A heavy nucleus X of mass number 240 and binding energy per nucleon 7.6 MeV is split into two fragments Y and Z of mass numbers 110 and 130. The binding energy of nucleons in Y and Z is 8.5 MeV per nucleon. Calculate the energy Q released per fission in MeV.

Explanation

Mass number of heavy nucleus X, A = 240
Binding energy per nucleon of nucleus X, B = 7.6 MeV `therefore` Total binding energy of heavy nucleus` = AB = 240 xx 7.6 MeV = 1824 MeV`
Mass numbers of fragments Y and Z are `A_(1) = 110` and `A_(2) = 130`
Binding energy per nucleon of each fragment `B_(1)=B_(2)=8.5MeV`
`therefore` Total binding energy of fission fragments=`A_(1)B_(1)+A_(2)B_(2)=110xx8.5+130xx8.5=2400MeV`
`therefore` Total energy Q released per fission=Binding energy of fission fragments-Binding energy of heavy nucleus=2040-1824=216MeV.