How Radioactive Decay Works: Half-Life, Carbon Dating, and Nuclear Medicine

Most atoms are stable. The carbon-12 atom in your hand today will still be carbon-12 in a billion years. But a minority of nuclei are not stable, and each of those will eventually rearrange itself, throwing off a particle or a burst of energy and often becoming a different element. That is radioactive decay. Henri Becquerel found it in 1896, and within a decade Ernest Rutherford and Frederick Soddy had described its central regularity: the half-life. The same rule now lets scientists date a mammoth tusk, measure the age of the Earth, and put a tracer into a patient that lights up a tumor.

Key takeaways

• Nuclear instability arises when a nucleus has the wrong balance of neutrons and protons, or is simply too large for the strong force to hold together.
• Alpha decay emits a helium-4 nucleus. Beta decay converts a neutron into a proton (or the reverse) and emits an electron or positron plus a neutrino. Gamma decay emits a high-energy photon and changes no particle counts.
• Half-life is the time for half of a large sample to decay. It is set by the nuclide and does not depend on how much material is present.
• Carbon-14 dating uses a half-life of about 5,730 years and works to roughly 50,000 years. Longer-lived pairs such as uranium-238 and lead-206 date rocks and meteorites.
• Nuclear medicine uses isotopes with half-lives of hours to days, chosen so that they decay quickly after doing their job.

What makes a nucleus unstable?

A nucleus is a tight bundle of protons and neutrons held together by the strong nuclear force, the strongest of the four fundamental forces but one that reaches only a few femtometers (a femtometer is 10⁻¹⁵ meters). Working against it is the electromagnetic repulsion between the positively charged protons. The strong force acts equally on protons and neutrons and only on near neighbors, while the electric repulsion acts between every pair of protons across the whole nucleus. Our overview of the four fundamental forces covers why one is short-ranged and the other is not.

That mismatch shapes which nuclei exist. In light nuclei the best arrangement is roughly equal numbers of protons and neutrons: carbon-12 has 6 and 6, and oxygen-16 has 8 and 8. As nuclei grow, the repulsion between protons builds faster than the strong-force attraction, so stable heavy nuclei carry extra neutrons to dilute it. Lead-208, with 82 protons and 126 neutrons, is the heaviest stable nucleus found.

The valley of stability

Plot every known nuclide with proton number on one axis and neutron number on the other and the stable ones form a narrow band. Physicists call it the valley of stability, and the picture to hold in your head is a marble on a curved landscape. Nuclei in the valley floor stay put. Nuclei on the slopes roll down toward it, and each roll is a decay. Too many neutrons, and the nucleus converts one into a proton. Too few, and it does the reverse. Too heavy, and it sheds an alpha particle to lose mass.

The nuclear shell model, developed in the late 1940s and early 1950s by Maria Goeppert Mayer and independently by J. Hans D. Jensen and colleagues, explains why certain nucleon counts, the "magic numbers" 2, 8, 20, 28, 50, 82, and 126, give especially stable nuclei. Lead-208 is doubly magic, with 82 protons and 126 neutrons, which is part of why it is the last stable stop on the way down the periodic table. Goeppert Mayer and Jensen shared the 1963 Nobel Prize in Physics for the work. You can read more about her in our profile of Maria Goeppert Mayer.

By one count, there are 251 stable nuclides and 35 additional radionuclides with half-lives long enough that they have survived since the solar system formed, for a total of 286 "primordial" nuclides (Wikipedia, primordial nuclide). Lead is the heaviest element with stable isotopes, and every isotope of every element from bismuth (atomic number 83) upward is radioactive, though bismuth-209 is so slow to decay that it long passed as stable. Technetium (43 protons) and promethium (61) have no stable isotopes at all, which is why they are essentially absent from the Earth's crust.

Types of radioactive decay

The three classic types were named by Rutherford, who needed labels for radiation he could not yet identify. Each one changes the nucleus in a specific, bookkeeping-friendly way.

