Mass defect: the missing mass

Weigh a helium-4 atom very carefully and then weigh its parts separately. You will find that they do not add up.

Using atomic masses, which keep the electrons on both sides so they cancel:

• 2 hydrogen-1 atoms (2 protons + 2 electrons): 2 × 1.007825 u = 2.015650 u
• 2 neutrons: 2 × 1.008665 u = 2.017330 u
• Total: 4.032980 u
• Measured mass of one helium-4 atom: 4.002603 u

The difference, 0.030378 u, is the mass defect. The assembled nucleus is lighter than the pieces.

Where did the mass go? Einstein's relation E = mc² says that mass and energy are two faces of one thing. If a system gives up energy, its mass drops by E/c². When two protons and two neutrons fall together into a helium nucleus, they release energy (as gamma rays and motion), and the nucleus left behind weighs less by that amount.

The conversion factor is handy to remember: 1 u of mass corresponds to 931.494 MeV of energy (written 931.494 MeV/c²). So

0.030378 u × 931.494 MeV/u ≈ 28.3 MeV.

That is the binding energy of helium-4. It is exactly the energy you would have to put in to pull the nucleus apart into free nucleons. Divided by 4 nucleons it is 7.07 MeV per nucleon, the number we call B/A. A higher B/A means a more tightly bound nucleus.

Scale check. An electronvolt (eV) is the energy of one electron through one volt, and a megaelectronvolt (MeV) is a million of them. In chemistry, burning one carbon atom in oxygen releases about 4 eV. Forming one helium-4 nucleus releases 28 million eV. Nuclear energy per atom is millions of times bigger than chemical energy per atom, and that single fact is why nuclear fuel is so concentrated.

In everyday units, 1 gram of mass fully converted to energy would be about 9 × 10¹³ J, enough to run a household for roughly two thousand years. In real life no process converts a gram of matter completely, but it shows what the factor c² means.