question_answer

A neutron is moving with velocity u. It collides head on and elastically with an atom of mass number A. If the initial kinetic energy of the neutron be E, how much kinetic energy will be retained by the neutron after collision?

A) \[{{\left( \frac{A}{A+1} \right)}^{2}}E\]

B) \[\frac{A}{{{(A+1)}^{2}}}E\]

C) \[{{\left( \frac{A-1}{A+1} \right)}^{2}}E\]

D) \[\frac{A-1}{{{(A+1)}^{2}}}E\]

Correct Answer: C

Solution :

 The fraction of total energy retained by nucleus \[{{\left( \frac{\Delta K}{K} \right)}_{retained}}={{\left( \frac{{{m}_{2}}-{{m}_{1}}}{{{m}_{1}}+{{m}_{2}}} \right)}^{2}}={{\left( \frac{A-1}{1+A} \right)}^{2}}\] \[\therefore \]Kinetic energy retained by neutron after collision is \[{{\left( \frac{A-1}{A+1} \right)}^{2}}E\]