Atoms And Nuclei Question 285
Question: A neutron travelling with a velocity v and kinetic energy E has a perfectly elastic head-on collision with a nucleus of an atom of mass number A at rest. The fraction of total energy retained by the neutron is approximately
Options:
A) $ {{[ ( A-1 )( A+1 ) ]}^{2}} $
B) $ {{[ ( A+1 )( A-1 ) ]}^{2}} $
C) $ {{[ ( A-1 )/A ]}^{2}} $
D) $ {{[ ( A+1 )/A ]}^{2}} $
Show Answer
Answer:
Correct Answer: A
Solution:
- $ v{’ _{1}}=\frac{( m _{1}-m _{2} )v _{1}+2m _{2}v _{2}}{m _{1}+m _{2}} $
As $ v _{2} $ is zero, $ m _{2}>m _{1},v{’ _{1}} $ is in the opposite direction. $ m _{1}=1,m _{2}=A. $
$ \therefore | v{’ _{1}} |=\frac{( A-1 )}{( A+1 )}v _{1} $
The fraction of total energy retained is $ \frac{1/2mv’ _{1}^{2}}{1/2v _{1}^{2}}=\frac{( A-1 )}{( A+1 )} $
