{ "metadata": { "name": "", "signature": "sha256:975fe0f8501e7b87da57a68589b53423b16e7dfd2c8a554c8366dabc3d2d73d7" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter7-Gamma -Radiation" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex1-pg292" ] }, { "cell_type": "code", "collapsed": false, "input": [ "## Exa7.1: : Page-292 (2011)\n", "#find The distance to be moved for obtaining first order Bragg reflection \n", "import math\n", "h = 6.6261e-034; ## Planck's constant, joule sec\n", "C = 2.998e+08; ## Velocity of light, metre per sec\n", "f = 2.; ## Radius of focal circle, metre\n", "d = 1.18e-010; ## Interplaner spacing for quartz crystal, metre\n", "E_1 = 1.17*1.6022e-013; ## Energy of the gamma rays, joule\n", "E_2 = 1.33*1.6022e-013; ## Energy of the gamma rays, joule\n", "D = h*C*f*(1./E_1-1./E_2)*1./(2.*d); ##Distance to be moved for obtaining first order reflection for two different energies, metre\n", "print'%s %.2e %s'%(\"\\nThe distance to be moved for obtaining first order Bragg reflection = \",D,\" metre\");\n", "\n", "## Result\n", "## The distance to be moved for obtaining first order Bragg reflection = 1.08e-003 metre " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "The distance to be moved for obtaining first order Bragg reflection = 1.08e-03 metre\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex2-pg293" ] }, { "cell_type": "code", "collapsed": false, "input": [ "## Exa7.2: : Page-293 (2011)\n", "#find The energy of the gamma rays\n", "import math\n", "m_0 = 9.1094e-031; ## Rest mass of the electron, Kg\n", "B_R = 1250e-06; ## Magnetic field,tesla metre\n", "e = 1.6022e-019; ## Charge of the electron, coulomb\n", "C = 3e+08; ## Velocity of the light, metre per sec\n", "E_k = 0.089; ## Binding energy of the K-shell electron,MeV\n", "v = B_R*e/(m_0*math.sqrt(1.+B_R**2.*e**2./(m_0**2*C**2))); ## Velocity of the photoelectron, metre per sec\n", "E_pe = m_0/(1.6022e-013)*C**2*(1./math.sqrt(1-v**2/C**2)-1.); ## Energy of the photoelectron,MeV\n", "E_g = E_pe+E_k; ## Energy of the gamma rays, MeV\n", "print'%s %.3f %s'%(\"\\nThe energy of the gamma rays = \",E_g,\" MeV\");\n", "\n", "## Result\n", "## The energy of the gamma rays = 0.212 MeV " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "The energy of the gamma rays = 0.212 MeV\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3-pg293" ] }, { "cell_type": "code", "collapsed": false, "input": [ "## Exa7.3: : Page-292 (2011)\n", "#find The attenuation of beam of X-rays in passing through human tissue \n", "import math\n", "a_c = 0.221; ## Attenuation coefficient, cm^2/g\n", "A = (1-math.exp(-0.22))*100.; ## Attenuation of beam of X-rays in passing through human tissue\n", "print'%s %.2f %s'%(\"\\nThe attenuation of beam of X-rays in passing through human tissue = \",math.ceil(A),\" percent\");\n", "\n", "## Result\n", "## The attenuation of beam of X-rays in passing through human tissue = 20 percent " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "The attenuation of beam of X-rays in passing through human tissue = 20.00 percent\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex4-pg293" ] }, { "cell_type": "code", "collapsed": false, "input": [ "## Exa7.4: : Page-293 (2011)\n", "#find The partial life time for gamma emission \n", "import math\n", "alpha_k = 45.; ## Ratio between decay constants\n", "sum_alpha = 0.08; ## Sum of alphas\n", "P = 0.35*1/60.; ## Probability of the isomeric transition,per hour\n", "lambda_g = P*sum_alpha/alpha_k; ## Decay constant of the gamma radiations, per hour\n", "T_g = 1/(lambda_g*365.*24.); ## Partial life time for gamma emission,years\n", "print'%s %.2f %s'%(\"\\nThe partial life time for gamma emission = \",T_g,\" years\");\n", "\n", "## Result\n", "## The partial life time for gamma emission = 11.008 years \n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "The partial life time for gamma emission = 11.01 years\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex5-pg294" ] }, { "cell_type": "code", "collapsed": false, "input": [ "## Exa7.5: : Page-294 (2011)\n", "import math\n", "#find The required gamma width\n", "A = 11.; ## Mass number of boron\n", "E_g = 4.82; ## Energy of the gamma radiation, mega electron volts\n", "W_g = 0.0675*A**(2./3.)