11: Natural Radioactivity

Example number 11.1, Page number 222

In [4]:
#import modules
import math
from __future__ import division

#Variable declaration
ttg=8378-1898;       #total time gap(yrs)
hf=1620;      #half life(yrs)
n=ttg/hf;     #number of half-periods
Mo=200;       #amount of radium(mg)

#Calculation
M=Mo*(0.5)**n;     #amount of radium left(mg)

#Result
print "amount of radium left is",M,"mg"

amount of radium left is 12.5 mg

Example number 11.2, Page number 222

In [3]:
#import modules
import math
from __future__ import division

#Variable declaration
T=30;      #half life(days)
#M is intial conc.

#Calculation
lamda=0.693/T;     #radioactive disintegration constant(per day)
#M/4 is left
t1=-math.log(1/4)/lamda;     #time taken(days)
#M/8 is left
t2=-math.log(1/8)/lamda;      #time taken(days)

#Result
print "radioactive disintegration constant is",lamda,"per day"
print "time taken for 3/4th of original is",int(t1),"days"
print "time taken for 1/8th of original is",int(t2),"days"

radioactive disintegration constant is 0.0231 per day
time taken for 3/4th of original is 60 days
time taken for 1/8th of original is 90 days

Example number 11.3, Page number 222

In [2]:
#import modules
import math
from __future__ import division

#Variable declaration
No=4750;      #count rate(per minute)
N=2700;       #rate(counts/minute)
t=5;          #time(minutes)

#Calculation 
lamda=math.log(No/N)/t;     #decay constant(per minute)
T=0.693/lamda;          #half life(minutes)

#Result
print "radioactive disintegration constant is",round(lamda,3),"per minute"
print "half life of sample is",round(T,1),"minutes"

radioactive disintegration constant is 0.113 per minute
half life of sample is 6.1 minutes

Example number 11.4, Page number 223

In [5]:
#import modules
import math
from __future__ import division

#Variable declaration
m=4.00387;     #mass of alpha particle(amu)
M=10**-6;      #mass of Pu-239(kg) 

#Calculation
m=m*1.66*10**-24;     #mass of alpha particle(g)
Mo=2300*m;       #mass of 2300 alpha particles(g)
lamda=(Mo/1)/M;     #radioactive disintegration constant(per second)
T=0.693/lamda;      #half life period(seconds)
T=T/(365*24*3600);    #half life period(years)

#Result
print "half life is",round(T/1e+6,3),"*10**6 years"
print "answer given in the book varies due to rounding off errors"

half life is 1.438 *10**6 years
answer given in the book varies due to rounding off errors

Example number 11.5, Page number 223

In [6]:
#import modules
import math
from __future__ import division

#Variable declaration
T=2.48*10**5;    #half life(yrs)
lamda=8.88*10**-14    #decay constant (per second)
Mo=4;      #intial mass(mg)
t=62000;             #time(years)
Na=6.02*10**23;    #Avgraodo no.(per g-mol)

#Calculation
lamdat=0.693/T*t;      
M=Mo*(math.exp(-lamdat));     #mass remained unchanged(mg) 
N=M*10**-3*Na/234;
A=lamda*N;        #activity(disintegrations/second)

#Result
print "mass remained unchanged is",round(M,3),"mg"
print "Activity is",round(A/1e+5,3),"*10**5 disintegrations/second"

mass remained unchanged is 3.364 mg
Activity is 7.684 *10**5 disintegrations/second

Example number 11.6, Page number 223

In [7]:
#import modules
import math
from __future__ import division

#Variable declaration
T=1620;       #half life(years)
Mo=1/100;     #mass(g)

#Calculation
lamda=0.693/T;      #radioactive constant(per years)   
M=(1-Mo);           #amount of radium left behind(g)  
t=math.log(1/M)/lamda;         #time required to lose 1 centigram(years)
t1=math.log(1/Mo)/lamda;         #time required to be reduced to 1 centigram(years)

#Result
print "time required to lose 1 centigram is",round(t,1),"years"
print "time required to be reduced to 1 centigram is",int(t1),"years"
print "answer given in the book varies due to rounding off errors"

time required to lose 1 centigram is 23.5 years
time required to be reduced to 1 centigram is 10765 years
answer given in the book varies due to rounding off errors

Example number 11.7, Page number 232

In [8]:
#import modules
import math
from __future__ import division

#Variable declaration
T=2*10**-4;           #dead time(seconds)
n=500;                #number of pulses(per second)

#Calculation
n0=n/(1-(n*T));       #number of incoming particles(per second)
r=n*T*100;               #relative error of counting(%)

#Result
print "intensity of the incoming beam is",int(n0),"particles/second"
print "relative error of counting is",int(r),"%"
print "answer for intensity given in the book is wrong"

intensity of the incoming beam is 555 particles/second
relative error of counting is 10 %
answer for intensity given in the book is wrong