Physics

Problem

Four nuclear reactions are listed below. According to the shape of the average binding-energy-per-nucleon curve, which reaction should release the greatest amount of energy per nucleon of reactant? I.

^{238}\text{U} + n \rightarrow ^{140}\text{Xe} + ^{94}\text{Sr} + 2n

II.

^{14}\text{N} + ^{4}\text{He} \rightarrow ^{18}\text{F} + \gamma

III.

^{2}\text{H} + ^{3}\text{H} \rightarrow ^{4}\text{He} + n

IV.

^{56}\text{Fe} \rightarrow 13\; ^{4}\text{He}

a) Reaction II; it forms a nucleus closer to the iron peak, so it releases the most energy. b) Reaction I; it is induced fission of a heavy nucleus, like that used in nuclear reactors. c) Reaction III; it is fusion of very light nuclei leading toward the binding-energy peak. d) Reaction IV; breaking Fe-56 into

\alpha

-particles must liberate a great deal of energy.

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