Question

Mass of ${}_{92}{U}^{235}$ required to produce electrical energy in a nuclear reactor for 30 days is $23.5kg$. If 40% of the energy released by the fission is converted into electrical energy, determine the power generated by the nuclear reactor. (Assume that $200MeV$ energy is released per fission of ${}_{92}{U}^{235}$ )

• A. 390 MW
• B. 297 W
• C. 297 MW
• D. 27MW

Answer 1

The correct option is C 297 MW

$n\left(\frac{235}{92}U\right)=\frac{23.5\times {10}^3}{235}\times 6.023\times {10}^{23}\text{atoms}$

$\begin{array}{c}\text{Energy released by fission}=200MeV\text{per atom}\\ \text{Total energy released}=0.1\times {10}^3\times 6.023\times {10}^{23}\times 200\times {10}^6\times 1.6\times {10}^{-19}J\\ =6.023\times 2\times 1.6\times {10}^{14}J\end{array}$

$\begin{array}{c}\text{Electricity produced}=\frac{40}{100}\times 6.023\times 2\times 1.6\times {10}^{14}J\\ \text{Power}=\frac{0.4\times 6.023\times 2\times 1.6\times {10}^{14}}{30\times 24\times 60\times 60}\\ =296.29\times {10}^{6}W\end{array}$