Ionisation is the removal of an electron from a neutral atom. What is left behind is a positively charged ion, and the freed electron is negative. Together these are called an ion pair.
Radiation that carries enough energy to do this is called ionising radiation. Alpha particles, beta particles and gamma rays are all ionising.
The energy needed to remove one electron is the ionisation energy. If the incoming radiation has less energy than this, the atom is not ionised.
An alpha particle has a charge of +2 and is relatively heavy and slow. Its strong electric field pulls hard on the electrons of every atom it passes, so it creates a very large number of ion pairs in a short distance — several thousand per millimetre in air. Because it gives up its energy so quickly, it stops after only a few centimetres of air.
A beta particle has a charge of −1 and is much lighter, so it travels faster and interacts less strongly with each atom. It produces only about ten ion pairs per millimetre in air, so its energy lasts far longer and it travels metres rather than centimetres.
A gamma ray has no charge at all. It has no electric field to pull on electrons, so it can only ionise when it happens to interact directly with an atom. These interactions are rare, so gamma is the least ionising but travels the furthest.
Energy conversions use 1 eV = 1.60 × 10⁻¹⁹ J. For example, ionising a hydrogen atom needs 13.6 eV = 13.6 × 1.60 × 10⁻¹⁹ = 2.18 × 10⁻¹⁸ J.
There is an inverse relationship between ionising power and penetrating power, and both come from the same cause. A particle can only travel until it has given away all its energy. Alpha ionises so intensely that it exhausts its energy almost immediately, so it cannot penetrate. Gamma ionises so weakly that it can pass through metres of material before its energy is used up. The quantity that links them is the energy transferred per unit distance.
This explains an apparent contradiction in radiation safety. Alpha is the least dangerous outside the body, because the dead outer layer of skin (about 0.07 mm) stops it completely. But it is the most dangerous if inhaled or swallowed, because inside the body there is no dead layer, and all of that intense ionisation is deposited into a tiny volume of living tissue. Gamma behaves in the opposite way: it is a hazard from outside because it penetrates, but much of it passes straight through without depositing energy at all.
Alpha and beta have a definite range — a distance at which they stop entirely — because they lose energy continuously. Gamma instead follows exponential attenuation, I = I₀e^(−μx): each equal thickness of shielding removes the same fraction of the beam, so the intensity can be reduced as much as you like but never becomes exactly zero. This is why shielding is quoted as a half-value layer, and why lead shielding is described by how much it reduces intensity rather than by whether it "stops" the radiation.
Note that the average energy needed per ion pair in air (about 34 eV) is larger than the ionisation energy of the atoms themselves (about 14 eV). The difference is energy given to excitation — raising electrons to higher levels without freeing them — which is a reminder that ionisation is only one of the ways radiation can transfer energy to matter.