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 solve this problem, we need to calculate the total gain in the binding energy when a nucleus splits into two fragments. Let's walk through the solution step-by-step.

The essential concept here is the calculation of Binding Energy (BE), which is given by the formula:

\(BE = \text{Binding Energy per Nucleon} \times \text{Number of Nucleons}\)

We have the following information: 

• The mass number of the original nucleus: \(A = 240\)
• Binding energy per nucleon of unfragmented nucleus: \(7.6 \, \text{MeV}\)
• The mass number of each fragment: \(120\)
• Binding energy per nucleon of each fragment: \(8.5 \, \text{MeV}\)

Step 1: Calculate the Binding Energy of the original nucleus.

\(BE_{\text{original}} = 7.6 \, \text{MeV/nucleon} \times 240 = 1824 \, \text{MeV}\)

Step 2: Calculate the Binding Energy of the fragments.

\(BE_{\text{fragments}} = 8.5 \, \text{MeV/nucleon} \times 120 \, (\text{per fragment}) \times 2 \, (\text{for 2 fragments}) = 2040 \, \text{MeV}\)

Step 3: Calculate the total gain in Binding Energy.

The gain is the increase in total binding energy when the nucleus splits into two fragments, calculated as:

\(\Delta BE = BE_{\text{fragments}} - BE_{\text{original}}\)

\(\Delta BE = 2040 \, \text{MeV} - 1824 \, \text{MeV} = 216 \, \text{MeV}\)

This calculation confirms that the total gain in the binding energy is 216 MeV. The correct option is:

\(216 \, \text{MeV}\)