Questions

In a nuclear reactor fast moving neutron ( $m_{n}$ ) moving at a speed V , hits a moderator nucleus (M) which is originally static and gets scattered elastically by $180^{0}$ . Find the kinetic energy of the neutron after collision?

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12mnV2M−mnM+mn2

12mnV2M+mnM−mn2

12MV2M−mnM+mn2

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detailed solution

Correct option is A

Apply Momentum Conservation, mnV + M (0)=MV2−mnV1 ⇒MV2=mnV+mnV1 ⇒V2=mn(V+V1)M ⇒V22=mnM2V+V12→(1) Apply, Energy Conservation, 12mnV2=12mnV12+12Mv22 ⇒V22=mnMV2−V12 →(2) Equating (1) and (2) we get, mnM2V+V12=mnMV2−V12 ⇒mnMV+V1=V-V1 ⇒V1=M−mnM+mnV Hence, K.E. of neutron after collision, K.E=12mnV12=12mnM−mnM+mnV2

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