Question

A nucleus with mass number 240 breaks into two 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. 216 MeV
• B. 0.9 MeV
• C. 9.4 MeV
• D. 804 MeV

Answer 1

The Correct Option is A

To calculate the total gain in binding energy when a nucleus with a mass number of 240 breaks into two fragments each with a mass number of 120, we can follow these steps:

1. First, calculate the total initial binding energy of the unfragmented nucleus.

The binding energy per nucleon for the unfragmented nucleus is given as 7.6 MeV. Therefore, the total binding energy for the nucleus with mass number 240 is:

\(E_{\text{initial}} = 240 \times 7.6 \, \text{MeV}\)

Calculating this gives:

\(E_{\text{initial}} = 1824 \, \text{MeV}\)

1. Next, calculate the total binding energy of the two fragments.

Each fragment has a mass number of 120 and a binding energy per nucleon of 8.5 MeV. Therefore, the total binding energy for both fragments together is:

\(E_{\text{final}} = 2 \times (120 \times 8.5 \, \text{MeV})\)

Calculating this gives:

\(E_{\text{final}} = 2 \times 1020 \, \text{MeV} = 2040 \, \text{MeV}\)

1. Calculate the gain in binding energy as the difference between the final total binding energy and the initial total binding energy.

The gain in binding energy, \(\Delta E\), is given by:

\(\Delta E = E_{\text{final}} - E_{\text{initial}}\)

Substitute the values we have calculated:

\(\Delta E = 2040 \, \text{MeV} - 1824 \, \text{MeV}\)

Calculating this gives:

\(\Delta E = 216 \, \text{MeV}\)

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