Question

The energy released by the fission of one $_{92}U^{235}$ atom is $200 \, MeV$ . Calculate the energy released in $ \, kWh$ , when $1 \, g$ of $U^{235}$ undergoes fission.

• A. $2.270\times 10^{4}kWh$
• B. $2.278\times 10^{4}kWh$
• C. $2.268\times 10^{2}kWh$
• D. $2.288\times 10^{4}kWh$

Answer 1

Answer: (B)

Now, number of atoms in 1g of $U^{235}$
$=\frac{A v o g a d r o \, n u m b e r}{a t o m i c \, w e i g h t}=\frac{6.023 \, \times 10^{23}}{235}$
Energy released per fission = 200 MeV
Therefore, the energy released on the fission of 1 g of $U^{235}$
$=\frac{6.023 \, \times 10^{23} \times 200}{235}=5.126 \, \times 10^{23}MeV$
$=5.126 \, \times 10^{23}\times 1.6 \, \times 10^{- 13}J=8.2 \, \times 10^{10} \, W \, s$ $\left(\because 1 J = 1 \, W \, s\right)$
$=\frac{8.2 \, \times 10^{7}}{3600}=2.278 \, \times 10^{4}kWh$