Question

The isotopic masses of ${}_1^2\text{H}$ and ${}_2^4\text{He}$ are $2.0141$ and $4.0026$ amu respectively. The velocity of light in vacuum is $2.998\times {10}^{8}m/sec$. The quantity of energy liberated when two mole of ${}_1^2\text{H}$ undergo fusion to form 1 mole of ${}_2^4\text{He}$ is :

• A. $2.3\times {10}^{12}J$
• B. $4.3\times {10}^{12}J$
• C. $6.6\times {10}^{12}J$
• D. none of these

Answer 1

The correct option is A $2.3\times {10}^{12}J$

Fusion reaction is $2{}_1^2\text{H}{⟶}_2^4\text{He}+$ energy

Mass defect $=2\times$ mass of ${}_1^2\text{H}-$mass of ${}_2^4\text{He}$
$=2\times 2.0141-4.0026$
$=0.0256amu$

Energy liberated during fusion of 2 atoms of ${}_1^2\text{H}=\Delta m{c}^2$
$=0.0256\times 1.66\times {10}^{-27}\times (2.998\times {10}^8{)}^2$J
$=3.8\times {10}^{-12}$J

Hence, energy liberated during fusion of 2 moles (or 2 N atoms) of ${}_1^2\text{H}$ to give N atoms (or 1 mole) of

${}_2^4\text{He}=3.8\times {10}^{-12}\times 6.023\times {10}^{23}=2.3\times {10}^{12}J$