An explosion of atomic bomb release an energy of 7.6 x 10^13 J. If 200 MeV energy is released on fission of one U^235 atom calculate the number of uranium atoms undergoing fission.

Q: An explosion of atomic bomb release an energy of 7.6 × 1013 J. If 200 MeV energy is released on
fission of one U235 atom calculate (i) the number of uranium atoms undergoing fission. (ii) the mass of
uranium used in the atom bomb.

Sol: E = 7.6 × 103 J; Energy released per fission = 200 MeV

= 200 × 106 × 1.6 × 10-19 = 3.2 × 10-11 J

Number of uranium atoms (n) = (Total energy)/(Energy per fission)

n = (7.6 × 1013)/(3.2 × 10-11 ) = 2.375 × 1024 atoms

Avogadro number (N) = 6.023 × 1023 atoms

Mass of uranium = (n × 235)/N = (2.375 × 1024 × 235 )/(6.023 × 1023 ) = 92.66 g.