7.5 Mass-Energy Equivalence

Mass and energy are equivalent

Einstein's relation E = mc² shows that mass and energy are two forms of the same thing. Even an object at rest has rest energy proportional to its mass, where c is the speed of light. This means mass can be converted into energy (and vice versa), especially in nuclear reactions.

Mass defect and binding energy

The mass of a nucleus is slightly less than the sum of its individual protons and neutrons — this difference is the mass defect (Δm). That 'missing' mass was converted into binding energy that holds the nucleus together, calculated as ΔE = Δmc². This energy must be supplied to split the nucleus apart.

Fission and fusion release energy

In nuclear fission, a large nucleus splits into smaller nuclei; in nuclear fusion, small nuclei combine into a larger one. Both processes release enormous energy because the resulting nuclei have greater total binding energy per nucleon, meaning some mass converts to released energy via E = mc².

Key terms

E = mc²

Einstein's mass-energy equivalence equation; c is the speed of light in a vacuum.

Mass defect (Δm)

The difference between the mass of a nucleus and the sum of the masses of its individual nucleons.

Binding energy

The energy equivalent to the mass defect (ΔE = Δmc²); the energy required to separate a nucleus into individual nucleons.

Nuclear fission

A large nucleus splits into smaller nuclei, releasing energy as mass converts to energy.

Nuclear fusion

Small nuclei combine into a larger nucleus, releasing energy; powers stars like the Sun.

Try an AP-style question

How much energy is equivalent to 1.0 g of mass? (c = 3.0 × 10⁸ m/s)

1. 9.0 × 10¹³ J
2. 3.0 × 10¹¹ J
3. 3.0 × 10⁵ J
4. 9.0 × 10¹⁶ J