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 .
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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 `
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