When a neutron induces fisssion in a `._(92)U^(235)` nucleus, about `185MeV` of usable enegry is released. If a reactor continuously generates `100MW` of power using `._(92)U^(235)`as fuel, then how long will it take for `1 kg` of the uranium to be used up?

Explanation

Number of fissions `= (m)/(M)N_(A)`
Energy released, `E = (m)/(M) N_(A) xx 185 xx 1.6 xx 10^(-13) J`
Power `= (E)/(t) = (mN_(A)xx185xx1.6xx10^(-13))/(235xxt) = 100 xx10^(6)`
`t = (10^(3)xx6.023 xx 10^(23)xx185xx1.6xx10^(-13))/(235xx10^(8)) sec`
`=7.57 xx 10^(5)s = (7.57 xx 10^(5))/(24xx3600)`
`= 8.76 days`