*E_g**3; ## Gamma width, mega electron volts\n", "print'%s %.2f %s'%(\"\\nThe required gamma width = \",W_g,\" MeV\");\n", "\n", "## Result\n", "## The required gamma width = 37.39 MeV \n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "The required gamma width = 37.39 MeV\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex8-pg295" ] }, { "cell_type": "code", "collapsed": false, "input": [ "## Exa7.8: : Page-295 (2011)\n", "#find The excitation energy and The angular momentum\n", "import math\n", "e = 1.6022e-19; ## Charge of an electron, coulomb\n", "BR = 2370e-06; ## Magnetic field in an orbit, tesla metre\n", "m_0 = 9.1094e-31; ## Mass of an electron, Kg\n", "c = 3e+08; ## Velocity of light, metre per sec\n", "v = 1/math.sqrt((m_0/(BR*e))**2.+1./c**2); ## velocity of the particle, metre per sec\n", "E_e = m_0*c**2*((1.-(v/c)**2)**(-1/2.)-1)/1.6e-13; ## Energy of an electron, MeV\n", "E_b = 0.028; ## Binding energy, MeV\n", "E_g = E_e+E_b; ## Excitation energy, MeV\n", "alpha_k = 0.5; ## K conversion coefficient\n", "Z = 49.; ## Number of protons\n", "alpha = 1./137.; ## Fine structure constant\n", "L = (1/(1.-(Z**3/alpha_k*alpha**4.*(2.*0.511/0.392)**(15./2.))))/2.; ## Angular momentum\n", "l = 1; ## Orbital angular momentum\n", "I = l-1/2.; ## Parity\n", "print(\"\\nFor K-electron state:\" )\n", "print' %s %.2f %s %.2f %s %.2f %s'%( \"The excitation energy = \",E_g,\" MeV\" and \"The angular momentum = \",math.ceil(L),\" \" and \"\\nThe parity : \",I,\"\");\n", "## Result\n", "## For K-electron state:\n", "## The excitation energy = 0.393 MeV\n", "## The angular momentum = 5\n", "## The parity : 0.5 \n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "For K-electron state:\n", " The excitation energy = 0.39 The angular momentum = 5.00 \n", "The parity : 0.50 \n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex9-pg295" ] }, { "cell_type": "code", "collapsed": false, "input": [ "## Exa7.9: : Page-295 (2011)\n", "#find The radioactive life time\n", "import math\n", "c = 3e+10; ## Velocity of light, centimetre per sec\n", "R_0 = 1.4e-13; ## Distance of closest approach, centimetre \n", "alpha = 1./137.; ## Fine scattering constant\n", "A = 17.; ## Mass number\n", "E_g = 5.*1.6e-06; ## Energy of gamma transition, ergs\n", "h_cut = 1.054571628e-27; ## Reduced planck constant, ergs per sec\n", "D = c/4.*R_0**2.*alpha*(E_g/(h_cut*c))**3.*A**(2./3.); ## Disintegration constant, per sec\n", "tau = 1/D; ## Radioactive lifr\\e time, sec\n", "print'%s %.1e %s'%(\"\\nThe radioactive life time = \",tau,\" sec\");\n", "\n", "## Result\n", "## The radioactive life time = 9e-018 sec \n", "print(\"error in answer due to round off error\")\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "The radioactive life time = 8.7e-18 sec\n", "error in answer due to round off error\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex10-pg296" ] }, { "cell_type": "code", "collapsed": false, "input": [ "## Exa7.10: : Page-296 (2011)\n", "#find The possible multipolarities are\n", "import math\n", "l = 2,3,4\n", "print(\"\\nThe possible multipolarities are \")\n", "for l in range( 2,4):\n", " if l == 2:\n", " print'%s %.2f %s'%(\"E\",l,\" \" );\n", " elif l == 3:\n", " print'%s %.2f %s'%(\" M\",l,\" \");\n", " elif l == 4:\n", " print'%s %.2f %s'%(\" and E \",l,\" \");\n", " \n", "\n", "for l in range( 2,4):\n", " if l == 2 :\n", " print'%s %.2f %s'%(\"\\nThe transition E\",l,\" dominates\");\n", " \n", "\n", "\n", "## Result\n", "## The possible multipolarities are E2, M3 and E4\n", "## The transition E2 dominates \n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "The possible multipolarities are \n", "E 2.00 \n", " M 3.00 \n", "\n", "The transition E 2.00 dominates\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex13-pg297" ] }, { "cell_type": "code", "collapsed": false, "input": [ "## Exa7.13: : Page-297 (2011)\n", "#find The relative source absorber velocity\n", "import math\n", "E_0 = 0.014*1.6022e-13; ## Energy of the gamma rays, joule\n", "A = 57.; ## Mass number\n", "m = 1.67e-27; ## Mass of each nucleon, Kg\n", "c = 3e+08; ## Velocity of light, metre per sec\n", "N = 1000.; ## Number of atoms in the lattice\n", "v = E_0/(A*N*m*c); ## Ralative velocity, metre per sec\n", "print'%s %.2f %s'%(\"\\nThe relative source absorber velocity = \",v,\" m/s\");\n", "\n", "## Result\n", "## The relative source absorber velocity = 0.079 m/s \n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "The relative source absorber velocity = 0.08 m/s\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex14-pg297" ] }, { "cell_type": "code", "collapsed": false, "input": [ "## Exa7.14: : Page-297 (2011)\n", "#find The required frequency shift of the photon\n", "import math\n", "g = 9.8; ## Acceleration due to gravity, metre per square sec\n", "c = 3e+08; ## Velocity of light, metre per sec\n", "y = 20.; ## Vertical distance between source and absorber, metre\n", "delta_v = g*y/c**2; ## Frequency shift\n", "print'%s %.2e %s'%(\"\\nThe required frequency shift of the photon = \", delta_v,\"\");\n", "\n", "## Result\n", "## The required frequency shift of the photon = 2.18e-015 \n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "The required frequency shift of the photon = 2.18e-15 \n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex15-pg246" ] }, { "cell_type": "code", "collapsed": false, "input": [ "## Exa6.15: : Page-246 (2011)\n", "#find they are parallel spin or anti\n", "import math\n", "import numpy\n", "a='antiparallel spin'\n", "b='parallel spin'\n", "S=([a, b])\n", "\n", "\n", "for i in range (0,1):\n", " if S[i] == 'antiparallel spin' :\n", " print(\"\\nFor Fermi types :\")\n", " print(\"\\n\\n The selection rules for allowed transitions are : \\n\\tdelta I is zero \\n\\tdelta pi is plus \\nThe emited neutrino and electron have %s\")\n", " print \"S(i,1)\"\n", " elif S[i] == 'parallel spin':\n", " print(\"\\nFor Gamow-Teller types :\")\n", " print(\"\\nThe selection rules for allowed transitions are : \\n\\tdelta I is zero,plus one and minus one\\n\\tdelta pi is plus\\nThe emited neutrino and electron have %s\")\n", " print(\"S(i,1)\") \n", " \n", "\n", "## Calculation of ratio of transition probability\n", "M_F = 1.; ## Matrix for Fermi particles\n", "g_F = 1.; ## Coupling constant of fermi particles\n", "M_GT = 5/3.; ## Matrix for Gamow Teller\n", "g_GT = 1.24; ## Coupling constant of Gamow Teller\n", "T_prob = g_F**2*M_F/(g_GT**2*M_GT); ## Ratio of transition probability\n", "## Calculation of Space phase factor\n", "e = 1.6e-19; ## Charge of an electron, coulomb\n", "c = 3e+08; ## Velocity of light, metre per sec\n", "K = 8.99e+9; ## Coulomb constant\n", "R_0 = 1.2e-15; ## Distance of closest approach, metre\n", "A = 57.; ## Mass number\n", "Z = 28.; ## Atomic number \n", "m_n = 1.6749e-27; ## Mass of neutron, Kg\n", "m_p = 1.6726e-27; ## Mass of proton, Kg\n", "m_e = 9.1e-31; ## Mass of electron. Kg\n", "E_1 = 0.76; ## First excited state of nickel\n", "delta_E = ((3*e**2*K/(5*R_0*A**(1/3.))*((Z+1.)**2-Z**2))-(m_n-m_p)*c**2)/1.6e-13; ## Mass difference, mega electron volts\n", "E_0 = delta_E-(2*m_e*c**2)/1.6e-13; ## End point energy, mega electron volts\n", "P_factor = (E_0-E_1)**5/E_0**5; ## Space phase factor \n", "print'%s %.2f %s %.2f %s '%(\"\\nThe ratio of transition probability =\",T_prob,\"\"and\"\\nThe space phase factor =\",P_factor,\"\");\n", " \n", "## Result\n", "## The emited neutrino and electron have antiparallel spin\n", "## For Gamow-Teller types :\n", "## The selection rules for allowed transitions are : \n", "##\tdelta I is zero,plus one and minus one\n", "##\tdelta pi is plus\n", "## The emited neutrino and electron have parallel spin\n", "## The ratio of transition probability = 0.39\n", "## The space phase factor = 0.62 a" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "For Fermi types :\n", "\n", "\n", " The selection rules for allowed transitions are : \n", "\tdelta I is zero \n", "\tdelta pi is plus \n", "The emited neutrino and electron have %s\n", "S(i,1)\n", "\n", "The ratio of transition probability = 0.39 0.62 \n" ] } ], "prompt_number": 2 } ], "metadata": {} } ] }