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{
"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": {}
}
]
}
|
