Two candidate fusion reactions are being evaluated for a compact fusion power system

PHYSICS · Multi-part · CBSE · Physics · Nuclei · Nuclei

Problem

Two candidate fusion reactions are being evaluated for a compact fusion power system. Reaction 1:

_{1}^{2}\text{H}+_{1}^{2}\text{H}\;\longrightarrow\;_{2}^{3}\text{He}+_{0}^{1}\text{n}

Reaction 2:

_{1}^{1}\text{H}+_{1}^{3}\text{H}\;\longrightarrow\;_{2}^{4}\text{He}+\gamma

Relevant nuclear masses (in u): •

m(_{1}^{1}\text{H}) = 1.007825\,\text{u}

•

m(_{1}^{2}\text{H}) = 2.014102\,\text{u}

•

m(_{1}^{3}\text{H}) = 3.016049\,\text{u}

•

m(_{2}^{3}\text{He}) = 3.016029\,\text{u}

•

m(_{2}^{4}\text{He}) = 4.002603\,\text{u}

•

m(_{0}^{1}\text{n}) = 1.008665\,\text{u}

Assume

1\,\text{u} = 931.5\,\text{MeV}/c^{2}

. The photon mass may be taken as zero. (a) Determine the energy released by Reaction 1. (b) Determine the energy released by Reaction 2. (c) For each reaction, calculate the energy released per nucleon of fuel (use the total number of nucleons in the reactants). Identify which reaction is more energy-efficient on a per-nucleon basis and briefly justify your conclusion.

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