In other words, the probability of a radioactive atom decaying within its half-life is 50%. Įor example, the image on the right is a simulation of many identical atoms undergoing radioactive decay. Note that after one half-life there are not exactly one-half of the atoms remaining, only approximately, because of the random variation in the process. Nevertheless, when there are many identical atoms decaying (right boxes), the law of large numbers suggests that it is a very good approximation to say that half of the atoms remain after one half-life.

Formulas for half-life in exponential decay įurther information: Exponential decay § Applications and examples Various simple exercises can demonstrate probabilistic decay, for example involving flipping coins or running a statistical computer program. As noted above, in radioactive decay the half-life is the length of time after which there is a 50% chance that an atom will have undergone nuclear decay.There is a half-life describing any exponential-decay process. The current flowing through an RC circuit or RL circuit decays with a half-life of ln(2) RC or ln(2) L/R, respectively.It varies depending on the atom type and isotope, and is usually determined experimentally. In a chemical reaction, the half-life of a species is the time it takes for the concentration of that substance to fall to half of its initial value.For this example the term half time tends to be used rather than 'half-life', but they mean the same thing. In a first-order reaction the half-life of the reactant is ln(2)/ λ, where λ is the reaction rate constant. The term 'half-life' is almost exclusively used for decay processes that are exponential (such as radioactive decay or the other examples above), or approximately exponential (such as biological half-life discussed below).

In a decay process that is not even close to exponential, the half-life will change dramatically while the decay is happening.

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