Munish designed an atomic power plant which produces 250 MW power by using `"_92U^235`. If fission of each atom of `"_92U^235` produces 200 MeV of heat energy and the plant converts 75% of it into electric energy then how many grams of `"_92U^235` will be consumed at that plant in a day ?

Explanation

Output power = 250 MW
`= 250 xx 10^(6)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)`
As the plant converts 75% of total energy into electric energy
`rArr` Efficiency of power plant `eta` = 75%
`= (75)/(100)`
But `eta = (P_(0))/(P_(i))`
`rArr P_(i) = (P_(0))/(eta) = (2.5 xx 10^(8))/(75//100)`
`= 3.33 xx 10^(8) J//s`
Total energy produced per second
`= 3.33 xx 10^(+8)J`
Total energy produced in a day
`= 3.33 xx 10^(8) xx 24 xx 60 xx 60`
`= 2877.1 xx 10^(10)J`
`= 2.877 xx 10^(13) J`
Number of fissions taking place in a day
`= ("Total energy")/("Energy released per fission")`
`= (2.877 xx 10^(13))/(3.2 xx 10^(-11))`
`= 0.899 xx 10^(24)`
`= 8.99 xx 10^(23)`
Mass of `6.02 xx 10^(23)` atoms = 235 g
Mass of `8.99 xx 10^(23)` atoms
`= (235)/(6.02 xx 10^(23)) xx 8.99 xx 10^(23)`
`= 350.96 g`