7: Nuclear Structure

Example number 1, Page number 235

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

#Variable declaration  
mp=1.6725*10**-27;         #mass of proton(kg)
mn=1.6748*10**-27;         #mass of neutron(kg)

#Calculations
m=(3*mp)+(4*mn);           #total mass(kg)

#Result
print "total mass is",m*10**27,"*10**-27 kg"

total mass is 11.7167 *10**-27 kg

Example number 2, Page number 235

In [10]:
#importing modules
import math
from __future__ import division

#Variable declaration  
N=6*10**23;         #avagadro number

#Calculations
e=6*N;              #number of electrons
p=6*N;              #number of protons
n=8*N;              #number of neutrons

#Result
print "number of electrons is",int(e/10**23),"*10**23"
print "number of protons is",int(p/10**23),"*10**23"
print "number of neutrons is",int(n/10**23),"*10**23"

number of electrons is 36 *10**23
number of protons is 36 *10**23
number of neutrons is 48 *10**23

Example number 3, Page number 235

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

#Variable declaration  
r=2.71*10**-15;       #radius(m)
r0=1.3*10**-15;       

#Calculations
A=(r/r0)**3;          #mass number of nucleus

#Result
print "mass number of nucleus is",int(A)

mass number of nucleus is 9

Example number 4, Page number 235

In [20]:
#importing modules
import math
from __future__ import division

#Variable declaration  
r1=7.731;       #radius(fermi)
A1=165;         #mass number of Ho
A2=4;           #mass number of He       

#Calculations
r2=r1*(A2/A1)**(1/3);       #radius of He(fermi)

#Result
print "radius of He is",round(r2,4),"fermi"

radius of He is 2.2375 fermi

Example number 5, Page number 236

In [23]:
#importing modules
import math
from __future__ import division

#Variable declaration  
r1=6;       #radius(fermi)
A1=125;     #mass number of nucleus
A2=64;      #mass number of nucleus   

#Calculations
r2=r1*(A2/A1)**(1/3);       #radius of nucleus(fermi)

#Result
print "radius of nucleus is",r2,"fermi"

radius of nucleus is 4.8 fermi

Example number 6, Page number 236

In [25]:
#importing modules
import math
from __future__ import division

#Variable declaration  
A=1;     #assume
r=1.3*A**(1/3)*10**-15;       #radius(m)   
amu=1.66*10**-27;     #amu(kg)

#Calculations
V=4*math.pi*r**3/3;     #volume(m**3)
M=A*amu;
rho=M/V;                #density of nuclear matter(kg/m**3)

#Result
print "density of nuclear matter is",round(rho/10**17,1),"*10**17 kg/m**3"

density of nuclear matter is 1.8 *10**17 kg/m**3

Example number 7, Page number 236

In [33]:
#importing modules
import math
from __future__ import division

#Variable declaration  
A=235/2;     #mass number
r=1.3*A**(1/3)*10**-15;       #radius(m)   
Z=46;                         #atomic number
e=1.6*10**-19;                #charge(coulomb)
epsilon0=8.65*10**-12;       

#Calculations
U=(Z*e)**2/(4*math.pi*epsilon0*2*r);     #electrostatic potential energy(eV)

#Result
print "electrostatic potential energy is",round(U*10**11,2),"*10**-11 eV"
print "answer given in the book is wrong"

electrostatic potential energy is 3.91 *10**-11 eV
answer given in the book is wrong

Example number 8, Page number 240

In [38]:
#importing modules
import math
from __future__ import division

#Variable declaration  
mp=1.007277;         #mass of proton(amu)
mhn=4.001265;        #mass of helium nucleus(amu)
mn=1.008666;         #mass of neutron(amu)
amu=931.4812;        #amu(MeV)

#Calculations
m=(2*mp)+(2*mn);           #total initial mass(amu)
deltam=m-mhn;              #mass defect(amu)
BEalpha=deltam*amu;        #binding energy of alpha particle(MeV)
BEn=BEalpha/4;             #binding energy per nucleon(MeV)

#Result
print "binding energy of alpha particle is",round(BEalpha,4),"MeV"
print "binding energy per nucleon is",round(BEn,4),"MeV"
print "answer given in the book is wrong"

binding energy of alpha particle is 28.5229 MeV
binding energy per nucleon is 7.1307 MeV
answer given in the book is wrong

Example number 9, Page number 240

In [45]:
#importing modules
import math
from __future__ import division

#Variable declaration  
mh=1*10**-3;         #mass of hydrogen(kg)
mhe=0.993*10**-3;    #mass of helium(kg)
e=5/100;             #efficiency
c=3*10**8;           #velocity of light(m/sec)
x=36*10**5;     

#Calculations
deltam=mh-mhe;              #mass defect(kg)
E=deltam*c**2;                   #energy released(J)
EE=e*E/x;                   #electrical energy(kilowatt hour)

#Result
print "energy released is",E/10**10,"*10**10  J"
print "electrical energy is",round(EE/10**3,2),"*10**3 kilowatt hour"

energy released is 63.0 *10**10  J
electrical energy is 8.75 *10**3 kilowatt hour

Example number 10, Page number 241

In [47]:
#importing modules
import math
from __future__ import division

#Variable declaration  
mp=1.6725*10**-27;         #mass of proton(kg)
me=9*10**-31;              #mass of electron(kg)
mn=1.6747*10**-27;         #mass of neutron(kg)
c=3*10**8;                 #velocity of light(m/sec)
e=1.6*10**-19;             #charge(coulomb)

#Calculations
deltam=mn-(mp+me);         #mass defect(kg)
E=deltam*c**2/(e*10**6);             #energy released(MeV)

#Result
print "energy released is",round(E,2),"MeV"

energy released is 0.73 MeV

Example number 11, Page number 241

In [53]:
#importing modules
import math
from __future__ import division

#Variable declaration  
mp=1.007825;         #mass of proton(amu)
mn=1.008665;         #mass of neutron(amu)
BE=298;              #binding energy(MeV)
amu=931.5;           #amu(MeV)

#Calculations
m=(17*mp)+(18*mn);           #total initial mass(amu)
deltam=BE/amu;                 #mass defect(amu)
Am=m-deltam;                 #atomic mass(amu)

#Result
print "atomic mass is",round(Am,5),"amu"

atomic mass is 34.96908 amu