September 28, 2023

# Introduction

The amount of time needed for a quantity (of substance) to decrease to half of its starting value is denoted by the symbol t12. In nuclear physics, the phrase is frequently used to indicate how rapidly unstable atoms decay radioactively or how long stable atoms last. The phrase is also used more broadly to describe exponential decay (or, very infrequently, nonexponential decay). For instance, the biological half-life of medications and other compounds in the human body is a term used in the medical sciences. Half-life’s opposite in exponential growth is time’s doubling.

After Ernest Rutherford discovered the principle in 1907, the original word, half-life period, was abbreviated to half-life in the early 1950s.[1] Rutherford measured the time it took for radium to decay into lead-206 to apply the idea of a radioactive element’s half-life to studies on dating rocks.

Half-life is a characteristic unit for the exponential decay equation and is constant across the lifespan of an exponentially decaying quantity. The reduction of a quantity is displayed in the accompanying table as a function of the number of half-lives that have passed.

## Nature is Probabilistic

When discrete entities like radioactive atoms decay, a half-life is frequently used to characterize it. The concept that “half-life is the time required for exactly half of the entities to decay” does not apply in this situation. There won’t be “half of an atom” left after one second, for instance, if there is only one radioactive atom and its half-life is one second.

The half-life is instead described in terms of probability: “Half-life is the average time needed for exactly half of the entities to decay.” In other words, there is a 50% chance that a radioactive atom will decay during its half-life.[2]

For instance, the simulation of several similar atoms going through radioactive decay can be seen on the right. Due to the random variance in the process, it should be noted that after one half-life, there are approximately half the atoms left. However, the law of large numbers shows that it is a fairly good approximation to claim that half of the atoms remain after one half-life when numerous identical atoms are decaying (right boxes).

Probabilistic decay can be demonstrated using a variety of easy tasks, such as coin tosses or the execution of a statistical computer program.[3][4][5]

## Examples

Any process involving exponential decay has a half-life. For instance:

• The period after which there is a 50% chance that an atom would have undergone nuclear decay is known as the half-life in radioactive decay, as was previously mentioned. It is often calculated empirically and varies based on the isotope and kind of atom. check out the List of nuclides.
• The half-life of the current flowing through an RC circuit or an RL circuit is ln(2)RC or ln(2)L/R, respectively. Although “half-life” is more frequently used in this case than “half-time,” they both refer to the same thing.
• The amount of time it takes for a species’ concentration to drop to half of its starting value in a chemical reaction is known as its half-life. The reactant’s half-life in a first-order reaction is equal to ln(2)/k, where k is the reaction rate constant.

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