The time it takes for a single parent atom to decay to an atom of its daughter isotope can vary widely, not only between different parent-daughter pairs, but also randomly between identical pairings of parent and daughter isotopes. The decay of each single atom occurs spontaneously, and the decay of an initial population of identical atoms over time "t", follows a decaying exponential distribution, "e−λt", where λ is called a decay constant. One of the properties of an isotope is its half-life, the time by which half of an initial number of identical parent radioisotopes have decayed to their daughters, which is inversely related to λ. Half-lives have been determined in laboratories for many radioisotopes (or radionuclides). These can range from nearly instantaneous (less than 10−21 seconds) to more than 1019 years.