Suppose India has a target of producing by `2020 AD, 200,000 MW` of electric power, ten percent of which was to be obtained from nuclear power plants. Suppose we are given that, on an avedrage, the efficiency of utilization(i.e conversion to electric energy) of thermal energy produced in a reactor was `25%`. How much amount of fissionable uranium would our country need per year by `2020`? Take the heat energy per fission of `.^(235)U` to be about `200 MeV`.

Explanation

Required power from nuclear plants `= 10 %` of `2,00,000 Mw = 2 x 10 ^(10)` w
Required electric energy from nuclear plants in one year `= 2 x 10^(10) x 365 x 24 x 60 x 60`
`= 2x 10 ^(10) x 3.15 x 10 ^(7) = 6.30 x 10 ^(7) J`
Available electric energy per fission `= 25 % or 200MeV = 50 MeV = 8x 10 ^(-12)J`
Req. no. of fission per year=
`(6. 30 xx 10 ^(17))/(8 xx 10 ^(-12)) = 0.7875 x 10 ^(29)`
Req. no. of moles of `U ^(238)`
` = (0.7875xx 10 ^(29))/(6. 023 xx 10 ^(23)) = 0.1307 x 10^(6)`
Reqired mass of `U ^(238) = 0.1307 x 235 x 10 ^(6) g`
`= 30.71 x 10 ^(6) gm = 30.71 x 10 ^(6) x 10 ^(-3) kg`
` = 0.03071 x 10 ^(6) kg = 3. 071 x 10 ^(4) kg`