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| author | hardythe1 | 2015-06-03 15:27:17 +0530 |
|---|---|---|
| committer | hardythe1 | 2015-06-03 15:27:17 +0530 |
| commit | 47d7279a724246ef7aa0f5359cf417992ed04449 (patch) | |
| tree | c613e5e4813d846d24d67f46507a6a69d1a42d87 /Nuclear_Physics/Chapter7.ipynb | |
| parent | 435840cef00c596d9e608f9eb2d96f522ea8505a (diff) | |
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diff --git a/Nuclear_Physics/Chapter7.ipynb b/Nuclear_Physics/Chapter7.ipynb new file mode 100755 index 00000000..366baa46 --- /dev/null +++ b/Nuclear_Physics/Chapter7.ipynb @@ -0,0 +1,548 @@ +{
+ "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": {}
+ }
+ ]
+}
\ No newline at end of file |