Question

(a) Calculate the energy released by the fission of `2g` of `._(92)U^(235)` in `kWh`. Given that the energy released per fission is `200MeV`.
(b) Assuming that `200MeV` of enrgy is released per fission of uranium atom, find the number of fissions per second required to released `1` kilowatt power.
(c) Find the amount of energy produced in joules due to fission of `1g` of `._(92)U^(235)`assuming that `0.1%` of mass is transformed into enrgy.`._(92)U^(235) = 235 amu`, Avogadro number `= 6.023 xx 10^(23)`

Answer 1

(a) Number of fissions `=` Number of atoms
`= (m)/(M)N_(A) = (2)/(235) xx 6.023 xx 10^(23)`
Total energy released
`=(2)/(235) xx 6.023 xx 10^(23) xx 200 xx 10^(6) xx 1.6 xx10^(-19)J`
`= 16.4 xx 10^(10) J`
`= (16.4xx10^(10))/(3.6xx10^(6)) = 4.55 xx 10^(4)kWh`
`(1kWh = 3.6 xx 10^(6)J)`
(b) `E = 1kW = 10^(3) J//sec`
Number of fissions/sec `= (10^(3))/(200xx1.6xx10^(13)) = 3.125xx10^(13)`
(c) Mass used `m = (0.1)/(100) xx 1=10^(-3) g`
Number of fissions `= (10^(-3))/(235) xx 6.023 xx 10^(23)`
Enegry produced `= (6.023xx10^(20))/(235) xx 200 xx 1.6 xx 10^(-13)`
`= 8.2 xx 10^(7) J`