Physics

Problem

Two identical medium-mass nuclei

^{40}\!\mathrm{Ca}

are hypothetically fused to form a single

^{80}\!\mathrm{Kr}

nucleus:

^{40}\!\mathrm{Ca} + {}^{40}\!\mathrm{Ca} \;\longrightarrow\; {}^{80}\!\mathrm{Kr}

. Atomic masses (in

u

) are:

^{40}\!\mathrm{Ca}=39.962591

^{80}\!\mathrm{Kr}=79.916378

. (a) Compute the energy change

Q

(in MeV) for one fusion event. (b) Determine the energy change per nucleon for this reaction. (c) Referring to the general shape of the binding-energy curve, explain whether such a fusion reaction is naturally favourable or would require external energy input. (d) Suggest, with reason, whether an endothermic fusion of this type could ever be useful in a practical application. a. Calculate

Q

-value for the fusion event b. Energy change per nucleon c. Reasoning on natural favourability d. Speculation on practical usefulness

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