Mass-energy equivalence

Also called E equals mc squared, Rest mass energy

Mass-energy equivalence is the statement that mass and energy are two accountings of one conserved thing, linked by E = mc squared. In a nuclear reaction the drop in total mass is exactly the energy released.

For nuclear reactions the CED states it at 15.7.A.4: mass and energy may be exchanged, with relevant equation E=mc2E = mc^2. Read exchanged literally. Mass is not destroyed and energy conjured; the same conserved quantity is being moved between two columns of one ledger.

An object's rest energy is the energy equivalent of its mass. Using the sheet's me=9.11×10−31m_e = 9.11 \times 10^{-31} kg and c=3.00×108c = 3.00 \times 10^8 m/s, an electron's rest energy is 8.20×10−148.20 \times 10^{-14} J, which is 0.512 MeV.

For nuclear work the sheet's conversion does the job in one step: 1 u=1.66×10−27 kg=931 MeV/c21 \, \text{u} = 1.66 \times 10^{-27} \, \text{kg} = 931 \, \text{MeV}/c^2. A reaction whose total mass falls by 0.100 u releases 0.100×931=93.10.100 \times 931 = 93.1 MeV. No squaring, no powers of ten.

One caution on that line. Its two halves are rounded independently, so the SI route through 1.66×10−271.66 \times 10^{-27} kg lands near 934 MeV rather than 931. The gap is rounding in the reference table, not an error in your working.

This equation is what makes binding energy measurable, and it is the reason both fission and fusion can release energy.

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