What is radioactivity? Decay, isotopes and half-life

Radioactivity is what happens when the nucleus of an atom is unstable and breaks down on its own, giving off energy as radiation: alpha particles, beta particles or gamma rays. Each decay turns the atom into a different element or a calmer form of the same one. No one can say when a given nucleus will decay, but a large sample decays at a steady rate, measured by its half-life, the time it takes for half of it to go.

In short

• Some nuclei have an unstable mix of protons and neutrons. They decay by throwing out particles or energy, and the radiation can ionize atoms in its path.
• Isotopes are versions of one element with different numbers of neutrons. Carbon-12 is stable; carbon-14 is radioactive.
• After one half-life, half a sample is left; after two, a quarter; after ten, about a thousandth. That steady rate is what makes radiocarbon dating work.

What makes an atom radioactive?

An atom has a tiny nucleus of protons and neutrons. The protons all carry positive charge and repel each other; what holds the nucleus together is the strong nuclear force, which acts between protons and neutrons but only over very short distances. Neutrons add strong-force glue without adding repulsion. A nucleus is stable only with the right balance. With too many neutrons, too few, or simply too many particles in all, it is unstable, and sooner or later it changes into something more stable.

The number of protons decides the element: every carbon atom has 6. The number of neutrons can vary, and atoms of one element with different neutron counts are called isotopes, named by their total of protons plus neutrons. Carbon-12 has 6 neutrons and carbon-13 has 7; both are stable. Carbon-14 has 8, one or two too many, and it is radioactive. Chemically the three behave almost identically, which is why carbon-14 ends up in living things alongside ordinary carbon.

Most elements have at least one stable isotope, but every element heavier than lead has none: their nuclei are simply too big for the strong force to hold indefinitely. Uranium, thorium and radium are all radioactive for that reason.

What are alpha, beta and gamma radiation?

Unstable nuclei decay in three main ways, named by Ernest Rutherford and others in the years after radioactivity was found.

Type	What it is	What happens to the nucleus	What stops it
Alpha (α)	Two protons and two neutrons, a helium nucleus	Loses 2 protons, becomes an element two places down the periodic table	A sheet of paper, or the outer layer of skin
Beta (β)	A fast electron, made when a neutron turns into a proton (a rarer kind emits a positron instead, as a proton turns into a neutron)	Gains a proton, becomes the next element up	A few millimeters of aluminum or plastic
Gamma (γ)	A high-energy photon, light far beyond the visible	Sheds extra energy, stays the same element	Thick lead or concrete, which reduce it rather than stop it entirely

Carbon-14, for example, decays by beta decay: one of its neutrons becomes a proton, an electron flies out, and the atom becomes nitrogen-14. Uranium-238 decays by alpha decay into thorium-234. Gamma rays often follow either kind, as the new nucleus settles. They sit at the top of the electromagnetic spectrum.

All three are ionizing: they carry enough energy to knock electrons off atoms, which is what makes them able to damage living cells. That energy comes from the nucleus itself. The products of a decay have slightly less mass than the original nucleus, and the difference is released as energy, by E = mc², millions of times more per atom than any chemical reaction.

Which type is most dangerous depends on where the source is. Outside the body, alpha particles barely get through skin, while gamma rays pass deep into tissue. Inside the body, breathed in or swallowed, an alpha emitter is the worst, dumping all its energy into a tiny volume of tissue.

What is a half-life?

A half-life is the time it takes for half of the radioactive atoms in a sample to decay. It is fixed for each isotope and unaffected by heat, pressure or chemistry. Half-lives range from fractions of a second to billions of years: uranium-238's is about 4.5 billion years, close to the age of Earth.

Decay is random. A single nucleus has no age and no countdown; in any one half-life it has a 50% chance of decaying, whatever its history. But with trillions of atoms, the randomness averages out into a smooth curve. Each half-life removes half of what is left, so the amount falls by the same fraction in each equal stretch of time. That is exponential decay, the mirror image of exponential growth.

A worked example: iodine-131 over 80 days

Iodine-131 is released by nuclear reactors and bombs and used in medicine to treat thyroid disease. Its half-life is about 8 days. Start with 1,000,000 atoms.

