If M₀ is the mass of isotope ₅¹² B, Mₚ and Mₙ are the masses of proton and neutron, then nuclear binding energy of isotope is:

Solution

Physics sir · 3 steps

Binding energy is what the nucleus lost: free parts minus the nucleus, times c².

1. Count the nucleons. In ¹²₅B the atomic number is 5, so there are 5 protons. The mass number is 12, so there are 12 - 5 = 7 neutrons.
2. Mass defect. The separate nucleons weigh more than the bound nucleus. The difference is the mass defect, and it is always positive: Δ m = 5Mₚ + 7Mₙ - M₀.

   E_b = Δ m c² = (5Mₚ + 7Mₙ - M₀)c²

3. So. The binding energy is (5Mₚ + 7Mₙ - M₀)c², which is option (a).

The idea to keep. Binding energy is always positive: take the mass of the free protons and neutrons, subtract the nucleus, then multiply by c². Get Z protons and A minus Z neutrons from the symbol.

Answer from the NTA final answer key. Solution by PrepWiser.