Jagriti designed an atomic power which produces 200 MW power by using `"_92U^235`. If fission of each atom of `"_92U^235` produces 200 MeV of heat energy and the plant converts 80% of it into electric energy then how many grams of `"_92U^235` will be consumed by that plant in a day.

Explanation

Output power = 200 MW
`= 200 xx 10^(6) W`
`= 2 xx 10^(8)W`
`= 2 xx 10^(8)J//s`
Energy released per fission = 200 MeV
`= 200 xx 1.6 xx 10^(-13)J`
`= 3.2 xx 10^(-11)J`
`because` Plant converts 80% of total energy into electric energy
`therefore` Efficiency of rector `= eta = 80% = (80)/(100)`
`= (4)/(5)`
`eta = (P_(0))/(P_(i))`
`rArr P_(i) = (P_(0))/(n) = (2 xx 10^(8))/(4//5)`
Total energy produced per second
`= 2.5 xx 10^(8)J`
Total energy prodcued in a day
`= 2.5 xx 10^(8) xx 24 xx 60 xx 60J`
`= 2160 xx 10^(10)J`
`= 2.160 xx 10^(13)J`
Number of fissions taking place in a day
`= ("Total energy")/("Energy released per fission")`
`= (2.16 xx 10^(13))/(3.2 xx 10^(-11))`
`= 0.675 xx 10^(24)J`
`= 6.75 xx 10^(23)`
Mass of `6.02 xx 10^(23)` atoms = 235 g
Mass of `6.75 xx 10^(23)` atoms = 235 g
Mass of `6.75 xx 10^(23)` atoms
`= (235)/(6.02 xx 10^(23)) xx 6.75 xx 10^(23)`
= 263.5 g