Binding energy of a certain nucleus is 18 × 10⁸ J. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus:

Solution

Physics sir · 4 steps

Binding energy is just the mass defect times c², so divide by c² and convert kilograms carefully.

1. Mass defect meaning. The total mass of the free nucleons minus the nuclear mass is the mass defect Δ m. This missing mass appears as the binding energy, through Einstein's relation.

   Δ m = E_b/c² = (18 × 10⁸)/(3 × 10⁸)² kg

2. Put in numbers. c² = 9 × 10¹⁶ m² s⁻², so Δ m = (18 × 10⁸)/(9 × 10¹⁶) = 2 × 10⁻⁸ kg.
3. Convert to micrograms. One microgram is 10⁻⁶ g = 10⁻⁹ kg. So 2 × 10⁻⁸ kg = 20 × 10⁻⁹ kg = 20 μg.
4. So. The mass difference is 20 μg, which is option (a).

The idea to keep. Mass defect and binding energy are the same thing in two units: E_b = Δ m c². Work in SI, get kg first, and remember 1 μg = 10⁻⁹ kg.

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