Cu = 29; // Atomic number of Cu-64\n",
+"A = 64; // Mass number, amu\n",
+"M_Ni = 63.927958; // Mass of Ni-64\n",
+"M_Cu = 63.929759; // Mass of Cu-64\n",
+"m_e = 0.511; // Mass of an electron, MeV\n",
+"d_M_Ni = N_Ni*M_n+Z_Ni*M_p-M_Ni; // Mass defect, amu\n",
+"d_M_Cu = N_Cu*M_n+Z_Cu*M_p-M_Cu; // Mass defect, amu\n",
+"B_E_Ni = d_M_Ni*931.49; // Binding energy of Ni-64, MeV\n",
+"B_E_Cu = d_M_Cu*931.49; // Binding energy of Cu-64, MeV\n",
+"Av_B_E_Ni = B_E_Ni/A; // Average binding energy of Ni-64, MeV\n",
+"Av_B_E_Cu = B_E_Cu/A; // Average binding energy of Cu-64, MeV\n",
+"printf('\nBinding energy of Ni-64 : %7.3f MeV \nBinding energy of CU-64 : %7.3f MeV \nAverage binding energy of Ni-64 : %5.3f MeV \nAverage binding energy of Cu-64 : %5.3f MeV ', B_E_Ni, B_E_Cu, Av_B_E_Ni, Av_B_E_Cu);\n",
+"if (M_Cu - M_Ni)*931.48 > 2*m_e then\n",
+" printf('\nNi-64 is not a beta emitter but Cu-64 is a beta emitter');\n",
+"end\n",
+"\n",
+"// Result\n",
+"// Binding energy of Ni-64 : 561.765 MeV \n",
+"// Binding energy of CU-64 : 559.305 MeV \n",
+"// Average binding energy of Ni-64 : 8.778 MeV \n",
+"// Average binding energy of Cu-64 : 8.739 MeV \n",
+"// Ni-64 is not a beta emitter but Cu-64 is a beta emitter "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.12: Calculation_of_energy_released_during_nuclear_fusion_reaction.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Exa1.12 : : Page 55 (2011)\n",
+"clc; clear;\n",
+"M_n = 1.008665*931.49; // Mass of neutron, MeV\n",
+"M_p = 1.007825*931.49; // Mass of proton, MeV\n",
+"M_He = 2*M_p+2*M_n-28; // Mass of He-4 nucleus, MeV\n",
+"M_H = M_p+M_n-2.2; // Mass of H-2 nucleus, MeV\n",
+"d_E = 2*M_H-M_He; // Energy released during fusion reaction, MeV\n",
+"printf('\nEnergy released during fusion reaction : %4.1f MeV ',d_E);\n",
+"\n",
+"// Result\n",
+"// Energy released during fusion reaction : 23.6 MeV "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.13: To_find_the_stable_Isobar.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Ex1.13 : : P.No.55 (2011)\n",
+"// We have to determine for mass numbers 80 and 97.\n",
+"clc; clear;\n",
+"A = [80, 97]; // Matrix of Mass numbers\n",
+"Element = ['Br','Mo']; // Matrix of elements\n",
+"M_n = 939.6; // Mass of neutron, MeV\n",
+"M_H = 938.8; // Mass of proton, MeV\n",
+"a_v = 14.0; // Volume energy, MeV\n",
+"a_s = 13.0; // Surface energy, MeV\n",
+"a_c = 0.583; // Coulomb energy, MeV\n",
+"a_a = 19.3; // Asymmetry energy, MeV\n",
+"a_p = 33.5; // Pairing energy, MeV\n",
+"for i = 1:1:2\n",
+"Z = poly(0,'Z'); // Declare the polynomial variable\n",
+"M_AZ = M_n*(A(i)-Z)+M_H*Z-a_v*A(i)+a_s*A(i)^(2/3)+a_c*Z*(Z-1)*A(i)^(-1/3)+a_a*(A(i)-2*Z)^2/A(i)+a_p*A(i)^(-3/4); // Mass of the nuclide, MeV/c^2\n",
+"Z = roots(derivat(M_AZ));\n",
+"printf('\nFor A = %d, the most stable isobar is %s(%d,%d)', A(i), Element(i), Z, A(i)); \n",
+"end\n",
+"\n",
+"// Result\n",
+"// For A = 80, the most stable isobar is Br(35,80)\n",
+"// For A = 97, the most stable isobar is Mo(42,97) "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.14: To_calculate_the_pairing_energy_term.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Exa1.14 : : P.no. 56(2011)\n",
