23.1 Mass Defect and Nuclear Binding Energy

1. Mass–Energy Equivalence: E = mc²

The Big Idea

You may have learned in chemistry that mass is always conserved in a reaction — meaning the total mass of the reactants equals the total mass of the products. In nuclear physics, this is not quite true. A tiny amount of mass can actually disappear during a nuclear reaction — and that missing mass is converted directly into energy.

This idea was proposed by Albert Einstein and is summarised by one of the most famous equations in science:

$\boxed{E = mc^2}$

Where:

• E = energy (measured in Joules, J)
• m = mass (measured in kilograms, kg)
• c = the speed of light in a vacuum = 3.0 × 10⁸ m s⁻¹

What does it mean?

This equation tells us that mass and energy are two different forms of the same thing. You can convert mass into energy, and you can convert energy into mass.

• If mass disappears during a reaction → energy is released.
• If mass appears during a reaction → energy must be put in.

Because c² is an enormous number (9 × 10¹⁶), even a tiny amount of mass produces a huge amount of energy. This is why nuclear reactions release so much more energy than ordinary chemical reactions (like burning fuel).