Question

A nucleus with mass number 242 and binding energy per nucleon as 7.6 MeV breaks into fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as 8.1 MeV, the total gain in binding energy is ____MeV.

Hint:

Binding energy gain indicates increased stability after nuclear reactions

Answer 1

Correct Answer: 121

To determine the total gain in binding energy when a nucleus with a mass number of 242 breaks into two fragments each with a mass number of 121, we follow these steps:

Step 1: Calculate Initial Total Binding Energy
The nucleus with mass number 242 has a binding energy per nucleon of 7.6 MeV.
Initial Total Binding Energy = 242 × 7.6 MeV = 1839.2 MeV.

Step 2: Calculate Final Total Binding Energy
Each fragment has a mass number of 121 and a binding energy per nucleon of 8.1 MeV.
Final Total Binding Energy = 2 × (121 × 8.1 MeV) = 2 × 980.1 MeV = 1960.2 MeV.

Step 3: Calculate Gain in Binding Energy
Gain in Binding Energy = Final Total Binding Energy - Initial Total Binding Energy
= 1960.2 MeV - 1839.2 MeV = 121 MeV.

Step 4: Verify the Range
The computed gain in binding energy is 121 MeV, which fits within the given range of 121,121.