Decay	Particle emitted	Change in protons (Z)	Change in mass number (A)	Typical shielding
Alpha	Helium-4 nucleus (2 protons, 2 neutrons)	−2	−4	Paper, outer layer of skin
Beta-minus	Electron and antineutrino	+1	0	Aluminum, a few millimeters
Beta-plus	Positron and neutrino	−1	0	Aluminum, a few millimeters
Electron capture	Neutrino (nucleus absorbs an inner electron)	−1	0	Gamma or X-rays follow
Gamma	High-energy photon	0	0	Lead, thick concrete

Shielding figures follow the standard summary in the radioactive decay article: alpha particles can be stopped by a sheet of paper, beta particles by aluminium, and gamma rays need something substantial such as lead.

Alpha decay

In alpha decay, the nucleus ejects an alpha particle, a tightly bound cluster of two protons and two neutrons identical to a helium-4 nucleus. The parent loses two protons and two neutrons and turns into a different element. Uranium-238 becomes thorium-234 this way.

The odd part is how it happens. The alpha particle does not have enough energy to climb over the barrier that holds it inside the nucleus, and yet it gets out. In 1928, George Gamow explained the escape as quantum tunneling, and Ronald Gurney and Edward Condon reached the same idea almost simultaneously. The particle has a small but nonzero chance of appearing on the far side of the barrier on every attempt, and that tiny chance is what the half-life reflects. A slightly more energetic alpha makes the barrier thinner, so half-lives change by an enormous factor for a modest change in energy. Our article on quantum tunneling shows the same effect in other settings.

Alpha particles are heavy and doubly charged, so they hit atoms constantly and stop within centimeters of air. That makes an alpha source outside the body fairly harmless, since the dead outer layer of skin stops it. It also makes alpha emitters dangerous when inhaled or swallowed, because all that energy gets deposited in a small volume of living tissue.

Beta decay

Beta decay comes in two forms, both governed by the weak force.

In beta-minus decay, a neutron in the nucleus turns into a proton and emits an electron and an electron antineutrino. The atomic number goes up by one and the mass number stays the same. Carbon-14 decays to nitrogen-14 this way, and iodine-131 decays to xenon-131.

In beta-plus decay, a proton turns into a neutron and emits a positron, the antimatter twin of the electron, along with a neutrino. Fluorine-18 decays to oxygen-18 mostly by this route. A competing process, electron capture, has the nucleus absorb one of its own inner electrons to make the same change. According to the fluorine-18 entry, about 96.7% of fluorine-18 decays are positron emission and about 3.3% are electron capture.

The neutrino has a story of its own. Early measurements in the 1920s showed that electrons from beta decay came out with a continuous range of energies, as if some energy were missing, which appeared to violate conservation of energy. In 1930, Wolfgang Pauli proposed that an unseen neutral particle carried off the difference, and Enrico Fermi built the full theory of beta decay a few years later. The neutrino was finally detected in 1956 by Clyde Cowan and Frederick Reines, 26 years after Pauli's guess. Read about the experiment in Project Poltergeist.

Gamma decay

Gamma decay changes neither the proton count nor the neutron count. A nucleus left in an excited energy state, usually by an earlier alpha or beta decay, drops to a lower state and emits a gamma-ray photon, typically carrying from tens of kiloelectronvolts to a few megaelectronvolts. Gamma rays pass through a lot of material, so shielding takes dense material such as lead or thick concrete, and they can ionize atoms and damage DNA well away from the source.

The mathematics of half-life

Radioactive decay has a feature that surprises people at first: each individual nucleus has a fixed probability of decaying in the next second, and that probability never changes. The nucleus does not age. A uranium-238 atom that has existed for 4 billion years is exactly as likely to decay in the next second as one formed yesterday. Radioactive decay is memoryless in the way a coin flip is memoryless: a coin that has landed heads ten times is still a fair coin.

Picture a crowd of one million people, each flipping a weighted coin once a second and leaving the room if it lands on a particular side. You cannot predict which person leaves next, but you can predict very well how many leave in a minute. Since each remaining person has the same chance, the number leaving per second is proportional to the number still present. That gives exponential decay:

N(t) = N₀ × e^(−λt)

Here N₀ is the starting number of nuclei, N(t) is the number left after time t, and λ (lambda) is the decay constant, the probability per unit time that one nucleus decays. The activity, or number of decays per second, is A = λN. The SI unit of activity is the becquerel (Bq), defined as one decay per second. An older unit, the curie, is defined as 3.7 × 10¹⁰ decays per second (source).

