Question

The energy released by the fission of one ${}_{92}{U}^{235}$ atom is $200MeV$ . Calculate the energy released in $kWh$ , when $1g$ 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 $U^{235}$
$=\frac{Avogadronumber}{atomicweight}=\frac{6.023\times 10^{23}}{235}$
Energy released per fission = 200 MeV
Therefore, the energy released on the fission of 1 g of $U^{235}$
$=\frac{6.023\times 10^{23}\times 200}{235}=5.126\times 10^{23}MeV$
$=5.126\times 10^{23}\times 1.6\times 10^{-13}J=8.2\times 10^{10}Ws$ $\left(\because 1J=1Ws\right)$
$=\frac{8.2\times 10^7}{3600}=2.278\times 10^{4}kWh$