• Tags: mass-defect, binding-energy, stability
• Difficulty: Moderate

The mass of any nucleus is less than the sum of its free constituent nucleons. This difference is the mass defect: $Delta_m$ = Z*$m_p$ + (A-Z)$m_n$ - $M_{nucleus}$. The binding energy BE = $Delta_m$ x 931.5 MeV represents the energy needed to completely disassemble the nucleus. Equivalently, it's the energy released when free nucleons assemble into the nucleus. For He-4: $Delta_m$ = 2(1.00728) + 2(1.00866) - 4.00260 = 0.02928 u, giving BE = 27.28 MeV. When using atomic masses (which include electrons), use hydrogen atom mass instead of proton mass: $Delta_m$ = Z$m_H$ + (A-Z)*$m_n$ - $M_{atom}$. The Z electron masses cancel automatically. This is the standard approach in JEE problems where atomic masses are given. The binding energy is always positive for stable nuclei.