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 the binding energy when a nucleus with a mass number of 240 breaks into two fragments each of mass number 120, we need to calculate the difference in binding energy before and after the break-up.

1. The binding energy per nucleon of the original nucleus is given as \(7.6 \, \text{MeV}\).
2. The mass number of the original nucleus is 240. Therefore, the total binding energy of the original nucleus is: 
   \(B.E._{\text{original}} = 240 \times 7.6 = 1824 \, \text{MeV}\).
3. Each fragment has a mass number of 120 and a binding energy per nucleon of \(8.5 \, \text{MeV}\).
4. The total binding energy for each fragment is: 
   \(B.E._{\text{fragment}} = 120 \times 8.5 = 1020 \, \text{MeV}\).
5. Since there are two fragments, the total binding energy for the fragments is: 
   \(B.E._{\text{total fragments}} = 2 \times 1020 = 2040 \, \text{MeV}\).
6. The gain in the binding energy is the difference between the total binding energy of the fragments and that of the original nucleus: 
   \(\text{Gain} = B.E._{\text{total fragments}} - B.E._{\text{original}} = 2040 \, \text{MeV} - 1824 \, \text{MeV} = 216 \, \text{MeV}\).

Thus, the total gain in the binding energy in the process is 216 MeV, which matches the given correct answer.