Question: 7. 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 :
(1) 0.9 MeV
(2) 9.4 MeV
(3) 804 MeV
(4) 216 MeV
Answer: Option (4)
Explanation:
Binding energy of the original nucleus is given by the product of mass number and
binding energy per nucleon.
Total binding energy before fission = 240 \times 7.6 MeV.
= 1824 MeV.
After fission, the nucleus breaks into two fragments, each having mass number 120.
Total binding energy of one fragment = 120 \times 8.5 MeV.
= 1020 MeV.
Total binding energy of two fragments = 2 \times 1020 MeV.
= 2040 MeV.
The gain in binding energy is the difference between final and initial binding energies.
Gain in binding energy = 2040 - 1824 MeV.
= 216 MeV.
Hence, the total gain in binding energy during the process is 216 MeV.