Nuclear Reactions and Binding Energy

One of the most profound ideas in physics is that mass and energy are interchangeable. Einstein's equation E = mc² tells us that a small amount of mass corresponds to an enormous amount of energy. Nowhere is this more apparent than in nuclear physics, where the mass of a nucleus is measurably less than the mass of its individual nucleons — and this "missing mass" is the key to understanding nuclear energy.

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Mass Defect

If you could weigh a nucleus and then separately weigh all its individual protons and neutrons, you would find that the nucleus weighs less. This difference is called the mass defect (Δm):

Δm = (Z × mₚ + N × mₙ) − M_nucleus

where:

• Z = number of protons, mₚ = mass of a proton
• N = number of neutrons, mₙ = mass of a neutron
• M_nucleus = measured mass of the nucleus

The mass defect is always positive for bound nuclei. The "missing" mass has been converted into energy — the energy that was released when the nucleons were brought together to form the nucleus.

Example: Helium-4