Question

A nucleus with mass number $240$ breaks into two a fragments each of mass number $120$, the binding energy per nucleon of unfragmented nuclei is $7.6\, MeV$ while that of fragments is $8.5\, MeV$. The total gain in the Binding Energy in the process is :

• A. 0.9 MeV
• B. 9.4 MeV
• C. 804 MeV
• D. 216 MeV

Answer 1

The Correct Option is D

To find the total gain in binding energy after the nuclear reaction, we need to calculate the difference in total binding energy between the fragment nuclei and the original nucleus.

1. The total binding energy of the original nucleus with mass number $A = 240$ and binding energy per nucleon $7.6 \, \text{MeV}$ is calculated as:
   • Total binding energy of the original nucleus = $7.6 \, \text{MeV/nucleon} \times 240 \, \text{nucleons} = 1824 \, \text{MeV}$
2. Each of the two fragments has a mass number of $A = 120$, and the binding energy per nucleon is $8.5 \, \text{MeV}$.
   • Total binding energy of one fragment = $8.5 \, \text{MeV/nucleon} \times 120 \, \text{nucleons} = 1020 \, \text{MeV}$
   • Total binding energy of both fragments = $2 \times 1020 \, \text{MeV} = 2040 \, \text{MeV}$
3. Total gain in binding energy due to the splitting is the difference between the binding energy of the fragments and the binding energy of the original nucleus:
   • Gain in binding energy = Total binding energy of fragments - Total binding energy of original nucleus
   • = $2040 \, \text{MeV} - 1824 \, \text{MeV} = 216 \, \text{MeV}$

Thus, the total gain in the binding energy in the nuclear fission process is 216 MeV. This matches the provided correct answer.