17: Nuclear properties

Example number 17.1, Page number 324

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

#Variable declaration
m=1.67*10**-27;    #nucleon mass(kg)
R0=1.2*10**-15;    #radius of nucleus(m)

#Calculation
d=m*3/(4*math.pi*R0**3);   #density of nucleus(kg/m**3)

#Result
print "density of nucleus is",round(d/10**17,1),"*10**17 kg/m**3"

density of nucleus is 2.3 *10**17 kg/m**3

Example number 17.2, Page number 324

In [5]:
#importing modules
import math
from __future__ import division

#Variable declaration
a=1.2*10**-15;
k=9*10**9;   #value of N(Nm**2/C**2)
q1=2;
q2=90;
e=1.6*10**-19;   #conversion factor from J to eV

#Calculation
r=a*((4**(1/3))+(228**(1/3)));    #distance(m)
E=k*q1*q2*e**2/r;    #kinetic energy(J)
E=E/(e*10**6);     #kinetic energy(MeV)

#Result
print "potential energy is 0. kinetic energy is",round(E,1),"MeV"

potential energy is 0. kinetic energy is 28.1 MeV

Example number 17.3, Page number 326

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

#Variable declaration
E=2.48*10**4;    #electric field(V/m)
m=1.6605*10**-27;    #nucleon mass(kg)
e=1.6*10**-19;   #conversion factor from J to eV
B=0.75;    #magnetic field(T)

#Calculation
r1=E*12*m/(e*B**2);    #distance on photographic plate for 12C(m)
r1=r1*10**3;   #distance on photographic plate for 12C(mm)
r2=E*13*m/(e*B**2);    #distance on photographic plate for 13C(m)
r2=r2*10**3;   #distance on photographic plate for 13C(mm)
r3=E*14*m/(e*B**2);    #distance on photographic plate for 14C(m)
r3=r3*10**3;   #distance on photographic plate for 14C(mm)
r4=(2*r2)-(2*r1);   #distance between lines of 13C and 12C(mm)
r5=(2*r3)-(2*r2);   #distance between lines of 14C and 13C(mm)
r=r4/2;    #distance if ions are doubly charged(mm)

#Result
print "distance on photographic plate for 12C is",round(r1,2),"mm"
print "distance on photographic plate for 13C is",round(r2,2),"mm"
print "distance on photographic plate for 14C is",round(r3,2),"mm"
print "distance if ions are doubly charged is",round(r,2),"mm"

distance on photographic plate for 12C is 5.49 mm
distance on photographic plate for 13C is 5.95 mm
distance on photographic plate for 14C is 6.41 mm
distance if ions are doubly charged is 0.46 mm

Example number 17.4, Page number 327

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

#Variable declaration
n=6;   #number of neutrons
p=6;   #number of protons
M=12;  #mass of 12C6(u)
E=931.5;  #energy(MeV)

#Calculation
mn=n*1.008665;   #mass of neutrons(u)
mp=p*1.007825;    #mass of hydrogen atoms(u)
m=mp+mn;   #total mass(u)
md=m-M;    #mass deficiency(u)
BE=md*E;   #binding energy(MeV)
be=BE/12;  #average binding energy per nucleon(MeV)

#Result
print "binding energy is",round(BE,2),"MeV"
print "average binding energy per nucleon is",round(be,2),"MeV"

binding energy is 92.16 MeV
average binding energy per nucleon is 7.68 MeV

Example number 17.6, Page number 335

In [11]:
#importing modules
import math
from __future__ import division

#Variable declaration
M22Na=21.9944;   #mass of 22Na(u)
m=1.008665;   #mass of last neutron(u)
M23Na=22.989767;   #mass of 23Na(u)
E=931.5;  #energy(MeV)

#Calculation
M=M22Na+m;   
md=M-M23Na;     #mass deficiency(u)
BE=md*E;    #binding energy(MeV)

#Result
print "binding energy is",round(BE,1),"MeV"

binding energy is 12.4 MeV

Example number 17.7, Page number 341

In [13]:
#importing modules
import math
from __future__ import division

#Variable declaration
hbar=1.05*10**-34;   
c=3*10**8;   #speed of light(m/s)
mpi=140;    #mass of pi-meson(MeV/c**2)
e=1.6*10**-13;

#Calculation
r=hbar*c/(mpi*e);    #range of nuclear force(m)

#Result
print "range of nuclear force is",round(r*10**15,1),"fm"

range of nuclear force is 1.4 fm