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"
```

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"
```

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"
```

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"
```

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"
```

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"
```

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"
```