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. 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. Formulas for half-life in exponential decay ДЇurther information: Exponential decay В§В 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. ДЇor 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.ДЄ 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. This relationship enables the determination of all values, as long as at least one is known.Half-life (symbol t 1вЃ„2) is the time required for a quantity to reduce to half of its initial value. Using the above equations, it is also possible for a relationship to be derived between t 1/2, П„, and О». Derivation of the Relationship Between Half-Life Constants This means that the fossil is 11,460 years old. If an archaeologist found a fossil sample that contained 25% carbon-14 in comparison to a living sample, the time of the fossil sample's death could be determined by rearranging equation 1, since N t, N 0, and t 1/2 are known. N t is the remaining quantity after time, t The carbon-14 undergoes radioactive decay once the plant or animal dies, and measuring the amount of carbon-14 in a sample conveys information about when the plant or animal died.Д«elow are shown three equivalent formulas describing exponential decay: It is incorporated into plants through photosynthesis, and then into animals when they consume plants. The process of carbon-14 dating was developed by William Libby, and is based on the fact that carbon-14 is constantly being made in the atmosphere. The half-life of carbon-14 is approximately 5,730 years, and it can be reliably used to measure dates up to around 50,000 years ago. One of the most well-known applications of half-life is carbon-14 dating. The term is most commonly used in relation to atoms undergoing radioactive decay, but can be used to describe other types of decay, whether exponential or not. Half-life is defined as the amount of time it takes a given quantity to decrease to half of its initial value.

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