Question

In a nuclear power generating station, \(^{235}_{92}U\) is used as “the fuel”. Fission of one atom of \(^{235}_{92}U\) releases 200 MeV of energy. The efficiency of generating plant is 80%. The (reactor) plant consumes 256 mg of uranium fuel in 4 hours. Its power output, in MW is (nearly),

(1) 142

(2) 178

(3) 221

(4) 276

Answer 1

(2) 178

Energy produced due to fission of one atom of \(^{235}_{92}U\) = 200 MeV

The number of atoms, in 256 mg of \(^{235}_{92}U\) = \(\frac{6.023\times10^{23}}{0.256\times 235}≃10^{22}\)

∴ Total energy produced due to fission of the given mass of \(^{235}_{92}U\) = 200 x 10²² MeV = 2 x 10²⁴ MeV