Question

Consider the reaction,
${}_1^{2}H+{}_1^{2}H⟶{}_2^{3}He+{}_0^{1}n$
$m\left({}_1^{2}H\right)=2.014082u,m\left({}_2^{3}He\right)=3.016029u,m\left({}_0^{1}n\right)=1.008665u$ Then, mark the correct option.

• A. Threshold energy of 3.23 MeV is required to initiate the reaction
• B. Reaction occurs when total KE of reactants exceeds 3.23 MeV
• C. Reaction occurs such that final total KE is 3.23 MeV lesser than total initial KE
• D. No, threshold energy is required for the reaction

Answer 1

Answer: (D)

As, $m\left({}_1^{2}H\right)=2.014082u$
and $m\left({}_2^{3}He\right)=3.016029$
and $m\left({}_0^{1}n\right)=1.008665$
$\Delta m=$ mass defect
$=2m\left({}_1^{2}H\right)-m3\left({}_2^{3}He\right)-m\left({}_0^{1}n\right)$
$=2\times 2.014082-3.016029-1.008665$
$\Rightarrow Q$-value =Energy liberated in reaction
$=[\text{ mass }(\text{ reactants })-\text{mass}(\text{ products })]\times 931.5$
$=\Delta m\times 931.5MeV=3.232MeV$
As $Q$-value is positive, so no threshold energy is required.