Alpha decay

Alpha decay is a nuclear transformation in which a heavy unstable nucleus emits an alpha particle, the nucleus of helium-4. The bookkeeping is simple, but the physics behind the decay is richer: energy conservation, recoil and quantum tunnelling all matter.

The nuclear bookkeeping

An alpha particle contains two protons and two neutrons. If a parent nucleus has mass number A and atomic number Z, the daughter has A - 4 and Z - 2.

Parent → daughter + alpha

(A, Z) → (A - 4, Z - 2) + helium-4 nucleus

This immediately tells you which element the daughter is: reducing Z by two moves two places to the left in the periodic table. Nucleon number and electric charge balance across the equation.

One alpha emission removes four nucleons and two units of nuclear charge. The daughter is a different element.

Where the released energy goes

If the total rest mass of the products is smaller than that of the parent, the difference appears as released energy. In the parent nucleus's rest frame, the daughter and alpha particle recoil with equal and opposite momenta. Because the daughter is much heavier, the alpha particle receives most of the kinetic energy.

For transitions between well-defined nuclear states, alpha energies are close to discrete values. Measuring those energies can therefore help identify radionuclides and reveal nuclear level structure.

The alpha particle need not classically climb over the whole barrier. Quantum tunnelling gives it a finite escape probability.

Why a positive Q-value can still give a long half-life

Energy release tells us that a decay is energetically allowed; it does not tell us how rapidly it occurs. The preformed alpha-like cluster must still escape through the electrostatic barrier surrounding the daughter nucleus. The tunnelling probability is extremely sensitive to the alpha energy, so modest energy changes can correspond to enormous differences in half-life.

Interaction with matter

Alpha particles are relatively massive and carry charge +2e. They lose energy rapidly by ionizing matter, so their range is short compared with beta particles or gamma photons. That short range does not make every alpha source harmless: the effect depends strongly on where the radioactive material is located and how energy is deposited. Penetrating power and biological impact are different questions.

Worked examples

1. Complete an alpha-decay equation

Solution

Uranium-238 has A = 238 and Z = 92. After alpha emission, A = 234 and Z = 90, so the daughter is thorium-234.

2. Check conservation

Solution

For a parent with A = 226 and Z = 88, the daughter after alpha decay must have A = 222 and Z = 86. The emitted alpha contributes A = 4 and Z = 2, restoring the original totals.

3. Compare recoil energies

Solution

The alpha particle and daughter have equal momentum magnitudes. Since kinetic energy at the same momentum is larger for the smaller mass, the much lighter alpha particle receives most of the kinetic energy.