In a fission of single nucleus of `""_(92)U^(258)` , about 200 MeV energy is released. How many fissions must occur to generate power of 10 kW?

Explanation

Let n be the number of fissions per second. Given, energy released in the fission of single nucleus = 200 MeV
Then,
energy released per second `=n xx 200` MeV
`= n xx 200 xx 1.6 xx 10^(-13)` J
Given, power required,
P = 10 kW = 10,000 W
`therefore` Energy required per second `= P xx t`
`=10,000 W xx 1 s = 10,000 J`
`therefore n xx 200 xx 1.6 xx 10^(-13) = 10,000`
`rArr n=10,000/(200 xx 1.6 xx 10^(-13)) = 3.125 xx 10^(14)`