Aman designed an atomic power plant which produces 100 MW power by using `"_92U^235`. If fission of each atom of `"_92U^235` produces 200 Me V of heat energy and the plant converts 90% of it into electric energy then how many grams of `"_92U^235` will be consumed at that plant in a day ?

Explanation

Output power = 100 MW
`= 250 xx 10^(6)W`
`P_(0) = 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 plants converts 90% of total energy into electrical energy
Efficiency of reactor `eta = 90%`
`= (90)/(100)`
`eta = (P_(0))/(P_(i))`
`P_(i) = (P_(0))/(eta) = (10^(8) xx 100)/(90)`
`= (10)/(9) xx 10^(8)J//s`
Total energy produced per second `= (10)/(9) xx 10^(8)J`
Total energy produced in a day
`= (10)/(9) xx 10^(8) xx 24 xx 60 xx 60 J`
`= 96 xx 10^(11)J`
Number of fissions taking place in a day
`= ("Total energy")/("Energy released per fission")`
`= (96 xx 10^(11))/(3.2 xx 10^(-11))`
`= 30 xx 10^(22)`
`= 3 xx 10^(23)`
Mass of `6.02 xx 10^(23)` atoms = 235 g
Mass of `3 xx 10^(23)` atoms
`= (235)/(6.02 xx 10^(23)) xx 3 xx 10^(23)`
= 117.1 g