E.3.4—Mass-energy equivalence

Use E=mc²

A change in rest mass corresponds to energy through $E=mc^2$. In a nuclear reaction, compare the total mass before and after to find the mass converted into released or absorbed energy.

Worked example — energy from a mass decrease

For $\Delta m=2.0\times10^{-12}\,\mathrm{kg}$, $\Delta E=(2.0\times10^{-12})(3.00\times10^8)^2=1.8\times10^5\,\mathrm{J}$. A smaller total rest mass of the products means this energy is released.

Compare energy yields

Energy released per reaction is proportional to mass converted. Energy released per unit mass also depends on the converted fraction: divide the energy from one reaction by the mass of fuel involved.

Track the system

Mass–energy equivalence applies to the mass difference of the defined reaction system. Do not compare only the total mass of the reactants without accounting for products.

Common trap

Do not confuse a large energy per reaction with a large energy per unit mass. The question’s denominator determines the comparison.