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

Output power `P = 1000MW = 10^(9)W`
`eta`, efficiency `= ("output power",P)/("input power",P_(i))`
`(10)/(100) = (10^(9))/(P_(i)) rArr P_(i) = 10^(10)W`
Let mass of uranium `=m`
Number of fission `=` number of atoms `=(m)/(M)N_(A)`
Energy produced `= (mN_(A))/(M) xx 200 xx 1.6 xx 10^(-13)J`
Power `= (mN_(A))/(M) xx (200xx1.6xx10^(-13))/(10y) = 10^(10)`
`(m xx 6.023xx10^(23) xx200xx1.6xx10^(-13))/(235xx10xx36xx24xx3600) = 10^(10)`
`m xx 2.6 xx10^(2) = 10^(10)`
`m = 0.38 xx 10^(8)g`
`= 38 xx 10^(3) kg`