Question

Calculate the Q-values of the following fusion reactions:
(a) ${}_1{}^2\mathrm{H}+{}_1{}^2\mathrm{H}\to {}_1{}^3\mathrm{H}+{}_1{}^1\mathrm{H}$
(b) ${}_1{}^2\mathrm{H}+{}_1{}^2\mathrm{H}\to {}_2{}^3\mathrm{He}+n$
(c) ${}_1{}^2\mathrm{H}+{}_1{}^3\mathrm{H}\to {}_2{}^4\mathrm{He}+n$.
Atomic masses are
$$\begin{gathered} m\left({}_1{}^{2}H\right)=2.014102\mathrm{u}, \\ m\left({}_1{}^{3}H\right)=3.016049\mathrm{u}, \\ m\left({}_2{}^{3}He\right)=3.016029\mathrm{u}, \\ m\left({}_2{}^{4}He\right)=4.002603\mathrm{u}. \end{gathered}$$

Answer 1

$$\begin{gathered} \left(\mathrm{a}\right)Q=\left[2\times m\mathit{}{}_1{}^2\mathrm{H}-\left(m\left({}_3{}^{3}H\right)+m\left({}_1{}^{3}H\right)\right)\right]{\mathrm{c}}^2 \\ =(4.028204-4.023874)\times 931\mathrm{MeV} \\ =4.05\mathrm{MeV} \\ \left(\mathrm{b}\right)Q=\left[2\times m{}_1{}^2\mathrm{H}-(m{}_2{}^{3}H+m_n)\right]c^2 \\ =[4.028204-4.024694)\times 931 \\ =0.00351\times 931 \\ =3.25\mathrm{MeV} \\ \left(\mathrm{c}\right)Q=\left[m{}_1{}^2\mathrm{H}+m{}_1{}^3\mathrm{H}-m{}_1{}^4\mathrm{He}-m_n\right]c^2 \\ =(2.014102+3.016049-4.002603-1.008665)\times 931 \\ =17.57\mathrm{MeV} \end{gathered}$$