Question

The binding energy of $\text{deuteron}$ is $2.2\text{MeV}$ and that of ${}_2{\text{He}}^4$ is $28\text{MeV}$. If two deuterons are fused to form one ${}_2{\text{He}}^4$, then the energy released is

• A. $30.2\text{MeV}$
• B. $25.8\text{MeV}$
• C. $23.6\text{MeV}$
• D. $19.2\text{MeV}$

Answer 1

The correct option is C $23.6\text{MeV}$

${}_1{\text{H}}^2+{}_1{\text{H}}^2\to {}_2{\text{He}}^4+Q$

Where, $Q$ is the energy released in the reaction.

By conservation of energy,

$Q=(B.E{)}_{\text{product}}-(B.E{)}_{\text{reactants}}$

$\Rightarrow Q=(B.E\text{of}{}_2{\text{He}}^4)-2(B.E\text{of}{}_1{\text{H}}^2)$

$\Rightarrow Q=28\text{MeV}-4.4\text{MeV}$

$\Rightarrow Q=23.6\text{MeV}$

Hence, option $\left(C\right)$ is correct.