How Do You Use Mass-Energy Equivalence (E = mc²) in Nuclear Reactions?

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and then use mass-energy equivalence:

Here, $Q$ is the energy released or absorbed by the reaction.

The sign of $Q$ follows from energy conservation. When $Q$ is positive, the lost rest mass becomes kinetic energy of the products and, where applicable, photon energy. When $Q$ is negative, at least (|Q|) must be supplied for the reaction to occur.

There are two standard calculation routes:

• If mass is in kilograms, use $c=3.00\times10^8\ \mathrm{m\,s^{-1}}$. The energy is obtained in joules.
• If mass is in unified atomic mass units, use $1\ \mathrm{u}=931.5\ \mathrm{MeV}\,c^{-2}$, so $Q=\Delta m\times931.5\ \mathrm{MeV}$.

For alpha decay,

Using atomic masses:

Therefore,

The reaction releases approximately $4.27\ \mathrm{MeV}$, mainly as kinetic energy of the products. Momentum is also conserved, so the alpha particle and thorium nucleus recoil with equal and opposite momenta; the lighter alpha particle receives most of the kinetic energy.

When using atomic masses, electron masses cancel only if the total number of electrons is equal on both sides. Otherwise, account for missing or additional electron masses explicitly. Never mix nuclear masses with atomic masses in the same calculation.

A common misconception is that all the reactant mass disappears. Only the small difference in total rest mass is converted into other forms of energy; total mass-energy remains conserved.

Exam Technique

In a Calculate question, show the balanced nuclear equation, initial and final mass totals, $\Delta m$, the conversion equation and the final energy with its unit. Check that atomic masses are used consistently and that electron numbers balance.