• Tags: mass-energy, amu, conversion
• Difficulty: Foundation

Einstein's E = $mc^2$ connects mass and energy. The atomic mass unit (1 u) = 1/12 the mass of C-12 = 1.66054 x 10^-27 kg. Converting: 1 u x $c^2$ = 1.66054 x 10^-27 x (3 x 10^8)^2 = 1.4924 x 10^-10 J = 931.5 MeV. So 1 u = 931.5 MeV/$c^2$. This conversion factor is essential for all nuclear energy calculations. Key masses: proton = 1.00728 u = 938.3 MeV/$c^2$, neutron = 1.00866 u = 939.6 MeV/$c^2$, electron = 0.00055 u = 0.511 MeV/$c^2$. The neutron is heavier than the proton by 1.293 MeV, which is why free neutrons are unstable (beta decay with half-life ~10.2 minutes). When working with atomic masses (which include electron masses), use hydrogen atom mass (1.00783 u) instead of proton mass to automatically account for electron masses in the mass defect calculation.