Elements of radioactive dating
The recognition that the rate of decay of any radioactive parent atom is proportional to the number of atoms () of the parent remaining at any time gives rise to the following expression: Converting this proportion to an equation incorporates the additional observation that different radioisotopes have different disintegration rates even when the same number of atoms are observed undergoing decay.
Values of λ vary widely—from 10 is the time elapsed since time zero.
For a single element, these atoms are called isotopes.
Because isotopes differ in mass, their relative abundance can be determined if the masses are separated in a mass spectrometer (see below Use of mass spectrometers).
Half-life is defined as the time period that must elapse in order to halve the initial number of radioactive atoms.
The half-life and the decay constant are inversely proportional because rapidly decaying radioisotopes have a high decay constant but a short half-life.