The half-life is the time for N to fall to half of N₀, and solving the equation gives t½ = ln(2)/λ, or about 0.693/λ. The related mean lifetime is τ = 1/λ, which is about 1.44 times the half-life. Because half-life depends only on λ, it is a property of the nuclide, not of the sample size, and the same fractions apply no matter where you start.

Half-lives elapsed	Fraction remaining	Percent remaining
1	1/2	50%
2	1/4	25%
3	1/8	12.5%
4	1/16	6.25%
5	1/32	3.1%
7	1/128	0.78%
10	1/1,024	0.098%

A worked example: how radioactive is a gram of radium?

Radium-226 has a half-life of about 1,600 years. A gram contains 6.022 × 10²³ ÷ 226 ≈ 2.66 × 10²¹ atoms. Converting the half-life to seconds gives about 5.05 × 10¹⁰ s, so λ = 0.693 ÷ 5.05 × 10¹⁰ ≈ 1.37 × 10⁻¹¹ per second. Multiply: A = λN ≈ 3.7 × 10¹⁰ becquerels, about one curie. Slow decay and a huge number of atoms combine to produce a large decay rate, which is how Marie Curie's samples glowed and fogged photographic plates.

Why half-lives are statistical

Half-life describes a crowd, not a person. For a single atom the concept does not apply, because it either decays or it does not. For a million atoms, the actual count of decays in a given interval fluctuates by roughly the square root of the expected number, which is about 0.1% when 1,000,000 decays are counted. That counting noise sets the precision of every measurement in this article.

The range of half-lives

Half-lives cover more than 30 orders of magnitude, from a fraction of a second to figures that dwarf the age of the universe.

Nuclide	Half-life	Decay mode	Where it matters
Polonium-214	about 164 microseconds	Alpha	Short-lived link in the uranium series
Fluorine-18	109.734 minutes	Beta-plus (96.7%)	PET scans
Technetium-99m	6.0066 hours	Gamma	Most common diagnostic isotope
Iodine-131	8.0249 days	Beta-minus	Thyroid treatment
Radium-226	about 1,600 years	Alpha	Early radiotherapy, radon source
Carbon-14	about 5,730 years	Beta-minus	Radiocarbon dating
Uranium-235	704 million years	Alpha	Fission fuel, dating
Potassium-40	1.25 billion years	Electron capture, beta-minus	Natural radioactivity of the body
Uranium-238	4.46 billion years	Alpha	Dating the Earth
Rubidium-87	about 49.2 billion years	Beta-minus	Dating old rocks
Bismuth-209	about 2 × 10¹⁹ years	Alpha	Once thought stable

Bismuth-209 deserves a footnote. In 2003, a team at the Institut d'Astrophysique Spatiale in Orsay, led by Pierre de Marcillac and Noël Coron, saw it decay by alpha emission using a cryogenic scintillating bolometer, and measured a half-life of (1.9 ± 0.2) × 10¹⁹ years (Nature 422, 876, 2003). A 2012 measurement at Gran Sasso gave (2.01 ± 0.08) × 10¹⁹ years, which is why the table says "about 2 × 10¹⁹". That is more than a billion times the age of the universe, yet not infinite. Half-lives for the other entries come from the Wikipedia pages on Technetium-99m, Fluorine-18, Iodine-131, and primordial nuclides.

Decay chains: when the daughter is radioactive too

Often the product of a decay is radioactive as well, so one atom can pass through a long series of transformations before reaching a stable end. Nature has four such chains, each headed by a long-lived parent.

Series	Long-lived parent (half-life)	Stable end product	Alpha and beta decays
Thorium	Thorium-232 (about 14 billion years)	Lead-208	6 alpha, 4 beta
Neptunium	Neptunium-237 (2.144 million years)	Thallium-205	8 alpha, 4 beta
Uranium (radium)	Uranium-238 (4.463 billion years)	Lead-206	8 alpha, 6 beta
Actinium	Uranium-235 (704 million years)	Lead-207	7 alpha, 4 beta

Figures are from the decay chain article. The neptunium series is effectively extinct in nature because its parent has long since decayed, apart from the very slow final step of bismuth-209.

