Radiochemical dating and radioactive isotopes
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.
The recognition that the rate of decay of any radioactive parent atom is proportional to the number of atoms ( 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.
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The same is true regarding gravitational, magnetic, and electric fields, as well as the chemical state in which the atom resides.
In short, the process of radioactive decay is immutable under all known conditions.