# chapter 7:nuclear reactions¶

## example 7.1;pg no: 111¶

In [1]:
#cal of reproduction factor for the reactor
#intiation of all variables
# Chapter 7
print"Example 7.1, Page:111  \n \n"
# Given:

f=1.03;# fast fission factor
n=1.32;# no. of fast neutrons generated per thermal radiations
ref=0.89;# resonance escape factor
tuf=0.87;# thermal utilization factor

# Solution
rf=f*n*ref*tuf;#reproduction factor
print"The reproduction factor for the reactor is = ",round(rf,3)

Example 7.1, Page:111

The reproduction factor for the reactor is =  1.053


## example 7.2;pg no: 111¶

In [2]:
#cal of approximate critical dimensionsof a Pu 239 and radius of the reactor
#intiation of all variables
# Chapter 7
print"Example 7.2, Page:111  \n \n"
# Given:
import math
k=1.04;
m=0.032;# in m^2 i.e., migration area M^2
# Solution: (a) Cubical reactor
a=3.14*math.sqrt(3*m/(k-1));
print"\n The approximate critical dimensionsof a Pu 239 in (m)=",round(a,2)
# Solution: (a) Spherical reactor
r=a/math.sqrt(3);
print"\n \n The radius of the reactor in (m)=",round(r,2)

Example 7.2, Page:111

The approximate critical dimensionsof a Pu 239 in (m)= 4.86

The radius of the reactor in (m)= 2.81


## example 7.3;pg no: 111¶

In [3]:
#cal of design parameter for H2O,D2O,C
#intiation of all variables
# Chapter 7
print"Example 7.3, Page:111  \n \n"
# Given:
a1=687; # neutron absorption cross section for U 235 in barns
a2=0.66 # neutron absorption cross section for H2O in barns
a3=0.0093; # neutron absorption cross section for D2O in barns
a4=0.0045; # neutron absorption cross section for C in barns

#Solution:

F1=1.07*a1/a2;#design parameter for H2O part(a)
print"\n The design parameter for H2O is =",round(F1)

F2=1.07*a1/a3;#design parameter for D2O part(b)
print"\n \n The design parameter for D2O is =",round(F2)

F3=1.07*a1/a4;#design parameter for C part(c)
print"\n \n The design parameter for C is =",round(F3)#cal of design parameter for H2O,D2O,C
#intiation of all variables
# Chapter 7
print"Example 7.3, Page:111  \n \n"
# Given:
a1=687; # neutron absorption cross section for U 235 in barns
a2=0.66 # neutron absorption cross section for H2O in barns
a3=0.0093; # neutron absorption cross section for D2O in barns
a4=0.0045; # neutron absorption cross section for C in barns

#Solution:

F1=1.07*a1/a2;#design parameter for H2O part(a)
print"\n The design parameter for H2O is =",round(F1)

F2=1.07*a1/a3;#design parameter for D2O part(b)
print"\n \n The design parameter for D2O is =",round(F2)

F3=1.07*a1/a4;#design parameter for C part(c)
print"\n \n The design parameter for C is =",round(F3)

Example 7.3, Page:111

The design parameter for H2O is = 1114.0

The design parameter for D2O is = 79042.0

The design parameter for C is = 163353.0
Example 7.3, Page:111

The design parameter for H2O is = 1114.0

The design parameter for D2O is = 79042.0

The design parameter for C is = 163353.0


## example 7.4;pg no: 112¶

In [4]:
#cal of no. of fissions per second
#intiation of all variables
# Chapter 7
print"Example 7.4, Page:112  \n \n"
# Given:
P=10*10**6; # power in watts
E=200*10**6; # in eV

# Solution:
e=E*1.6*10**-19;# in joules
# Thus for 1 fission occurs per second, rate of power generation is e
n=(P)/e;# no. of fissions
print"The no. of fissions per second are =",n

Example 7.4, Page:112

The no. of fissions per second are = 3.125e+17


## example 7.5;pg no: 112¶

In [5]:
#cal of thermal energy generated
#intiation of all variables
# Chapter 7
print"Example 7.5, Page:112  \n \n"
# Given:
density=19;# in g/cc
E1=200*10**6*(1.6*10**-19); # energy released per fission in J
flux1=10**12;# in cm^2/s
a1=590*10**-24;#fission cross-section in cm^2
Na1=6.02*10**23;

# Solution:

#Ntgt=volume of target*No.of atoms per cm^3

Ni=(30*((0.5)**2)*3.14*density*Na1*(0.72*10**-2))/238;

Np=Ni*a1*flux1;

E2=E1*Np;# Thermal energy generated in J

print"\n The thermal energy generated is =(J)",round(E2,2)
# Note: There is discrepancy in answer given in the textbook. After calculations the answer comes out to be 153.850366

Example 7.5, Page:112

The thermal energy generated is =(J) 153.85