Consider the fusion reaction

PHYSICS · Multi-part · ISC · Physics · Atoms and Nuclei · Work, Energy and Power

Problem

Consider the fusion reaction 12 ⁣H+13 ⁣H  ⟶  24 ⁣He+01 ⁣n^{2}_{1}\!\mathrm{H} + ^{3}_{1}\!\mathrm{H} \;\longrightarrow\; ^{4}_{2}\!\mathrm{He} + ^{1}_{0}\!\mathrm{n}. The relevant nuclear masses are: $\begin{aligned} m(^{2}\!\mathrm{H}) &= 2.014102\,\text{u}, & m(^{3}\!\mathrm{H}) &= 3.016049\,\text{u}, m(^{4}\!\mathrm{He}) &= 4.001506\,\text{u}, & m_n &= 1.008665\,\text{u}. \end{aligned}$ Take 1 u=931.5 MeV c ⁣−21\,\text{u} = 931.5\,\text{MeV}\,c^{\!-2}. (i) Calculate the total binding energy of the reactant nuclei. (ii) Calculate the total binding energy of the product nuclei. (iii) Determine the energy released per fusion event in MeV. (iv) Compute the binding energy per nucleon before and after the reaction and explain why the reaction is energetically favourable.

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