The energy released when one nucleus of `._(92)u^(235)` undergoes fission is 188 MeV. The energy released when 100g of undergoes fission is `._(92)u^(235)`

Options

A. `3.55xx10^(12)` J
B. `7.71xx10^(12)` J
C. `3.55xx10^(13)` J
D. `7.71xx10^(13)` J

Answer

D

Explanation

Given, energy released, `E_(0) = 188 MeV` per nucleus fission and mass, m = 100 gm
As number of nucleus in 100 gm of `._(92)U^(235)`
`N = (100)/(M) xx N_(A)`
where, `N_(A)` = Avogadro number and
M = molecular mass
`rArr N = (100)/(235) xx 6.022 xx 10^(23) = 2.56 xx 10^(23)` nucleus
Energy released in fission of one nucleus
`E._(0) = E_(0) = 188 xx 10^(6) xx 1.6 xx 10^(-19) J`
`= 300.8 xx 10^(-13) J`
So, Energy released in N-nucleus fission,
`E = E._(0)N = 2.5610^(23) xx 300.8 xx 10^(-13) J`
`rArr E = 7.71 xx 10^(12) J`
Hence, the correct option is (b).