Mass defect: Which statement expresses its relationship to binding energy?

Mass defect: Which statement expresses its relationship to binding energy?

• A. It has no physical meaning
• B. It is the difference between the sum of the masses of the nucleons and the mass of the bound nucleus
• C. It equals the total binding energy divided by c^2
• D. It is always zero

Answer: (C)

The key idea is energy-messure equivalence in binding. When nucleons come together, some mass disappears as energy—the binding energy is released. The mass defect is exactly this missing mass, and it is directly related to the binding energy by E = Δm c^2. Rewriting gives Δm = E_b / c^2, so the mass defect equals the total binding energy divided by c^2. This is the precise way to connect the mass difference to how tightly the nucleus is bound. For intuition, if the binding energy is 8 MeV, the mass defect is 8 MeV/c^2, which corresponds to about 0.0086 atomic mass units. The alternative definition—simply describing the mass difference between the sum of free nucleons and the bound nucleus—does describe what the mass defect is, but expressing it as E_b / c^2 directly shows its relationship to the binding energy through E = mc^2.

The key idea is energy-messure equivalence in binding. When nucleons come together, some mass disappears as energy—the binding energy is released. The mass defect is exactly this missing mass, and it is directly related to the binding energy by E = Δm c^2. Rewriting gives Δm = E_b / c^2, so the mass defect equals the total binding energy divided by c^2. This is the precise way to connect the mass difference to how tightly the nucleus is bound.

For intuition, if the binding energy is 8 MeV, the mass defect is 8 MeV/c^2, which corresponds to about 0.0086 atomic mass units. The alternative definition—simply describing the mass difference between the sum of free nucleons and the bound nucleus—does describe what the mass defect is, but expressing it as E_b / c^2 directly shows its relationship to the binding energy through E = mc^2.