Where the energy comes from, and why nuclei are unstable
Before looking at the individual decays, three questions apply to all of them: what sets a decay off, where its energy comes from, and why some nuclei decay at all.
The big idea: nothing hits it, it just drops to a lower energy
Nothing strikes, pushes or triggers a radioactive nucleus. Think of a ball resting in a small dip partway down a hill. It's stable for the moment, but a much lower valley exists on the other side of a ridge. Quantum mechanics lets the nucleus eventually end up in that lower arrangement on its own, at a completely random moment, and the energy difference gets released.
Every decay type is a different way of getting down: throw out a chunk (α), convert a neutron or proton (β⁻, β⁺, electron capture), or just shed excess energy as light (γ).
Where the energy comes from: mass disappears
Einstein's E = mc² says mass is a stored form of energy. Weigh a nucleus before it decays, then weigh all the pieces afterward, and the pieces come out lighter. The missing mass turns into the motion (kinetic energy) of the flying particles, plus any gamma rays. Here's uranium-238 alpha-decaying:
| What | Mass (u ≈ one proton's mass) | |
|---|---|---|
| Before | Uranium-238 atom | 238.05079 |
| After | Thorium-234 atom + helium-4 (the α) | 234.04360 + 4.00260 = 238.04620 |
| Missing | 0.00459 u, about 0.002% of the total | → 4.27 MeV of motion |
MeV (mega-electron-volt) is the energy unit used for nuclei. Burning one molecule of fuel releases a few eV. One nuclear decay releases millions of eV, which is why nuclear fuel holds about a million times more energy per kilogram than chemical fuel.
When does it happen? Completely at random
Each unstable nucleus has a fixed chance of decaying every second. It doesn't age, doesn't wear out, and nothing sets it off, so you can't predict when any single one will go. With a large crowd, though, the randomness averages out and half of them decay in a fixed time, called the half-life. That ranges from under a microsecond to billions of years depending on the nucleus. Press start:
Why are some nuclei unstable? The balance of protons and neutrons
Protons repel each other, and neutrons add strong-force glue without adding any repulsion, so a nucleus needs the right mix. Small stable nuclei have about equal numbers. Heavy ones need extra neutrons to dilute all that proton repulsion. Plot every known nucleus by its proton and neutron count and the stable ones form a narrow band, the "valley of stability." Each decay type is a way of moving a nucleus toward that band:
Right: zoomed into the chart around one parent nucleus. β⁻ swaps a neutron for a proton (one step right and down). β⁺ and electron capture do the reverse (one step left and up). α removes 2 of each (two steps diagonally toward the origin). γ doesn't move the nucleus at all because only its energy changes.