E.3.2—Binding energy and mass defect

Define mass defect

A bound nucleus has less mass than the separated protons and neutrons that form it. The missing mass is the mass defect $\Delta m$, associated with the energy released when the nucleus forms.

Convert mass to binding energy

Use $E_b=\Delta mc^2$. If $\Delta m$ is in unified atomic mass units, the convenient conversion is approximately $931.5\,\mathrm{MeV}/c^2$ per u, giving energy directly in MeV.

Worked example — mass defect

If separated nucleons have total mass $4.0320\,\mathrm{u}$ and the nucleus has mass $4.0015\,\mathrm{u}$, then $\Delta m=0.0305\,\mathrm{u}$. Hence $E_b=(0.0305)(931.5)=28.4\,\mathrm{MeV}$. The positive result is the energy needed to separate the nucleus, and the same energy magnitude was released when it formed.

Interpret the sign

Binding energy is the energy required to separate the nucleons completely, and the same amount is released when the bound nucleus forms. It is positive as a required or released energy magnitude.

Common trap

Do not multiply a mass difference in u by c² again after using 931.5 MeV per u; that conversion already includes the mass–energy relation.