There is a half-life describing any exponential-decay process. 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. 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. 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. įor example, the image on the right is a simulation of many identical atoms undergoing radioactive decay. In other words, the probability of a radioactive atom decaying within its half-life is 50%. Instead, the half-life is defined in terms of probability: "Half-life is the time required for exactly half of the entities to decay on average".
For example, if there is just one radioactive atom, and its half-life is one second, there will not be "half of an atom" left after one second.
In that case, it does not work to use the definition that states "half-life is the time required for exactly half of the entities to decay". Note the consequence of the law of large numbers: with more atoms, the overall decay is more regular and more predictable.Ī half-life usually describes the decay of discrete entities, such as radioactive atoms. The number at the top is how many half-lives have elapsed. Simulation of many identical atoms undergoing radioactive decay, starting with either 4 atoms per box (left) or 400 (right). The accompanying table shows the reduction of a quantity as a function of the number of half-lives elapsed. Half-life is constant over the lifetime of an exponentially decaying quantity, and it is a characteristic unit for the exponential decay equation.
Rutherford applied the principle of a radioactive element's half-life to studies of age determination of rocks by measuring the decay period of radium to lead-206. The original term, half-life period, dating to Ernest Rutherford's discovery of the principle in 1907, was shortened to half-life in the early 1950s.
The converse of half-life is doubling time. For example, the medical sciences refer to the biological half-life of drugs and other chemicals in the human body. The term is also used more generally to characterize any type of exponential or non-exponential decay. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. Half-life (symbol t 1⁄2) is the time required for a quantity to reduce to half of its initial value.
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