What Is Radioactive Decay?
Inside every atom is a nucleus — a dense core of protons and neutrons packed together by the strong nuclear force. For most elements, this arrangement is stable. But for some combinations of protons and neutrons, the nucleus is unstable. It has too much energy, the wrong ratio of particles, or an excess of one type. To reach a more stable state, it spontaneously transforms — emitting particles or energy in the process. This is radioactive decay.
The key word is spontaneous. We cannot predict when any individual atom will decay. It might happen in the next millisecond or in a billion years. But — and this is the remarkable part — when we have a large number of atoms, the overall rate of decay is perfectly predictable and follows a precise mathematical law.
N₀ = Initial number of atoms at t = 0
λ = Decay constant (unique to each isotope)
e = Euler's number ≈ 2.71828
What Is a Half-Life?
The half-life (symbol T½) is the time required for exactly half of the radioactive atoms in a sample to decay. After one half-life, 50% of the original atoms remain. After two half-lives, 25% remain. After ten half-lives, less than 0.1% remains.
The relationship between the decay constant λ and the half-life is:
Half-lives vary enormously across different isotopes — from fractions of a second to billions of years.
| Isotope | Half-Life | Common Use |
|---|---|---|
| Carbon-14 | 5,730 years | Archaeological dating |
| Iodine-131 | 8.02 days | Cancer treatment, nuclear fallout |
| Caesium-137 | 30.17 years | Nuclear waste concern |
| Cobalt-60 | 5.27 years | Radiation therapy, food irradiation |
| Plutonium-239 | 24,110 years | Nuclear weapons, fuel |
| Uranium-238 | 4.47 billion years | Nuclear power, geological dating |
| Polonium-214 | 0.000164 seconds | Decay chain product |
Types of Radioactive Decay
Not all radioactive decay works the same way. There are three primary types, each involving different particles and different transformations of the nucleus.
Alpha Decay (α)
The nucleus ejects an alpha particle — a bundle of 2 protons and 2 neutrons (identical to a helium-4 nucleus). The parent atom loses 2 protons and 2 neutrons, becoming a different element. Alpha particles are relatively large and slow, stopped easily by a sheet of paper or a few centimetres of air. However, if an alpha emitter is inhaled or ingested, it is extremely dangerous at close range to internal tissue.
Beta Decay (β)
A neutron in the nucleus converts into a proton (or vice versa), emitting either an electron (beta-minus) or a positron (beta-plus) along with a neutrino. The atomic number changes by 1, transforming the element, while the mass number stays the same. Beta particles penetrate further than alpha particles but are stopped by a few millimetres of aluminium.
Gamma Decay (γ)
The nucleus releases excess energy as a high-energy electromagnetic photon — a gamma ray. Unlike alpha and beta decay, gamma decay does not change the number of protons or neutrons. It simply releases energy. Gamma rays are extremely penetrating and require thick lead or concrete shielding.
Why Is Decay Exponential?
The exponential decay law emerges from a simple probability argument. Each atom has a fixed, constant probability of decaying per unit time — its decay constant λ. This probability does not change based on how old the atom is or how many other atoms have already decayed. Each atom is independent.
When you have a large number of atoms, the rate at which the population decreases is proportional to how many atoms currently exist. This leads directly to the exponential equation. The mathematics is identical to compound interest in reverse, or to a population with a constant death rate.
Practical Applications of Radioactive Decay
Far from being purely a theoretical concept, radioactive decay underlies a remarkable range of modern technologies and scientific tools.
Nuclear power: Uranium-235 and plutonium-239 are fissioned in reactors. The enormous energy release comes from both the kinetic energy of decay products and further reactions triggered by the emitted neutrons.
Medical imaging: PET scans use positron-emitting isotopes (like fluorine-18, half-life 110 minutes) injected into the patient. The positrons annihilate with electrons and produce gamma rays that detectors outside the body can image.
Smoke detectors: Most ionisation smoke detectors contain a tiny amount of Americium-241. It ionises the air inside a chamber, creating a small steady current. Smoke particles disrupt this current, triggering the alarm.
Nuclear waste: The challenge of nuclear waste storage is fundamentally a half-life problem. Some fission products have short half-lives (days to years) and decay quickly. Others, like Plutonium-239, have half-lives of tens of thousands of years, requiring secure storage for geological timescales.