Question

In a nuclear reaction` ^(235)U undergoes fission liberating `200 MeV ` energy . The reactor has a `10 %` efficiency and produces `1000`MW` power . If the reactor is to function for `10`year . Find the total mass of required .

Answer 1

Correct Answer - A::C::D
The formula for `eta` of power will be
`eta = (P_(out))/(P_(in))`
`:. P_(in) = (P_(out))/(eta) = (1000 xx 10^(6))/(0.1) = 10^(10)W`
Energy required for this power is given by
`E = P xx t`
` = 10^(10) xx 86,400 xx 365 xx 10`
`= 3.1536 xx 10^(18)J`
`200 xx 1.6 xx 10^(-13) J ` of energy is released by `1` fassion
`:. 3.1536 xx 10^(18)J` of energy is releasedby
`(3.1536 xx 10^(18))/(200 xx 1.6 xx 10^(-13)) ` fission
= 0.9855 xx 10^(29) ` fission
` = 0.023 xx 10^(23) ` atom of Uranium has mass `235 g`
`:. 0.9855 xx 10^(29) ` atom of Uranium has
`(235 xx 0.9855 xx 10^(29))/(6.023 xx 10^(23))` g = 38451 kg `