The uranium series is also the source of radon. Radon-222, with a half-life of 3.8215 days, appears in the middle of the chain as an inert gas that escapes from uranium-bearing rock and soil, drifts into basements, and decays into a series of solid alpha emitters that can lodge in lungs. A chain left alone for long enough reaches equilibrium, in which each daughter decays as fast as it is made and the whole sample gives off a steady, slowly declining stream of radiation.

Carbon-14 dating: reading time in dead organisms

Carbon-14 (¹⁴C) is a radioactive form of carbon with a half-life of about 5,730 years. It is made continuously in the upper atmosphere when neutrons released by cosmic rays strike nitrogen-14 and knock out a proton: ¹⁴N + n → ¹⁴C + p. The new carbon-14 combines with oxygen to make carbon dioxide, mixes through the atmosphere, and enters plants through photosynthesis and animals through the food chain. It is extraordinarily rare, roughly 1.25 atoms per trillion atoms of ordinary carbon-12 (source).

As long as an organism is alive, it keeps swapping carbon with its environment, and the ratio of ¹⁴C to ¹²C in its tissues matches the atmosphere's. At death the swapping stops. The ¹⁴C that is present keeps decaying and nothing replaces it, so the ratio falls along the exponential curve. Measure what is left and you can solve for the elapsed time:

t = (t½ / ln 2) × ln(N₀ / N)

A bone with one quarter of its original ¹⁴C has gone through two half-lives, about 11,460 years. One with one eighth has gone through three, about 17,190 years. The method was developed by Willard Libby at the University of Chicago in the late 1940s, who tested it in 1949 on samples from the tombs of two Egyptian kings, and it earned him the 1960 Nobel Prize in Chemistry. For a fuller history and the practical details of sample preparation, see Radiocarbon dating: how carbon-14 tells us the age of ancient things.

Where the method gets complicated

The simple formula is only the first step, because several things complicate the answer.

• The atmosphere's carbon-14 level has not been constant. Raw "radiocarbon years" are converted to calendar years using calibration curves built from tree rings and other records. The Northern Hemisphere IntCal20 tree-ring sequence extends to about 13,910 years before present, and older dates depend on less precise correlations.
• Reservoir effects. Marine samples typically show an apparent age of about 400 years because ocean water holds carbon that has been out of contact with the atmosphere. Hard water and volcanic carbon can distort ages by thousands of years.
• Humans changed the baseline twice. Burning fossil fuels, which contain almost no carbon-14, diluted atmospheric levels by about 3% (the Suess effect). Atmospheric nuclear testing from about 1950 to 1963 nearly doubled atmospheric carbon-14, with a peak around 1964 in the Northern Hemisphere.
• A convention fixes the half-life. Libby's original value was 5,568 years. At a 1962 conference, researchers agreed to keep that value for "conventional" radiocarbon ages, and calibration curves take care of the difference from the better-measured 5,730.

On the practical side, older labs counted beta particles emitted by the sample and needed at least about 10 grams. Modern accelerator mass spectrometry (AMS) counts ¹⁴C and ¹²C atoms directly and needs as little as 0.5 milligrams of carbon. The usual upper limit is about 50,000 years, with special preparation sometimes stretching it to 60,000 to 75,000. All of these numbers are from the radiocarbon dating summary of the primary literature.

Radiocarbon dating works only on material that was once alive. It cannot date a dinosaur bone, which is millions of years old and long past the limit, or a rock, which never took up carbon from the atmosphere.

Radiometric dating of rocks and the age of the Earth

For geological time, scientists use pairs with half-lives of hundreds of millions to tens of billions of years. The logic is the same as carbon dating but the clock is the ratio of a radioactive parent to its stable daughter in a mineral.