+"clc; clear;\n",
+"A = 50; // Mass number\n",
+"M_Sc = 49.951730; // Mass of scandium, atomic mass unit\n",
+"M_Ti = 49.944786; // Mass of titanium, atomic mass unit\n",
+"M_V = 49.947167; // Mass of vanadium, atomic mass unit\n",
+"M_Cr = 49.946055; // Mass of chromium, atomic mass unit\n",
+"M_Mn = 49.954215; // Mass of manganese, atomic mass unit\n",
+"a_p = (M_Mn-M_Cr+M_V-M_Ti)/(8*A^(-3/4))*931.5; // Pairing energy temr, mega electron volts\n",
+"printf('\nPairing energy term : %5.2f MeV', a_p);\n",
+"\n",
+"// Result\n",
+"// Pairing energy term : 23.08 MeV "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.17: Relative_error_in_the_electric_potential_at_the_first_Bohr_radius.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Ex1.17 : : Page 57 (2011)\n",
+"clc; clear;\n",
+"b = 1; // For simplicity assume minor axis length to be unity, unit\n",
+"a = 10/100+b; // Major axis length, unit\n",
+"A = 125; // Mass number of medium nucleus\n",
+"r = 0.53e-010; // Bohr's radius, m\n",
+"eps = (a-b)/(0.5*a+b); // Deformation parameter\n",
+"R = 1.2e-015*A^(1/3); // Radius of the nucleus, m\n",
+"Q = 1.22/15*R^2 // Electric Quadrupole moment, metre square\n",
+"V_rel_err = Q/r^2; // Relative error in the potential\n",
+"printf('\nThe relative error in the electric potential at the first Bohr radius : %e', V_rel_err);\n",
+"\n",
+"// Result\n",
+"// The relative error in the electric potential at the first Bohr radius : 1.042364e-09 "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.1: Distance_of_closest_approach.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Exa1.1 : : Page 51 (2011)\n",
+"clc; clear;\n",
+"Z = 79; // Atomic number of Gold \n",
+"z = 1; // Atomic number of Hydrogen\n",
+"e = 1.60218e-019; // Charge of an electron, coulomb\n",
+"K = 9e+09; // Coulomb constant, newton metre square per coulomb square\n",
+"E = 2*1.60218e-013; // Energy of the proton, joule\n",
+"b = Z*z*e^2*K/E; // Distance of closest approach, metre\n",
+"printf('\nDistance of closest approach : %7.5e metre', b);\n",
+"\n",
+"// Result\n",
+"// Distance of closest approach : 5.69575e-014 meter "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.21: Spherical_symmetry_of_Gadolinium_nucleus.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Exa1.21 : : Page-58(2011)\n",
+"clc; clear;\n",
+"Q = 130; // Quadrupole moment, square femto metre\n",
+"A = 155; // Mass number of gadolinium\n",
+"R_0 = 1.4*A^(1/3) // Distance of closest approach, fm\n",
+"Z = 64; // Atomic number\n",
+"delR0 = 5*Q/(6*Z*R_0^2)*100; // Change in the value of R_0, percent\n",
+"printf('\nChange in the value of fractional change in R_0 is only %4.2f percent \nThus, we can assumed that Gadolinium nucleus is spherical.', delR0);\n",
+"\n",
+"// Result\n",
+"// Change in the value of fractional change in R_0 is only 2.99 percent \n",
+"// Thus, we can assumed that Gadolinium nucleus is spherical. "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.2: Nuclear_Spi.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Exa1.2 : : Page 51 (2011)\n",
