8: Alpha and Beta Decays

Example number 1, Page number 282

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

#Variable declaration
e=1.6*10**-19;     #charge(coulomb)
Ek=0.5*10**6;      #kinetic energy(eV)
m0=9.11*10**-31;   #mass(kg)
c=3*10**8;         #velocity of light(m/s)
r=0.1;             #radius(m)

#Calculation
x=(Ek*e/(m0*c**2))+1;
y=1-(1/x)**2;
v=c*math.sqrt(y);     #velocity of beta article(m/s)
m=m0/math.sqrt(1-(v/c)**2);     #mass of beta particle(kg)
B=m*v/(e*r);                    #flux density(weber/m**2)

#Result
print "velocity of beta article is",round(v/c,4),"c"
print "mass of beta particle is",round(m/m0,2),"m0"
print "flux density is",round(B,6),"weber/m**2"
print "answer in the book varies due to rounding off errors"

velocity of beta article is 0.8624 c
mass of beta particle is 1.98 m0
flux density is 0.029106 weber/m**2
answer in the book varies due to rounding off errors

Example number 2, Page number 283

In [12]:
#importing modules
import math
from __future__ import division

#Variable declaration
A=226;       #atomic weight
Ra=226.02540;     #mass of Ra
Rn=222.017571;    #mass of Rn
He=4.002603;      #mass of He
m=931.5; 

#Calculation
Q=(Ra-Rn-He)*m;   
kalpha=(A-4)*Q/A;    #kinetic energy of alpha particle(MeV)

#Result
print "kinetic energy of alpha particle is",round(kalpha,3),"MeV"

kinetic energy of alpha particle is 4.782 MeV

Example number 3, Page number 283

In [15]:
#importing modules
import math
from __future__ import division

#Variable declaration
Ne=22.99465;     #mass of Ne
Na=22.989768;    #mass of Na
m=931.5; 

#Calculation
Q=(Ne-Na)*m;     #maximum kinetic energy of electrons(MeV)

#Result
print "maximum kinetic energy of electrons is",round(Q,3),"MeV"
print "answer given in the book is wrong"

maximum kinetic energy of electrons is 4.548 MeV
answer given in the book is wrong

Example number 4, Page number 284

In [18]:
#importing modules
import math
from __future__ import division

#Variable declaration
K=39.963999;     #mass of K
Ca=39.962591;    #mass of Ca
Ar=39.962384;    #mass of Ar
me=0.000549;     #mass of electron  
m=931.5; 

#Calculation
Q1=(K-Ar-(2*me))*m;   #Q value of 1st decay(MeV)
Q2=(K-Ar)*m;      #Q value of 2nd decay(MeV)

#Result
print "Q value of 1st decay is",round(Q1,3),"MeV"
print "Q value of 2nd decay is",round(Q2,3),"MeV"

Q value of 1st decay is 0.482 MeV
Q value of 2nd decay is 1.504 MeV