The minimum kinetic energy needed by an alpha particle to cause the nuclear reaction in a laboratory frame is (in MeV). Assume that is at rest in the laboratory frame. The masses of , , and can b

Question

The minimum kinetic energy needed by an alpha particle to cause the nuclear reaction  in a laboratory frame is  (in MeV). Assume that  is at rest in the laboratory frame. The masses of , ,  and  can be taken to be , ,  and , respectively, where . The value of  is  .

Canvas Classes · Accepted Answer

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- Find the threshold (minimum) kinetic energy of the alpha to trigger this reaction.

💡 First find the -value from the mass difference. The reaction is endothermic (), so a minimum (threshold) energy is required. Because the target  is at rest, the threshold energy in the lab frame is larger than  by the factor  (to conserve momentum).

✏️
Mass change: 
.

(endothermic).

Threshold KE of alpha: .

So  MeV.

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