![]() ![]() 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 first-order reaction the half-life of the reactant is ln(2)/ λ, where λ (also denoted as k) is the reaction rate constant. 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. 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 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 accompanying image 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 often describes the decay of discrete entities, such as radioactive atoms. The number at the top is how many half-lives have elapsed. Probabilistic nature 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 in 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 (in exponential growth) 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, rarely, 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 ½) is the time required for a quantity (of substance) to reduce to half of its initial value. ![]()
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