Question

The energy released during the fission of $1 \, kg$ of $U^{235}$ is $E_{1}$ and that produced during the fusion of $1 \, kg$ of hydrogen is $E_{2}$ . If energy released per fission of Uranium -235 is 200 MeV and that per fusion of hydrogen is 24.7 MeV, then the ratio $\frac{E_{2}}{E_{1}}$ is

• A. $2$
• B. $7$
• C. $10$
• D. $20$

Answer 1

Answer: (B)

Number of fissions that can occur in $1 \, kg$ of $U^{235}$ is $n_{1}=\frac{N_{A}}{235 \, \left(k g\right)}:N_{A}$ is the Avogadro number.
Number of fusions that can occur for $1 \, kg$ of hydrogen is $n_{2}=\frac{N_{A} / \left(1 \, k g\right)}{4}$ , because $4$ hydrogen nuclei fuse to form one helium nuclei.
$\frac{E_{2}}{E_{1}}=\frac{n_{2} \times 24.7 \, M e V}{n_{1} \times 200 M e V}=\frac{235 \times 24.7}{4 \times 200}=7.25$ (approx)
$=7$