Radioactive Decay and Radiometric Dating

Radioactivity is the spontaneous transformation of an unstable nuclide, which results in the emission of radiation. This is a random process, so all the nuclei in the sample have the same probability of decaying.

The number of disintegrations per unit time is called the activity, A, which is directly proportional to N, the number of radioactive nuclei. Lambda, the decay constant, is the average probability of decay per nucleus per unit time.

Activity is measured with radiation detectors and has the becquerel, which is one disintegration per second, as its SI unit. The curie, which is 37 billion becquerels, is still used for large-scale applications.

Different radionuclides have different decay rates. As the activity is proportional to the number of radioactive atoms, it decreases with time as the amount of unstable nuclei in the sample decreases.

The change in activity over time is calculated with an exponential equation, where A is the activity at time t, A₀ is the initial activity, lambda is the decay constant, and t is the time elapsed since the activity was A₀.

The half-life of a radionuclide, t_1/2, is the average time required for the activity of a sample to fall to half of that value. Thus, the equation can be rearranged to calculate the half-life from the decay constant, to which it is inversely proportional.

The half-life is an intrinsic property of a radionuclide, and it varies widely from nuclide to nuclide: radon-220 has a half-life of one minute, whereas thorium-232 has a half-life of 14 billion years.

The fixed half-lives of radionuclides are relevant for techniques like radiometric dating, which estimates the age of objects from the quantity of naturally occurring radionuclides.

The ratio of unstable carbon-14 to stable carbon-12 in living plants and animals matches that of the atmosphere.

The ratio is maintained by replenishment of carbon from the air and food. After death, the carbon-14 to carbon-12 ratio begins decreasing as the radioactive carbon-14 decays by emitting beta particles.

If a specimen has 25% as much carbon-14 as it did when it was alive, then two half-lives must have elapsed. The object must be 11,460 years old.