Maximum amount of energy the neutron can lose

[Sudikshya Pant]

A 1 keV fast neutron (relative mass 1) in a moderator collides elastically with a helium atom He (relative mass 4) at rest. What is the maximum amount of energy the neutron can lose?

My answer is 16/25 of 1ke but while deriving this answer I simply solved based on the question as if the "maximum" in the question didn't exist. But later on I wondered if it has some significance for which I should have applied different method than the general one i.e. using conservation of momentum and energy assuming different final velocities for both the masses.

I also wondered if the answer could be as the neutron 1ke it might lose all of its energy if it comes to a halt but again I doubt that it is possible because helium is not extremely large in mass compared to neutron.

I wanted help to know if there any significance of maximum in the question? I request you to give hint if it does!

 

[TSny]

There is the possibility that the the collision is not "head on".

 

[Sudikshya Pant]

There is the possibility that the the collision is not "head on".

Based on your comment I tried to solve assuming that the neutron formed certain angle after the collision and then worked the problem out in center of momentum frame. Finally, I reached a point where I had to choose the scattering angle for minimum final velocity of the neutron, which was the direction opposite to that of its initial velocity. The answer was 16/25 of 1keV.

Do you think the answer is wrong?

 

[TSny]

I think 16/25 keV is correct for the maximum loss of KE of the neutron. Your analysis in the center of mass frame is a good way to approach the problem.

This occurs for a head-on collision in which the neutron bounces straight back. If the collision is not head-on, then the neutron would lose less energy. Thus, you have found the maximum KE that the neutron could lose.

 

[Sudikshya Pant]

I think 16/25 keV is correct for the maximum loss of KE of the neutron. Your analysis in the center of mass frame is a good way to approach the problem.

This occurs for a head-on collision in which the neutron bounces straight back. If the collision is not head-on, then the neutron would lose less energy. Thus, you have found the maximum KE that the neutron could lose.

Thank you for your help.