Parent	Stable daughter	Half-life
Uranium-238	Lead-206	4.46 billion years
Uranium-235	Lead-207	704 million years
Thorium-232	Lead-208	about 14 billion years
Potassium-40	Argon-40 (and calcium-40)	1.25 billion years
Rubidium-87	Strontium-87	about 49 billion years

Half-lives are from the primordial nuclide listing. Potassium-40 splits two ways, mostly into calcium-40 and occasionally into argon-40, and geologists use the argon branch because argon is a gas that escapes from molten rock and starts the clock at zero when the rock solidifies.

The idea is older than most people expect. Rutherford gave a lecture at Yale in 1904 on dating with radioelements. In February 1907, the Yale chemist Bertram Boltwood published ages for ten mineral samples, one of which, a thorianite from Ceylon, came out at 2.2 billion years. His numbers were rough, partly because he used a radium half-life of 2,600 years, well above the roughly 1,600 years we now accept (APS News). But the principle was right, and it broke the ceiling that Lord Kelvin's cooling calculations of the 1860s, which gave tens of millions of years, had put on the age of the planet.

How we know the Earth is 4.54 billion years old

Earth's oldest rocks have been recycled by plate tectonics, so no rock on Earth's surface preserves the planet's birth. Geologists date the planet indirectly. They assume that Earth and the other solid bodies of the solar system formed at about the same time, then compare the lead-207 to lead-206 ratio in Earth's oldest lead ores with the primordial lead composition measured in iron meteorites such as Canyon Diablo. The result is an age of 4.54 billion years with an uncertainty of less than 1 percent, according to the USGS.

The cross-checks line up. The oldest surviving rocks, the Acasta Gneisses in northwestern Canada, are about 4.03 billion years old, and zircon crystals in Western Australia, the oldest materials found on Earth, have been dated to more than 4.3 billion years. More than 70 meteorites have been dated to between 4.53 and 4.58 billion years (USGS). Several independent isotope systems, each with a different half-life and different chemistry, agree within error, which is the strongest argument that the clocks are measuring something real. For the full story see our article on how scientists measure the age of Earth.

One more technique deserves a mention. Because a rock may start with some daughter isotope already present, geologists often measure several minerals from the same rock and plot the ratios against each other. Points that fall on a straight line, called an isochron, give the age from the slope and the initial daughter content from the intercept, which removes the need to guess the starting conditions.

Radioactivity in medicine

Medicine uses the same physics in reverse. Instead of waiting for time to pass, doctors choose an isotope whose half-life is just long enough to do the job and short enough to disappear afterward. Our overview of how the Geiger counter detects radiation describes one of the simpler detectors, but clinical imaging uses much more sensitive ones.

PET scanning (positron emission tomography). Fluorine-18 has a half-life of 109.734 minutes. It is produced in a cyclotron by firing protons of about 18 MeV at oxygen-18-enriched water, then built into fluorodeoxyglucose (FDG), a sugar analogue. Tumors often take up glucose faster than surrounding tissue, so FDG accumulates there. Each fluorine-18 decay emits a positron, which meets an electron within a millimeter or so and annihilates, sending out two gamma-ray photons of 511 keV in nearly opposite directions. A ring of detectors records coincident pairs and reconstructs where the decays happened. The short half-life is a logistics problem as well as a safety feature: six hours after production only about 10% of the fluorine-18 is left, so it has to be made near where it will be used. Our article on MRI covers a different way to image the body without ionizing radiation.

Technetium-99m. The "m" means metastable, an excited nuclear state that decays by emitting a 140.5 keV gamma ray, close to the energy of diagnostic X-rays and easy for a gamma camera to detect. Its half-life is about 6 hours, and the decay product has a half-life of 211,000 years but emits very little radiation. The isotope is used in an estimated 20 million diagnostic procedures a year and accounts for about 85% of diagnostic nuclear medicine imaging. Hospitals do not buy it directly. They buy generators holding molybdenum-99, which has a half-life of about 2.75 days, and "milk" the technetium from them as needed, which is also why the supply chain depends on a small number of research reactors (Technetium-99m).

