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

Step 1: Calculate initial and final binding energies - Initial binding energy \[ B_{\text{initial}} = 242 \times 7.6 = 1839.2 \, \text{MeV}. \] Final binding energy \[ B_{\text{final}} = 2 \times (121 \times 8.1) = 2 \times 980.1 = 1960.2 \, \text{MeV}. \]

Step 2: Calculate the gain in binding energy - Gain in binding energy is given by: \[ \text{Gain} = B_{\text{final}} - B_{\text{initial}} = 1960.2 - 1839.2 = 121 \, \text{MeV}. \]

Final Answer: The total gain in binding energy is 121 MeV.