+"clc; clear;\n",
+"A = 14; // Number of protons\n",
+"Z = 7; // Number of neutrons\n",
+"N = A-Z; // Number of electrons \n",
+"i = modulo((N+A),2); // Remainder\n",
+"// Check for even and odd number of particles !!!!! \n",
+"if i == 0 then // For even number of particles\n",
+" printf('\nParticles have integral spin');\n",
+" s = 1; // Nuclear spin\n",
+"end\n",
+" if i == 1 then // For odd number of particles\n",
+" printf(' \nParticles have half integral spin ');\n",
+" s = 1/2;\n",
+"end\n",
+"if s == 1 then\n",
+" printf( '\nMeasured value agree with the assumption');\n",
+"end\n",
+"if s == 1/2 then\n",
+" printf( '\nMeasured value disagree with the assumption' );\n",
+"end\n",
+"\n",
+"// Result\n",
+"// Particles have half integral spin \n",
+"// Measured value disagree with the assumption "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.3: Kinetic_energy_and_Coulomb_energy_for_an_electron_confined_within_the_nucleus.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Exa1.3 : : Page 52 (2011)\n",
+"clc; clear; \n",
+"p = 62; // Momentum of the electron, MeV/c\n",
+"K = 9e+09; // Coulomb constant\n",
+"E = 0.511; // Energy of the electron, MeV\n",
+"e = 1.60218e-019; // Charge of an electron, C\n",
+"Z = 23; // Atomic number\n",
+"R = 0.5*10^-14; // Diameter of the nucleus, meter\n",
+"T = sqrt(p^2+E^2)-E; // Kinetic energy of the electron,MeV\n",
+"E_c = -Z*K*e^2/(R*1.60218e-013); // Coulomb energy, MeV\n",
+"printf('\nKinetic energy of the electron : %5.2f MeV \nCoulomb energy per electron : %5.3f MeV',T,E_c);\n",
+"\n",
+"// Result\n",
+"// Kinetic energy of the electron : 61.49 MeV \n",
+"// Coulomb energy per electron : -6.633 MeV "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.4: Scattering_of_electron_from_target_nucleus.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Exa1.4 : : Page 52 (2011) \n",
+"clc; clear;\n",
+"K = 500*1.60218e-013; // Kinetic energy of the electron,joule\n",
+"h = 6.6262e-034; // Planck's constant, joule sec\n",
+"C = 3e+08; // Velocity of light, metre per sec\n",
+"p = K/C; // Momentum of the electron, joule sec per meter\n",
+"lambda = h/p; // de Broglie wavelength, metre\n",
+"A = 30*%pi/180; // Angle (in radian)\n",
+"r = lambda/(A*10^-15); // Radius of the target nucleus, femtometre\n",
+"printf('\nRadius of the target nucleus : %4.2f fm', r);\n",
+"\n",
+"// Result\n",
+"// Radius of the target nucleus : 4.74 fm"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.5: Positron_emission_from_Cl33_decays.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Exa1.5 : : Page 52 (2011) \n",
+"clc; clear;\n",
+"e = 1.60218e-019; // Charge of an electron, C\n",
+"A = 33; // Atomic mass of Chlorine, amu\n",
+"K = 9e+09; // Coulomb constant, newton metre sqaure per coulomb square\n",
+"E = 6.1*1.60218e-013; // Coulomb energy, joule\n",
+"R_0 = 3/5*K/E*e^2*(A)^(2/3); // Distance of closest approach, metre\n",
+"R = R_0*A^(1/3); // Radius of the nucleus, metre\n",
+"printf('\nRadius of the nucleus : %4.2e metre', R);\n",
+"\n",
+"// Result\n",
