Nuclear reactions reveal that mass is not a separately conserved quantity. Instead, a change in rest mass corresponds to an energy change, which can emerge in physically observable forms.

Mass and energy as a single conserved quantity

In classical mechanics, mass and energy are often treated as different ideas. In modern physics, they are linked. A nuclear reaction can change the total rest mass of the particles involved, but it does not violate conservation laws. The important conserved quantity is mass-energy.

This idea explains why a reaction can release enormous energy even when the measured mass change is extremely small. Because the speed of light is very large, the factor $c^2$ makes even tiny amounts of mass equivalent to large amounts of energy.

This equation does not mean that mass and energy are created from nothing. It means that if the mass of a system changes, there must be a corresponding energy change so that the total mass-energy of the system remains constant.

Why nuclear reactions can change mass

A nuclear reaction changes the arrangement of particles in the nucleus or produces new particles. Because the initial and final systems are not identical, their total rest masses may differ. Physicists compare the total mass of all reactants before the reaction with the total mass of all products after the reaction.

If the products have less total mass than the reactants, the missing mass has not disappeared.

Diagram comparing a nucleus as a bound system versus the same nucleons separated. It emphasizes that the separated nucleons have greater total mass, and the difference is the mass defect associated with binding energy via $E=\Delta mc^2$. Source

It has been converted into released energy. If the products have greater total mass than the reactants, then energy must have been supplied to the reaction.

Relating mass change to released energy

For AP Physics 2, the key relationship is that the energy released by a nuclear reaction depends on the decrease in total mass from the initial state to the final state.

This form is especially useful because it makes the direction of energy flow clear. When $m_i$ is greater than $m_f$, the reaction releases energy. When $m_f$ is greater than $m_i$, the reaction requires energy input rather than producing net energy output.

The masses used in this comparison must refer to the entire reaction, not just one particle. Leaving out a reactant or product gives an incorrect energy value. In problems, always compare the total initial mass with the total final mass.

Why a tiny mass change can mean a large energy release

Binding energy per nucleon versus mass number for many nuclei, showing a peak near iron (highest stability). The shape explains why fusion of light nuclei and fission of very heavy nuclei can be exothermic: products move toward higher binding energy per nucleon, corresponding to a mass decrease and released energy. Source

The number $c^2$ is about $9.0 \times 10^{16}$. That enormous conversion factor means a very small change in mass corresponds to a very large amount of energy. This is why nuclear processes can be powerful even though the actual mass difference is hard to notice on an ordinary scale.

In nuclear physics, the change being discussed is the change in rest mass of the whole system. The total mass-energy is still conserved, but part of it may no longer remain stored as rest mass after the reaction.

Forms of released energy

The specification emphasizes that released energy can appear in more than one way. In a nuclear reaction, the energy associated with the mass decrease does not stay in an abstract form. It becomes energy carried by the reaction products or by radiation.

Product kinetic energy

One common outcome is kinetic energy of the products. After the reaction, the particles produced may move away at high speeds. Their motion shows that some of the original mass of the system has been converted into kinetic energy.

This kinetic energy may be shared among several products. For example, two outgoing particles may both move, but not necessarily with equal kinetic energy. The exact distribution depends on the details of the reaction.

Energy carried by photons

Released energy may also appear as photons.

Diagram of nuclear radiation with a labeled gamma-ray (photon) component. It illustrates that photons can carry away released nuclear energy when a nucleus transitions from an excited state toward a lower-energy state. Source

A photon is a packet of electromagnetic energy, so emission of photons is another way a reaction can carry away energy. In nuclear processes, these photons are often very energetic.

Sometimes the energy release appears mostly as kinetic energy, sometimes mostly as photons, and sometimes as a combination of both. The important AP idea is that the decrease in mass can be accounted for by energy that leaves in observable forms.

If a reaction leaves a product in a higher-energy state at first, some energy may remain stored briefly and then be emitted later as radiation. Even in that case, the full energy accounting still follows the same mass-energy relationship.

Interpreting statements about mass and energy

Students sometimes hear that “mass is converted into energy” and think this breaks conservation of mass. In nuclear physics, it is better to say that rest mass can decrease while total mass-energy remains conserved. Mass by itself is not the separately conserved quantity in these reactions.

When solving or interpreting problems, keep these ideas in mind:

• Compare the total initial mass with the total final mass.

• A smaller final mass means the reaction released energy.

• A larger final mass means the reaction absorbed energy.

• The released energy may be observed as product kinetic energy, photons, or both.

• A reaction can release a large amount of energy even when the mass difference is very small.

In AP Physics 2 problems, the masses and needed constants are typically provided. Your task is usually to connect the sign and size of the mass change to the physical meaning of the energy change.