Days	Half-lives passed	Atoms left	Fraction left
0	0	1,000,000	1
8	1	500,000	1/2
16	2	250,000	1/4
24	3	125,000	1/8
40	5	31,250	1/32
80	10	about 977	1/1,024

After 80 days, under 0.1% is left. That is why iodine-131 was the main radiation danger in the first weeks after the Chernobyl accident, concentrating in milk and children's thyroids, and why it had faded away within months while longer-lived isotopes such as cesium-137, with a half-life of about 30 years, still contaminate the area.

A worked example: dating with carbon-14

Living things take in carbon from the air or from food, keeping the same small share of carbon-14 as the atmosphere. When they die, intake stops and the carbon-14 begins to decay with a half-life of about 5,700 years (older references give 5,730). Measure how much is left, compared with a living sample, and you can count back.

1. A piece of charcoal from an ancient hearth has 25% of the carbon-14 of living wood. 25% is a half of a half, so two half-lives have passed: 2 × 5,700 = about 11,400 years.
2. A bone has 30% left. That is between one and two half-lives. The number of half-lives is log₂(1 ÷ 0.30) = 1.74, so its age is 1.74 × 5,700, about 9,900 years. The base-2 logarithm here simply asks how many halvings take 1 down to 0.30, the question logarithms answer.

In practice labs correct for small changes in the atmosphere's carbon-14 over time, and the method works back to about 50,000 years, after which too little is left to measure.

How much radiation is dangerous?

Radiation dose to the body is measured in sieverts (Sv), usually in millisieverts (mSv, thousandths of a sievert). The sievert weighs the energy absorbed by the kind of radiation and the tissues hit, so doses from different sources can be compared. Everyone receives a dose all the time from natural sources, mostly radon gas seeping from rock and soil. The figures below are typical for the United States; this note explains the physics and is not medical advice.

Source or level	Typical effective dose
A coast-to-coast round-trip flight	about 0.03 mSv
An adult chest X-ray	about 0.1 mSv, roughly 10 days of natural background
Natural background in a year, US average	about 3 mSv, of which radon about 2 mSv
Average total in a year, US, including medical scans	about 6.2 mSv
A CT scan of the abdomen and pelvis	about 7.7 mSv
Level above which studies show a clearly raised cancer risk	100 mSv
Threshold for acute radiation syndrome	about 1,000 mSv (1 Sv)

The everyday figures are from RadiologyInfo, run by two radiology societies, and the U.S. Environmental Protection Agency; the thresholds are from the World Health Organization, which notes that some studies of children given CT scans suggest a raised risk at 50 to 100 mSv.

Still argued

What happens at low doses, well under 100 mSv, is not settled, because any extra cancers would be too few to pick out from the many cancers that happen anyway. Radiation protection bodies assume the linear no-threshold model: risk rises in proportion to dose, all the way down to zero, so no dose is entirely without risk. Some scientists argue that this overstates the danger of small doses, which cells may repair, and that it drives costly overreaction, such as the stressful mass evacuations after Fukushima. Defenders reply that the model is a deliberately cautious rule for setting limits, not a claim that every small dose causes harm, and that the data at low doses don't rule it out.

Who discovered radioactivity?

Henri Becquerel found it in 1896, when uranium salts blackened a photographic plate that was wrapped in black paper, with no light to expose it. Marie and Pierre Curie took it further, coining the word "radioactivity" and, in 1898, discovering two new radioactive elements, polonium and radium. The three shared the 1903 Nobel Prize in Physics. Marie Curie went on to win a second, in chemistry, in 1911. Within half a century the same physics, turned to splitting nuclei on purpose, gave the world nuclear power and the atomic bomb.

Check yourself

• Without looking back: what is the difference between carbon-12 and carbon-14, and why does only one of them decay?
• Why can't anyone predict when a single radioactive atom will decay, when a sample's half-life is known precisely?
• Why is an alpha emitter fairly harmless outside the body but dangerous if swallowed?

Sources

• Radioactive decay — Wikipedia
• Carbon-14 — Wikipedia
• Radiation Dose from X-Ray and CT Exams — RadiologyInfo.org, Radiological Society of North America and American College of Radiology
• Radiation Sources and Doses — U.S. Environmental Protection Agency
• Ionizing radiation and health effects — World Health Organization
• The Nobel Prize in Physics 1903 — Nobel Foundation