Chemistry · Semester B TEKS 14A-14C
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Helium-4's actual measured mass is 4.002602 amu. It is built from 2 protons and 2 neutrons — using the mass of a hydrogen-1 atom (1.007825 amu, which already includes 1 electron, matching how 2 H-1 atoms plus 2 neutrons account for helium's 2 protons, 2 neutrons, and 2 electrons) and a free neutron's mass (1.008665 amu), calculate helium-4's mass defect and resulting nuclear binding energy in MeV (1 amu of mass defect = 931.5 MeV of binding energy).
AMass defect ≈ 0.030378 amu; binding energy ≈ 28.3 MeV, matching helium-4's real, exceptionally high stability
BMass defect ≈ −0.030378 amu, from subtracting in the reverse order (actual mass minus the sum of separate parts)
CBinding energy ≈ 28.3 MeV, but computed from a mass defect found using only 1 proton-equivalent and 1 neutron instead of 2 of each
DThis calculation cannot be completed without also knowing the mass of a free electron separately from the hydrogen atom's given mass
Explanation
Sum of the separate parts: 2×1.007825 + 2×1.008665 = 2.01565 + 2.01733 = 4.03298 amu. Mass defect = (sum of separate parts) − (actual measured He-4 mass) = 4.03298 − 4.002602 ≈ 0.030378 amu. This 'missing' mass was converted into the binding energy holding the nucleus together, per E=mc². Converting to energy: 0.030378 × 931.5 ≈ 28.3 MeV, closely matching helium-4's real, well-documented binding energy — one of the most stable light nuclei, which is exactly why fusion reactions that produce helium-4 release so much energy. Subtracting in the reverse order (actual mass minus sum of parts, 4.002602 − 4.03298 ≈ −0.030378 amu) gets a negative mass defect, an impossible result since building a stable nucleus always releases energy rather than requiring more mass than its parts. Forgetting to multiply both proton-equivalent and neutron masses by 2 each (using just 1 of each: 1.007825+1.008665−4.002602, a large, physically nonsensical negative number) drastically undercounts the number of nucleons.
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