In the net proton–proton chain, four hydrogen atoms ultimately form one helium-4 atom plus other products. Use atomic masses m_H = 1.007825 u and m_He = 4.002603 u; electron masses cancel in this atomic-mass comparison. Calculate mass defect and energy released per reaction in MeV and joules. Estimate reactions per second needed for luminosity 3.83 × 10²⁶ W and mass converted to energy per second. Use 1 u = 931.5 MeV c⁻² and 1 eV = 1.602 × 10⁻¹⁹ J.

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Mass defect = 0.028697 u; energy ≈ 26.73 MeV = 4.282 × 10⁻¹² J. About 8.94 × 10³⁷ reactions s⁻¹ and 4.26 × 10⁹ kg s⁻¹ are required. Initial atomic mass is 4(1.007825) = 4.031300 u. Subtracting helium mass gives Δm = 4.031300−4.002603 = 0.028697 u. Energy is Δmc² = (0.028697)(931.5) = 26.73 MeV. Convert to joules: 26.73 × 10⁶ eV multiplied by 1.602 × 10⁻¹⁹ J eV⁻¹ gives 4.282 × 10⁻¹² J per net reaction. Reaction rate for luminosity L is L/E = (3.83 × 10²⁶)/(4.282 × 10⁻¹²) = 8.94 × 10³⁷ s⁻¹. Mass converted to radiant energy is L/c² = 3.83 × 10²⁶/(2.998 × 10⁸)² = 4.26 × 10⁹ kg s⁻¹. This is mass defect, not the much larger mass of hydrogen processed; neutrino losses would refine the luminosity link.

Mass defect and stellar fusion energy

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