11: Nuclear Radiations and Detectors

Example number 11.1, Page number 227

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

#Variable declaration
r0=1.2;              #radius(fm)
A=7;                 #mass number 

#Calculation                        
r=r0*A**(1/3);	     #radius of Li(fm) 

#Result
print "The radius of Li is",round(r,4),"fm"
The radius of Li is 2.2955 fm

Example number 11.2, Page number 227

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

#Variable declaration
M=235.043945;         #atomic mass of uranium(u)
Z=92;                 #atomic number of uranium
mp=1.007825;          #mass of proton(kg)
N=143;                #no.of neutrons
mn=1.008665;          #mass of neutron(kg)
A=235;                #number of nucleons

#Calculation                        
B=(((Z*mp)+(N*mn)-(M))/A)*931.5;            #Binding energy(MeV)

#Result
print "The binding energy per nucleon is",round(B,3),"MeV"
The binding energy per nucleon is 7.591 MeV

Example number 11.3, Page number 227

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

#Variable declaration
#After removing one neutron from Ca(A=43;Z=20) it becomes Ca(A=42;Z=20)
M=41.958622;             #mass of Ca(A=42;Z=20)(kg)
mn=1.008665;             #mass of neutron(kg)
E=42.95877;              #mass of Ca(A=43;Z=20)(kg)

#Calculation                        
C=M+mn;
D=C-E;
B=D*931.5;               #Binding energy of neutron(MeV)

#Result
print "The binding energy of neutron is",round(B,4),"MeV"
The binding energy of neutron is 7.9336 MeV

Example number 11.4, Page number 227

In [9]:
#importing modules
import math
from __future__ import division

#Variable declaration
mBe=9.012182;            #Atomic mass of beryllium(u)
mHe=4.002603;            #Atomic mass of helium
mn=1.008665;             #mass of neutron(kg)
mC=12.000000;            #Atomic mass of carbon

#Calculation                        
Q=(mBe+mHe-mn-mC)*931.5        #energy balance of the reaction(MeV)

#Result
print "The Q-value is",round(Q,1),"MeV"
The Q-value is 5.7 MeV

Example number 11.5, Page number 227

In [14]:
#importing modules
import math
from __future__ import division

#Variable declaration
mLi=7.016004;              #mass of Lithium(A=7)(u)
mH=1.007825;               #mass of Hydrogen(A=1)(u)
mHe=4.002603;              #mass of helium(A=4)(u)
p=0.5;                       #energy of proton(MeV)

#Calculation                        
Q=(mLi+mH-2*(mHe))*931.5     #energy balance of the reaction(MeV)
#The energy of 2 alpha particles is equal to the Q-value + energy of proton.
Ealpha=(Q+p)/2;              #energy of each alpha particle(MeV)

#Result
print "The Q-value of the reaction is",round(Q,2),"MeV"
print "The energy of each alpha particle is",round(Ealpha,3),"MeV"
print "answer for energy in the book varies due to rounding off errors"
The Q-value of the reaction is 17.35 MeV
The energy of each alpha particle is 8.924 MeV
answer for energy in the book varies due to rounding off errors

Example number 11.6, Page number 228

In [16]:
#importing modules
import math
from __future__ import division

#Variable declaration
wt=1000;            #weight(gm)
A=235;              #mass number of uranium
N=(6.02*10**23/A)*wt;         #no.of nuclei in 1kg of uranium
Q=208;                          #energy-balance of the reaction

#Calculation                        
E=N*Q;                          #Energy released(MeV)
#1MeV=4.45*10^-20kWh
E=E*4.45*10**-20;

#Result
print "The energy released is",round(E/10**7,3),"*10**7 kWh"
The energy released is 2.371 *10**7 kWh

Example number 11.7, Page number 228

In [19]:
#importing modules
import math
from __future__ import division

#Variable declaration
wt=5000;                   #weight(gm)
A=235;                     #mass number of uranium
Ef=208;                    #Energy released per fission(MeV)

#Calculation                        
N=(6.02*10**23/A)*wt;      #number of nuclei in 5 Kg
E=N*Ef;                    #Energy(MeV)
E=E*1.6*10**-13;           #Energy(J)
T=24*60*60;                #time
P=E/T;                     #power(MW)

#Result
print "The power output of a nuclear reactor is",round(P/10**6),"MW"
print "answer given in the book is wrong"
The power output of a nuclear reactor is 4934.0 MW
answer given in the book is wrong

