A neutron travelling with a velocity 𝑣 and K.E. 𝐸 collides perfectly elastically head on with the nucleus of an atom of mass number 𝐴 at rest. The fraction of total energy retained by neutron is

Question: A neutron travelling with a velocity 𝑣 and K.E. 𝐸 collides perfectly elastically head on with the nucleus of an atom of mass number 𝐴 at rest. The fraction of total energy retained by neutron is

(A) \left( \dfrac{A-1}{A+1}\right) ^{2}

(B) \left( \dfrac{A+1}{A-1}\right) ^{2}

(C) \left( \dfrac{A-1}{A}\right) ^{2}

(D) \left( \dfrac{A+1}{A}\right) ^{2}

Answer: Option (A)

Solution:

A neutron travelling with a velocity 𝑣 and K.E. 𝐸 collides perfectly elastically head on with the nucleus of an atom of mass number 𝐴 at rest. The fraction of total energy retained by neutron is
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