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diff --git a/Modern_Physics/chapter11.ipynb b/Modern_Physics/chapter11.ipynb new file mode 100755 index 00000000..f92c7d71 --- /dev/null +++ b/Modern_Physics/chapter11.ipynb @@ -0,0 +1,336 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:47ab953016e5f85b7389dfd03b89e4eaceb4217fd3c41781effc5a2eb8d08d3e"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "11: Natural Radioactivity"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 11.1, Page number 222"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#import modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "ttg=8378-1898; #total time gap(yrs)\n",
+ "hf=1620; #half life(yrs)\n",
+ "n=ttg/hf; #number of half-periods\n",
+ "Mo=200; #amount of radium(mg)\n",
+ "\n",
+ "#Calculation\n",
+ "M=Mo*(0.5)**n; #amount of radium left(mg)\n",
+ "\n",
+ "#Result\n",
+ "print \"amount of radium left is\",M,\"mg\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "amount of radium left is 12.5 mg\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 11.2, Page number 222"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#import modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "T=30; #half life(days)\n",
+ "#M is intial conc.\n",
+ "\n",
+ "#Calculation\n",
+ "lamda=0.693/T; #radioactive disintegration constant(per day)\n",
+ "#M/4 is left\n",
+ "t1=-math.log(1/4)/lamda; #time taken(days)\n",
+ "#M/8 is left\n",
+ "t2=-math.log(1/8)/lamda; #time taken(days)\n",
+ "\n",
+ "#Result\n",
+ "print \"radioactive disintegration constant is\",lamda,\"per day\"\n",
+ "print \"time taken for 3/4th of original is\",int(t1),\"days\"\n",
+ "print \"time taken for 1/8th of original is\",int(t2),\"days\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "radioactive disintegration constant is 0.0231 per day\n",
+ "time taken for 3/4th of original is 60 days\n",
+ "time taken for 1/8th of original is 90 days\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 11.3, Page number 222"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#import modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "No=4750; #count rate(per minute)\n",
+ "N=2700; #rate(counts/minute)\n",
+ "t=5; #time(minutes)\n",
+ "\n",
+ "#Calculation \n",
+ "lamda=math.log(No/N)/t; #decay constant(per minute)\n",
+ "T=0.693/lamda; #half life(minutes)\n",
+ "\n",
+ "#Result\n",
+ "print \"radioactive disintegration constant is\",round(lamda,3),\"per minute\"\n",
+ "print \"half life of sample is\",round(T,1),\"minutes\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "radioactive disintegration constant is 0.113 per minute\n",
+ "half life of sample is 6.1 minutes\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 11.4, Page number 223"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#import modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "m=4.00387; #mass of alpha particle(amu)\n",
+ "M=10**-6; #mass of Pu-239(kg) \n",
+ "\n",
+ "#Calculation\n",
+ "m=m*1.66*10**-24; #mass of alpha particle(g)\n",
+ "Mo=2300*m; #mass of 2300 alpha particles(g)\n",
+ "lamda=(Mo/1)/M; #radioactive disintegration constant(per second)\n",
+ "T=0.693/lamda; #half life period(seconds)\n",
+ "T=T/(365*24*3600); #half life period(years)\n",
+ "\n",
+ "#Result\n",
+ "print \"half life is\",round(T/1e+6,3),\"*10**6 years\"\n",
+ "print \"answer given in the book varies due to rounding off errors\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "half life is 1.438 *10**6 years\n",
+ "answer given in the book varies due to rounding off errors\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 11.5, Page number 223"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#import modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "T=2.48*10**5; #half life(yrs)\n",
+ "lamda=8.88*10**-14 #decay constant (per second)\n",
+ "Mo=4; #intial mass(mg)\n",
+ "t=62000; #time(years)\n",
+ "Na=6.02*10**23; #Avgraodo no.(per g-mol)\n",
+ "\n",
+ "#Calculation\n",
+ "lamdat=0.693/T*t; \n",
+ "M=Mo*(math.exp(-lamdat)); #mass remained unchanged(mg) \n",
+ "N=M*10**-3*Na/234;\n",
+ "A=lamda*N; #activity(disintegrations/second)\n",
+ "\n",
+ "#Result\n",
+ "print \"mass remained unchanged is\",round(M,3),\"mg\"\n",
+ "print \"Activity is\",round(A/1e+5,3),\"*10**5 disintegrations/second\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "mass remained unchanged is 3.364 mg\n",
+ "Activity is 7.684 *10**5 disintegrations/second\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 11.6, Page number 223"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#import modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "T=1620; #half life(years)\n",
+ "Mo=1/100; #mass(g)\n",
+ "\n",
+ "#Calculation\n",
+ "lamda=0.693/T; #radioactive constant(per years) \n",
+ "M=(1-Mo); #amount of radium left behind(g) \n",
+ "t=math.log(1/M)/lamda; #time required to lose 1 centigram(years)\n",
+ "t1=math.log(1/Mo)/lamda; #time required to be reduced to 1 centigram(years)\n",
+ "\n",
+ "#Result\n",
+ "print \"time required to lose 1 centigram is\",round(t,1),\"years\"\n",
+ "print \"time required to be reduced to 1 centigram is\",int(t1),\"years\"\n",
+ "print \"answer given in the book varies due to rounding off errors\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "time required to lose 1 centigram is 23.5 years\n",
+ "time required to be reduced to 1 centigram is 10765 years\n",
+ "answer given in the book varies due to rounding off errors\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 11.7, Page number 232"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#import modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "T=2*10**-4; #dead time(seconds)\n",
+ "n=500; #number of pulses(per second)\n",
+ "\n",
+ "#Calculation\n",
+ "n0=n/(1-(n*T)); #number of incoming particles(per second)\n",
+ "r=n*T*100; #relative error of counting(%)\n",
+ "\n",
+ "#Result\n",
+ "print \"intensity of the incoming beam is\",int(n0),\"particles/second\"\n",
+ "print \"relative error of counting is\",int(r),\"%\"\n",
+ "print \"answer for intensity given in the book is wrong\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "intensity of the incoming beam is 555 particles/second\n",
+ "relative error of counting is 10 %\n",
+ "answer for intensity given in the book is wrong\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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