Example number 11.8, Page number 228

In [22]:
#importing modules
import math
from __future__ import division

#Variable declaration
A=235;                  #mass number of uranium
p=1000;                 #amount of electric power produced(MW)
e=0.32;                 #energy conversion efficiency of the plant
f=200;                  #fission energy per event(MeV)

#Calculation                        
I=p/e;                  #Input nuclear energy(MW)
TE=I*(10**6)*3600*24*365;           #total energy(J)
EF=f*(10**6)*1.6*10**-19;           #Energy released per fission event(J)
N=TE/EF;                            #Number of nuclei required
M=N*A/(6.02*10**23);       #corresponding mass(g)

#Result
print "The amount of uranium required is",round(M*10**-3,1),"kg"
print "answer in the book varies due to rounding off errors"
The amount of uranium required is 1202.2 kg
answer in the book varies due to rounding off errors

Example number 11.9, Page number 229

In [28]:
#importing modules
import math
from __future__ import division

#Variable declaration
q=1.6*10**-19;                  #charge of the particle(c)
B=1;                            #magnetic field(T)
m=1.67*10**-27;                 #mass of proton(kg)
r=0.5;                              #radius(m)

#Calculation                        
omega=(q*B)/m;                  #angular frequency(radian/s)
v=(omega/(2*math.pi))*10**-8;           #frequency(MHz)
s=omega*r;                          #speed of proton(m/s)
K=(m*(s**2))*(1/2)*6.27*10**12;     #kinetic energy of protons emerging from cyclotron(MeV)

#Result
print "The frequency of oscillator to accelerate protons is",round(omega/10**8,2),"*10**8 radian/s"
print "The speed of proton is",round(s/10**7,1),"*10**7 m/s"
print "The kinetic energy of protons emerging from the cyclotron is",int(K),"MeV"
The frequency of oscillator to accelerate protons is 0.96 *10**8 radian/s
The speed of proton is 4.8 *10**7 m/s
The kinetic energy of protons emerging from the cyclotron is 12 MeV

Example number 11.10, Page number 229

In [30]:
#importing modules
import math
from __future__ import division

#Variable declaration
rho=1.83*10**17;                     #average density of carbon nucleus(kg/m^3)
m=12;                                #mass(u)
e=1.66*10**-27;

#Calculation                        
r=(m*e/((4/3)*math.pi*rho))**(1/3)*10**15;         #radius(fm)

#Result
print "The radius is",round(r,2),"fm"
The radius is 2.96 fm

Example number 11.11, Page number 229

In [32]:
#importing modules
import math
from __future__ import division

#Variable declaration
q=1.6*10**-19;              #charge of the particle(c)
B=5;                        #magnetic field(T)
m=9.1*10**-31;              #mass of electron(kg)

#Calculation                        
v=(q*B)/(2*math.pi*m);      #cyclotron frequency(Hz)

#Result
print "cyclotron frequency of electron is",round(v/10**11,1),"*10**11 Hz"
cyclotron frequency of electron is 1.4 *10**11 Hz

Example number 11.12, Page number 229

In [34]:
#importing modules
import math
from __future__ import division

#Variable declaration
k=1.5;                           #maximum kinetic energy(MeV)
m=1.67*10**-27;                  #mass of proton(kg)
q=1.6*10**-19;                   #charge of particle(c)
r=0.35;                          #radius(m)

#Calculation                        
B=math.sqrt(k*10**6*q*2*m)/(q*r);           #magnetic field(T)

#Result
print "The mgnetic field is",round(B,1),"T"
The mgnetic field is 0.5 T

Example number 11.13, Page number 229

In [37]:
#importing modules
import math
from __future__ import division

#Variable declaration
m=1.67*10**-27;                       #mass of proton(kg)
q=1.6*10**-19;                        #charge of particle(q)
v=25;                                 #cyclotron frequency(MHz)

#Calculation                        
B=(v*10**6*2*math.pi*m)/q;          #magnetic field(T)

#Result
print "The required magnetic field is",round(B,4),"T"
The required magnetic field is 1.6395 T

Example number 11.14, Page number 229

In [39]:
#importing modules
import math
from __future__ import division

#Variable declaration
v=20;                 #cyclotron frequency(MHz)
B=1.3;                #magnetic field(T)

#Calculation                        
d=2*math.pi*v*10**6/B;           #charge to mass ratio of proton(C/kg)

#Result
print "charge to mass ratio of proton is",round(d/10**6,2),"*10**6 C/kg"
charge to mass ratio of proton is 96.66 *10**6 C/kg