decay the time constant is related to the decay constant (?), and it represents both the mean lifetime of a decaying system (such as an atom) before it decays, or the time it takes for all but 36.8% of the atoms to decay. For this reason, the time constant is longer than the half-life, which is the time for only 50% of the atoms to decay.

In practical terms, the time constant is the characteristic time scale over which a first-order system responds to a