Determine the Q -value for the fusion reaction: ^ 2 _ 1 H + ^ 2 _ 1...

The $Q$-value of a nuclear reaction is determined by the mass defect $\Delta m$ between the reactants and the products.

The given fusion reaction is:
^{2}_{1}\text{H} + ^{2}_{1}\text{H} \to ^{3}_{2}\text{He} + n$<br><br>Calculate the total mass of the reactants:<br>Mass of reactants$= 2 \times m(^{2}_{1}\text{H}) = 2 \times 2.014102 \text{ u} = 4.028204 \text{ u}$<br><br>Calculate the total mass of the products using the standard mass of a neutron ($m_n \approx 1.008665 \text{ u}$):<br>Mass of products$= m(^{3}_{2}\text{He}) + m_n = 3.016029 \text{ u} + 1.008665 \text{ u} = 4.024694 \text{ u}$<br><br>Now, find the mass defect$\Delta m$:<br>$\Delta m = \text{Mass of reactants} - \text{Mass of products}$<br>$\Delta m = 4.028204 \text{ u} - 4.024694 \text{ u} = 0.00351 \text{ u}$<br><br>Convert the mass defect into energy ($Q$-value) using the conversion factor$1 \text{ u} = 931.5 \text{ MeV}$:<br>$Q = \Delta m \times 931.5 \text{ MeV/u}$<br>$Q = 0.00351 \times 931.5 \text{ MeV} \approx 3.27 \text{ MeV}$<br><br>The calculated$Q$-value is approximately$3.27 \text{ MeV}$, which is closest to the given option of$3.25 \text{ MeV}$.<br><br>Answer:$3.25 \text{ MeV}