Targeted radiotherapy. Here the aim is to deposit radiation inside diseased tissue. Iodine-131, a beta emitter with a half-life of about 8 days, is used to treat an overactive thyroid and thyroid cancer, because the thyroid takes up iodine from the blood. Typical oral doses are 400 to 600 megabecquerels for hyperthyroidism and 2,220 to 7,400 MBq to remove remnant thyroid tissue after surgery (Iodine-131). The beta electrons travel only about 0.6 to 2 millimeters in tissue, which is the point: the energy is delivered within a few cell diameters of where the iodine collects. Lutetium-177 oxodotreotide, a beta emitter attached to a molecule that binds somatostatin receptors on some neuroendocrine tumors, received FDA approval in January 2018 for gastroenteropancreatic tumors (Lutetium (177Lu) oxodotreotide).

Doses in diagnostic procedures are kept as low as practical, and decisions about whether a given test or treatment is appropriate belong to a patient's physician. The general principle is a trade-off: a radiation exposure with a small, statistical risk, accepted to get information or treatment that would otherwise be unavailable.

Natural background radiation

Radioactivity is not a human invention. The Earth's interior is kept warm in part by the decay of uranium, thorium, and potassium-40 in the crust and mantle. Measurements of antineutrinos from those decays, called geoneutrinos, by the KamLAND and Borexino detectors let scientists estimate the radiogenic share of the planet's roughly 47 terawatts of surface heat flow. The results are still uncertain. A commonly used model of the bulk silicate Earth assigns about 20 TW to radioactive decay, while Borexino's estimate was around 38 TW and KamLAND's around 11 TW, each with large error bars, so "about half" is a rough summary and not a settled number. The rest of the heat is thought to be left over from the planet's formation.

Your own body is also radioactive. A 70-kilogram person carries about 4,200 to 5,000 becquerels of potassium-40, since potassium is about 0.2% of body mass and a small fraction of all potassium is the radioactive isotope, plus about 3,000 becquerels of carbon-14 (Health Physics Society). About 10% of potassium-40 decays emit a gamma ray, so your body gives off roughly 400 to 500 gamma rays per second.

For the average American, according to the NCRP Report No. 160 figures reproduced by the EPA, the annual dose is about 6.2 millisieverts, with natural sources and medical procedures each contributing roughly half (48% from medical procedures). The largest single natural source is radon, which contributed about 2.3 millisieverts in the NCRP breakdown. A sievert is the unit of effective dose, which weights the energy absorbed by how biologically damaging each type of radiation is. Background radiation has been part of the environment throughout the history of life, and life evolved in it. For related reading on risk, see our look at whether nuclear energy is safe, and for a look at places where the background is far higher, the most radioactive places on Earth.

Common misconceptions

"A half-life ends and then it is safe." Half-life is a rate, and the decay does not stop at two half-lives. After ten half-lives, about 0.1% of the original is still present, which can matter a great deal for a substance that was dangerous to begin with. How long a material stays hazardous depends on the half-life, the type of radiation, and the starting amount.

"Short half-life means less dangerous." The reverse is closer to the truth at equal amounts: a short half-life means a high decay rate per atom, so more radiation per gram. That is why very long-lived isotopes such as uranium-238 are only weakly radioactive per gram, and why medical isotopes with half-lives of hours are strong enough to image a body in minutes.

"Radioactive materials glow." Most do not. A glow comes from some specific combination of the radiation and the surrounding material, such as the pale blue light of Cherenkov radiation in a reactor pool or the luminescence of an old radium paint dial, where the radiation excited a phosphor.

"Decay rates can never change." For nearly all practical purposes they cannot be altered by heat, pressure, or chemistry, and that constancy is what makes dating work. There are narrow exceptions. Electron capture depends on the presence of electrons near the nucleus, so its rate shifts very slightly with chemical environment, and experiments at the heavy-ion storage ring at GSI in Darmstadt showed that fully stripped ions can decay in ways neutral atoms cannot, such as the bound-state beta decay of fully ionized rhenium-187 (Bosch et al., Physical Review Letters 77, 5190, 1996). Those conditions do not occur in rocks or bones.

FAQ

Q: Can radioactive materials be "turned off" or neutralized? A: Not by chemistry, temperature, or pressure. Each nuclide's decay constant is a property of its nucleus, so waste can only be isolated until it decays, or transmuted in a reactor or accelerator into other nuclides, which is a nuclear process and not a chemical one. A few exotic cases, such as fully ionized atoms in a storage ring, show small or large changes, but they require conditions far from everyday matter.

