A neutron with mass m_{n} makes a head-on, elastic collision with a nucleus of mass M, which is initially at rest.

Part A
Find the kinetic energy that neutron loses during the collision, if the neutron's initial kinetic energy is K_0.
K_{\rm loss} =

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Part B
For what value of M does the incident neutron lose the most energy?
Express your answer in terms of the variable m_n.
M =

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Part C
When M has the value calculated in part B, what is the speed of the neutron after the collision?
v_{n\;{\rm final}} =

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