A `U^(235)` nuclear reactor generates energy at a rate of `3.70 x x10^(7) J/s`. Each fission liberates 185 MeV useful energy. If the reactor has to operate for `144 xx 10^(4) S`, then, the mass of the fuel needed is (Assume Avogadro's number = `6 x 10^(23) mol^(-1), 1eV = 1.6 x 10^(-19) J`).

Options

A. 70.5 kg
B. 0.705 kg
C. 13.1 kg
D. 1.31 kg

Answer

B

Explanation

`1s - 3.7 xx 10^(7)`J
`144xx10^(4)s - ?`
In`144xx10^(4)s` energy generated = `144xx10^(4)xx3.7xx10^(7)`J
Energy released in one fission = `185xx10^(6)xx1.6xx10^(-19)`
Number of fission = `144xx10^(4)xx3.7xx10^(7)/(185xx10^(6)xx1.6xx10^(-19))`
= `1.8 xx 10^(-24)` of ` U^(235)` atoms
Mass of fuel needed is
`rArr m = 235xx1.8xx10^(24)/(6.023xx10^(23))`
`:. m = 0.7kg`