Q: Why doesn't carbon-14 dating work on dinosaur fossils? A: Carbon-14 has a half-life of about 5,730 years, so after about 50,000 years too little remains to measure reliably. Dinosaur fossils are millions of years old, and most fossils are mineralized rock that no longer contains the original carbon. Geologists date the surrounding volcanic ash or rock layers with uranium-lead, potassium-argon, or similar long-lived systems.

Q: Does radiation cause cancer immediately? A: No. Ionizing radiation can damage DNA, and if the damage is misrepaired in a susceptible cell, it can contribute to cancer years or decades later. Whether that happens depends on dose, dose rate, type of radiation, and individual biology, so the effect is statistical. Very high doses can cause acute radiation sickness within hours to days. Low doses, such as normal background levels, carry small risks that are hard to measure directly.

Q: Is nuclear medicine safe? A: Diagnostic procedures use doses set as low as will still produce a usable image, and the isotopes are chosen to decay quickly. Therapeutic uses deliver large doses to a target by design, with the risk and benefit weighed for each patient by the treating physician. This article is general information, not medical advice.

Q: Why are some elements naturally radioactive and others not? A: It depends on the balance of forces in the nucleus. Stable nuclei sit in the valley of stability, with neutron-to-proton ratios near 1 for light elements and higher for heavy ones. Beyond lead, the electric repulsion of so many protons outweighs the short-range strong force even with extra neutrons, so every isotope of bismuth and heavier elements is radioactive, though some have half-lives far longer than the age of the universe.

Q: How is a half-life measured if it is billions of years? A: Nobody waits. Scientists count the decays from a known number of atoms over hours or weeks and compute the decay constant from the rate, using A = λN. For bismuth-209, the Orsay team counted alpha events from a bismuth germanate crystal over many days, which was enough to estimate a half-life near 2 × 10¹⁹ years. Counting precision improves with the square root of the number of events.

Q: What is the difference between radiation and radioactivity? A: Radioactivity is the property of an unstable nucleus that may decay. Radiation is the energy or particles it emits when it does. A source is radioactive, and the stream of alpha particles, beta particles, or gamma rays it produces is radiation. Contamination means radioactive material has ended up where it should not be, such as on a surface or in the body.

What this means

Radioactive decay is a random process with a predictable crowd. No one can say when a given nucleus will decay, yet the half-life of a large sample is measured to a fraction of a percent, and that gap between individual unpredictability and collective precision is what turns decay into a clock. The same regularity runs through very different settings: a bone from a Neolithic grave, a meteorite that is older than any rock on Earth, a glucose molecule carrying fluorine-18 into a tumor, and a gram of radium giving off about a curie.

The practical lesson is to match the half-life to the question. A clock for human history needs a half-life of thousands of years, and the atmosphere supplies one in carbon-14. A clock for the planet needs billions, and uranium provides it. A tracer for a patient needs hours, so it can leave before the scan is over. If you want to see where this fits in the history of physics, start with Becquerel's accidental discovery and follow it through Marie Curie's work.

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Sources

• Radioactive decay, Decay chain, and Primordial nuclide, Wikipedia (half-lives, units, chains, history).
• Radiocarbon dating, Wikipedia (Libby, IntCal20, reservoir effects, AMS).
• U.S. Geological Survey, Age of the Earth.
• American Physical Society, This Month in Physics History: Boltwood and the age of the Earth (January 2024).
• Health Physics Society, Are our bodies naturally radioactive?
• U.S. EPA, Radiation sources and doses, citing NCRP Report No. 160 (2009).
• Technetium-99m, Fluorine-18, Iodine-131, and Lutetium (177Lu) oxodotreotide, Wikipedia (medical isotopes).
• de Marcillac, P., Coron, N., et al. (2003). Experimental detection of alpha-particles from the radioactive decay of natural bismuth. Nature 422, 876-878.
• Bosch, F., et al. (1996). Observation of bound-state beta-minus decay of fully ionized rhenium-187. Physical Review Letters 77, 5190.

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