Question

The energy released during the fission of $1kg$ of $U^{235}$ is $E_1$ and that produced during the fusion of $1kg$ 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 $1kg$ of $U^{235}$ is $n_1=\frac{N_A}{235\left(kg\right)}:N_A$ is the Avogadro number.
Number of fusions that can occur for $1kg$ of hydrogen is $n_2=\frac{N_A/\left(1kg\right)}{4}$ , because $4$ hydrogen nuclei fuse to form one helium nuclei.
$\frac{E_2}{E_1}=\frac{n_2\times 24.7MeV}{n_1\times 200MeV}=\frac{235\times 24.7}{4\times 200}=7.25$ (approx)
$=7$