In a nuclear reactor `.^235U` undergoes fission liberating `200 MeV` of energy. The reactor has a `10%` efficiency and produces `1000 MW` power. If the reactor is to function for `10 yr`, find the total mass of uranium required.

Explanation

Total energy produced by the reactor in time `t = 10 years`
`E =1000 xx 10^(6) xx 10 xx 3.15 xx 10^(7) J`
`=3.15 xx 10^(7) J`
`Efficiency = ("output energy")/("input energy")`
` rarr` Input energy caused by fission `=(output energy)/(efficiency)`
`=(3.15 xx10^(17))/((10//100))=3.15xx10^(18) J`
Energy produced by `1` fission of `.^(135)U=200 MeV`
`=200 xx1.6xx10^(-13) J`
` =3.2 xx 10^(-11) J`
Therefore, Number of fissions required `=(Total energy )/(Energy per fission)`
`=(3.15 xx 10^(18))/(3.2 xx10^(28))`
`~~9.8 xx 10^(28)`
Hence, mass of nranium required is given by
` m=(N)/(N_(a)) xx 235 kg =(9.8xx 10^(28))/(6.02 xx 10^(26))`
`=38.2 xx 10^(3) kg`.