Nucleus ²⁴⁰U, which has a binding energy per nucleon as 7·6 MeV, disin

Nucleus ²⁴⁰U, which has a binding energy per nucleon as 7·6 MeV, disintegrates into two nuclei of ¹¹⁹⋅⁵Sn. Take ¹¹⁹⋅⁵Sn elements atomic mass number as 120 and binding energy per nucleon as 8·4 MeV. Which one among the following is the correct value of the energy released in the disintegration process ?

192 MeV
190 MeV
188 MeV
3840 MeV
This question was previously asked in
UPSC Geoscientist – 2024
Correct Answer: A
– The initial nucleus is ²⁴⁰U with A=240 and binding energy per nucleon = 7.6 MeV. Total binding energy of ²⁴⁰U = 240 * 7.6 MeV.
– The nucleus disintegrates into two nuclei of ¹¹⁹⋅⁵Sn. We are given to use the atomic mass number as 120 for calculation. So, the two product nuclei have A=120 and binding energy per nucleon = 8.4 MeV.
– Total binding energy of the two product nuclei = 2 * (120 * 8.4 MeV).
– The energy released in a nuclear reaction is the difference between the total binding energy of the products and the total binding energy of the reactants. Energy released = (Total binding energy of products) – (Total binding energy of reactants).
– Energy released = (2 * 120 * 8.4 MeV) – (240 * 7.6 MeV)
– Energy released = (240 * 8.4 MeV) – (240 * 7.6 MeV)
– Energy released = 240 * (8.4 – 7.6) MeV
– Energy released = 240 * 0.8 MeV
– Energy released = 192 MeV.
Binding energy represents the energy required to separate the nucleons (protons and neutrons) in a nucleus. A higher binding energy per nucleon indicates a more stable nucleus. In nuclear reactions like fission or fusion, energy is released when the products are more stable (have higher binding energy per nucleon) than the reactants. The mass difference between the reactant and product nuclei (mass defect) is converted into energy according to Einstein’s famous equation E=mc². The energy released can also be calculated from the difference in binding energies, as shown here.