Number of halflives elapsed 
Fraction remaining 
Percentage remaining 


0  ^{1}⁄_{1}  100  
1  ^{1}⁄_{2}  50  
2  ^{1}⁄_{4}  25  
3  ^{1}⁄_{8}  12  .5 
4  ^{1}⁄_{16}  6  .25 
5  ^{1}⁄_{32}  3  .125 
6  ^{1}⁄_{64}  1  .563 
7  ^{1}⁄_{128}  0  .781 
...  ...  ...  
n  ^{1}/_{2n}  ^{100}/_{2n} 
Halflife (symbol t_{1⁄2}) is the time required for a quantity to reduce to half its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo, or how long stable atoms survive, radioactive decay. The term is also used more generally to characterize any type of exponential or nonexponential decay. For example, the medical sciences refer to the biological halflife of drugs and other chemicals in the human body. The converse of halflife is doubling time.
The original term, halflife period, dating to Ernest Rutherford's discovery of the principle in 1907, was shortened to halflife in the early 1950s.^{[1]} Rutherford applied the principle of a radioactive element's halflife to studies of age determination of rocks by measuring the decay period of radium to lead206.
Halflife is constant over the lifetime of an exponentially decaying quantity, and it is a characteristic unit for the exponential decay equation. The accompanying table shows the reduction of a quantity as a function of the number of halflives elapsed.
A halflife usually describes the decay of discrete entities, such as radioactive atoms. In that case, it does not work to use the definition that states "halflife is the time required for exactly half of the entities to decay". For example, if there is just one radioactive atom, and its halflife is one second, there will not be "half of an atom" left after one second.
Instead, the halflife is defined in terms of probability: "Halflife is the time required for exactly half of the entities to decay on average". In other words, the probability of a radioactive atom decaying within its halflife is 50%.
For example, the image on the right is a simulation of many identical atoms undergoing radioactive decay. Note that after one halflife there are not exactly onehalf 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 halflife.
There are various simple exercises that demonstrate probabilistic decay, for example involving flipping coins or running a statistical computer program.^{[2]}^{[3]}^{[4]}
An exponential decay can be described by any of the following three equivalent formulas:
where
The three parameters t_{1⁄2}, τ, and λ are all directly related in the following way:
where ln(2) is the natural logarithm of 2 (approximately 0.693).
Click show to see a detailed derivation of the relationship between halflife, decay time, and decay constant. 

Start with the three equations
We want to find relationships among t_{1⁄2}, τ, and λ such that these three equations describe exactly the same exponential decay process. Comparing the equations, we find the following conditions, Next, we'll take the natural logarithm of each of these quantities. Using the properties of logarithms, this simplifies to the following: Since the natural logarithm of e is 1, we get: Canceling the factor of t and plugging in , the final result is: 
By plugging in and manipulating these relationships, we get all of the following equivalent descriptions of exponential decay, in terms of the halflife:
Regardless of how it's written, we can plug into the formula to get
Some quantities decay by two exponentialdecay processes simultaneously. In this case, the actual halflife T_{1⁄2} can be related to the halflives t_{1} and t_{2} that the quantity would have if each of the decay processes acted in isolation:
For three or more processes, the analogous formula is:
For a proof of these formulas, see Exponential decay § Decay by two or more processes.
There is a halflife describing any exponentialdecay process. For example:
The half life of a species is the time it takes for the concentration of the substance to fall to half of its initial value.
The term "halflife" 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 halflife discussed below). In a decay process that is not even close to exponential, the halflife will change dramatically while the decay is happening. In this situation it is generally uncommon to talk about halflife in the first place, but sometimes people will describe the decay in terms of its "first halflife", "second halflife", etc., where the first halflife is defined as the time required for decay from the initial value to 50%, the second halflife is from 50% to 25%, and so on.^{[5]}
A biological halflife or elimination halflife is the time it takes for a substance (drug, radioactive nuclide, or other) to lose onehalf of its pharmacologic, physiologic, or radiological activity. In a medical context, the halflife may also describe the time that it takes for the concentration of a substance in blood plasma to reach onehalf of its steadystate value (the "plasma halflife").
The relationship between the biological and plasma halflives of a substance can be complex, due to factors including accumulation in tissues, active metabolites, and receptor interactions.^{[6]}
While a radioactive isotope decays almost perfectly according to socalled "first order kinetics" where the rate constant is a fixed number, the elimination of a substance from a living organism usually follows more complex chemical kinetics.
For example, the biological halflife of water in a human being is about 9 to 10 days,^{[7]} though this can be altered by behavior and various other conditions. The biological halflife of caesium in human beings is between one and four months.
The concept of a halflife has also been utilized for pesticides in plants,^{[8]} and certain authors maintain that pesticide risk and impact assessment models rely on and are sensitive to information describing dissipation from plants.^{[9]}
Look up halflife in Wiktionary, the free dictionary. 
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