## 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

#Calculation

#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
#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)
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
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
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