+"// Radius of the nucleus : 4.6805e-015 metre "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.6: Charge_accelerated_in_mass_spectrometer.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Exa1.6: : Page 53 (2011)\n",
+"clc; clear;\n",
+"V = 1000; // Potential difference, volts\n",
+"R = 18.2e-02; // Radius of the orbit, metre\n",
+"B = 1000e-04; // Magnetic field, tesla\n",
+"e = 1.60218e-019; // Charge of an electron, C\n",
+"n = 1; // Number of the ion\n",
+"v = 2*V/(R*B); // Speed of the ion, metre per sec\n",
+"M = 2*n*e*V/v^2; // Mass of the ion, Kg\n",
+"printf('\nSpeed of the ion: %6.4e m/s \nMass of the ion : %4.2f u', v, M/1.67e-027);\n",
+"\n",
+"// Result\n",
+"// Speed of the ion: 1.0989e+05 m/s \n",
+"// Mass of the ion : 15.89 u "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.7: Ionized_atoms_in_Bainbridge_mass_spectrograph.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Exa1.7 : : Page 53 (2011)\n",
+"clc; clear;\n",
+"M = 20*1.66054e-027; //\n",
+"v = 10^5; // Speed of the ion, metre per sec\n",
+"B = 0.08; // Magnetic field, tesla\n",
+"e = 1.60218e-019; // Charge of an electron, C\n",
+"n = 1; // Number of the ion\n",
+"R_20 = M*v/(B*n*e) // Radius of the neon-20, metre\n",
+"R_22 = 22/20*R_20; // Radius of the neon-22, metre\n",
+"printf('\nRadius of the neon-20 : %5.3f metre \nRadius of the neon-22 : %5.3f metre', R_20, R_22);\n",
+"\n",
+"// Result\n",
+"// Radius of the neon-20 : 0.259 metre \n",
+"// Radius of the neon-22 : 0.285 metre "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.8: Calculating_the_mass_of_hydrogen.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Exa1.8 : : Page 53 (2011)\n",
+"clc; clear;\n",
+"a = 17.78e-03; // First doublet mass difference, u\n",
+"b = 72.97e-03; // Second doublet mass difference, u\n",
+"c = 87.33e-03; // Third doublet mass difference, u\n",
+"M_H = 1+1/32*(4*a+5*b-2*c); // Mass of the hydrogen,amu\n",
+"printf('\nMass of the hydrogen: %8.6f amu',M_H);\n",
+"\n",
+"// Result\n",
+"// Mass of the hydrogen: 1.008166 amu "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.9: Silver_ions_in_Smith_mass_spectrometer.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Exa1.9 : : Page 54 (2011)\n",
+"clc; clear;\n",
+"e = 1.60218e-019; // Charge of an electron,C\n",
+"B = 0.65; // Magnetic field, tesla\n",
+"d_S1_S2 = 27.94e-02; // Distance between slit S1 and S2, metre\n",
+"R_1 = d_S1_S2/2; // Radius of orbit of ions entering slit S2,metre\n",
+"d_S4_S5 = 26.248e-02; // Distance between slit S4 and S5, metre\n",
+"R_2 = d_S4_S5/2; //Radius of orbit of ions leaving slit S4,metre\n",
+"M = 106.9*1.66054e-027; // Mass of an ion(Ag+)Kg, \n",
+"T_1 = B^2*e^2*R_1^2/(2*M*1.60218e-019); // Kinetic energy of the ion entering slit S2,eV \n",
+"T_2 = B^2*e^2*R_2^2/(2*M*1.60218e-019); // Kinetic energy of the ion leaving slit S4,eV \n",
+"printf('\nKinetic energy of the ion entering slit S2 : %d eV \nKinetic energy of the ion leaving slit S4 : %d eV ',T_1,T_2)\n",
+"\n",
+"// Result\n",
+"// Kinetic energy of the ion entering slit S2 : 3721 eV \n",
+"// Kinetic energy of the ion leaving slit S4 : 3284 eV "
+ ]
+ }
+],
+"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
+}