No atom is “due”. Each one has the same small chance of decaying in any moment, whatever its age. Nothing you can do to it, hot or cold, changes that.
Add up enough coin tosses and the total is exact: half of the atoms are gone after one half-life, a quarter left after two. The wobble shrinks as the sample grows.
Each half-life halves what is left. After ten, about a thousandth remains; after thirty, about one in a billion. In practice the last atoms just run out.
For the same number of atoms, the shorter the half-life the more decays per second. The loud ones go quiet fast; the long-lived ones whisper for ages.
The average time an atom survives is not one half-life but 1.44 of them (1 divided by ln 2, or 1.4427). The half-life is the time for half to go, which is sooner, because the atoms that decay early are many and the long survivors few. After one mean life, 37% are left.
A living thing takes in carbon-14 from the air, and when it dies the carbon-14 starts to halve every 5,730 years. Nine half-lives is about 51,600 years, and by then only 0.2% is left, too little to separate from the carbon-14 that creeps in from outside. Older than that, other clocks are used, with longer half-lives, such as potassium-40 at 1.25 billion years.
This is the strange part. Watch an atom that has survived a million years and its chance of decaying in the next second is exactly the same as it was on day one. Nothing wears out. That is why the curve is an exponential, and why you can never say which atom will go next, only how many.
A becquerel is one decay a second. A gram of radium gives 3.66×1010 of them, which is how the curie began, and a gram of carbon-14 gives 1.65×1011. A gram of uranium-238 gives only 12,400, because its half-life is nearly three million times longer.
A short half-life means the danger passes quickly but is fierce while it lasts; a long one means a weak but nearly permanent source. Technetium-99m, 6 hours, is chosen for medical scans because it is gone within a day: a scan dose of 600 MBq is only about 3 nanograms of it. Plutonium-239, 24,110 years, is weakly active per gram but will be for hundreds of thousands of years.
You hold about 7,000 decays every second: potassium-40 in your muscles (about 4,400) and carbon-14 in everything you are made of (about 3,000). A banana, with its potassium, is about 15 becquerels. It is a normal part of being alive, and the dose from it is small compared with the radon in the air of most houses.
It follows one kind of atom decaying once. Real chains go on: radium-226 becomes radon-222, which becomes polonium-218 and so on down to lead, each with its own half-life. A few atoms, such as potassium-40, decay in more than one way. Dose, the harm to a body, depends on the energy absorbed and where; activity does not tell you that. The random numbers here are a computer’s, a good imitation of the real chance, and the sample is a toy next to the trillions in a real one.
The time it takes for half of the radioactive atoms in a sample to decay. After one half-life half remain, after two a quarter, after three an eighth. It is a fixed property of each kind of atom, from fractions of a microsecond to billions of years.
No: a quarter is left. Each half-life halves what remains, so the amount falls by half, then half again. It takes about seven half-lives to get below 1%, and ten to reach about a thousandth.
Because it is genuinely random, not just unknown. An atom has no memory and no clock: in every moment it has the same small chance of decaying, however long it has waited. Only for large numbers of atoms does the average become predictable.
Living things take in a steady fraction of carbon-14 from the air. When they die the intake stops and the carbon-14 halves every 5,730 years. Measure how much is left compared with a living thing and the age follows: a quarter left is two half-lives, about 11,460 years. It reaches back about 50,000 years, and needs a correction because the air’s carbon-14 has varied.
The half-life is the time for half to decay. The mean life is the average time an atom lasts, 1.44 times as long (1 / ln 2). After one mean life 37% are left. Both describe the same exponential; the half-life is just easier to picture.
One decay per second: the unit of activity. A curie, the older unit, is 37 billion of them, roughly a gram of radium. Neither says how harmful it is: that is measured in sieverts, which weigh the energy absorbed by the type of radiation and the part of the body.
It is more active for the same number of atoms, so a dose arrives faster; but it is also gone sooner. Neither is simply safer. Iodine-131 (8 days) is intense but fades in months, while plutonium-239 (24,110 years) is weaker but lasts. What matters is how much you take in, where it goes in the body, and what kind of radiation it gives.
It holds potassium, and 0.0117% of all potassium is potassium-40, which has a half-life of 1.25 billion years and decays about 15 times a second in a banana. All food has some. The dose is tiny, and it is the same potassium that your body is already full of.
Its atoms decay rarely, so few go each second, but there are many atoms. A gram of uranium-238 gives about 12,400 decays a second: enough to detect, far too few to hurt, and it will carry on for billions of years.
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