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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  1/2^{n}  100(1/2^{n}) 
The halflife of a quantity whose value decreases with time is the interval required for the quantity to decay to half of its initial value. The concept originated in describing how long it takes atoms to undergo radioactive decay but also applies in a wide variety of other situations.
The term "halflife" dates to 1907. The original term was "halflife period", but that was shortened to "halflife" starting in the early 1950s.^{[1]}
Halflives are very often used to describe quantities undergoing exponential decay—for example radioactive decay—where the halflife is constant over the whole life of the decay, and is a characteristic unit (a natural unit of scale) for the exponential decay equation. However, a halflife can also be defined for nonexponential decay processes, although in these cases the halflife varies throughout the decay process. For a general introduction and description of exponential decay, see the article exponential decay. For a general introduction and description of nonexponential decay, see the article rate law.
The converse for exponential growth is the doubling time.
The table at right shows the reduction of the quantity in terms of the number of halflives elapsed.
Contents 
A halflife often describes the decay of discrete entities, such as radioactive atoms. In that case, it does not work to use the definition "halflife is the time required for exactly half of the entities to decay". For example, if there is just one radioactive atom with a halflife of 1 second, there will not be "half of an atom" left after 1 second. There will be either zero atoms left or one atom left, depending on whether or not the atom happens to decay.
Instead, the halflife is defined in terms of probability. It is the time when the expected value of the number of entities that have decayed is equal to half the original number. For example, one can start with a single radioactive atom, wait its halflife, and measure whether or not it decays in that period of time. Perhaps it will and perhaps it will not. But if this experiment is repeated again and again, it will be seen that it decays within the half life 50% of the time.
In some experiments (such as the synthesis of a superheavy element), there is in fact only one radioactive atom produced at a time, with its lifetime individually measured. In this case, statistical analysis is required to infer the halflife. In other cases, a very large number of identical radioactive atoms decay in the timerange measured. In this case, the central limit theorem ensures that the number of atoms that actually decay is essentially equal to the number of atoms that are expected to decay. In other words, with a large enough number of decaying atoms, the probabilistic aspects of the process can be ignored.
There are various simple exercises that demonstrate probabilistic decay, for example involving flipping coins or running a computer program. See the following websites: [1], [2], [3].
An exponential decay process can be described by any of the following three equivalent formulae:
where
The three parameters $t\_\{1/2\}$, $\backslash tau$, 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 a relationship between $t\_\{1/2\}$, $\backslash tau$, and λ, such that these three equations describe exactly the same exponential decay process. Comparing the equations, we find the following condition:
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 $\backslash ln\backslash left(\backslash frac\; \{1\}\{2\}\backslash right)=\backslash ln\; 2$, the eventual 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 formulae, see Decay by two or more processes.
There is a halflife describing any exponentialdecay process. For example:
Many quantities decay in a way not described by exponential decay—for example, the evaporation of water from a puddle, or (often) the chemical reaction of a molecule. In this case, the halflife is defined the same way as before: The time elapsed before half of the original quantity has decayed. However, unlike in an exponential decay, the halflife depends on the initial quantity, and changes over time as the quantity decays.
As an example, the radioactive decay of carbon14 is exponential with a halflife of 5730 years. If you have a quantity of carbon14, half of it (on average) will have decayed after 5730 years, regardless of how big or small the original quantity was. If you wait another 5730 years, onequarter of the original will remain. On the other hand, the time it will take a puddle to halfevaporate depends on how deep the puddle is. Perhaps a puddle of a certain size will evaporate down to half its original volume in one day. But if you wait a second day, there is no reason to expect that precisely onequarter of the puddle will remain; in fact, it will probably be much less than that. This is an example where the halflife reduces as time goes on. (In other nonexponential decays, it can increase instead.)
For specific, quantitative examples of halflives in nonexponential decays, see the article Rate equation.
A biological halflife is also a type of halflife associated with a nonexponential decay, namely the decay of the activity of a drug or other substance after it is introduced into the body.
The decay of a mixture of two or more materials that each have different halflives is not a simple exponential, as each material decays at a rate independent of the other. Mathematically, the sum of two exponential functions is not a single exponential function, A common example of such a situation is the waste of nuclear power stations, which is a mix of substances with vastly different halflives. Consider a sample containing a rapidly decaying element A, with a halflife of 1 second, and of slowly decaying element B, with a halflife of one year. After a few seconds, almost all atoms of element A have decayed after repeated halving of the initial total number of atoms but very few atoms of element B will have decayed yet as not even one halflife has elapsed. Thus, the mixture taken as a whole does not decay by halves.
Look up halflife in Wiktionary, the free dictionary. 
Contents 
HalfLife  

Developer(s)  Valve Corporation 
Publisher(s)  
Engine  GoldSrc 
Release date(s) 

Genre(s)  FPS 
System(s)  Windows, PlayStation 2, Steam 
Players  132 
Rating(s)  
System requirements (help) 

Expansion pack(s)  HalfLife: Opposing Force HalfLife: Blue Shift HalfLife: Decay 
Followed by  HalfLife 2 
Series  HalfLife 
Alternate box artwork.

Inside cover of above box.

Artwork for the game.

The iconic opening scene of the game.

editHalfLife series
Portal: Shooters  HalfLife at Combine OverWiki 

HalfLife  
Developer(s)  Valve Software 
Publisher(s)  Sierra Entertainment 
Engine  HalfLife engine 
Release date  November, 1998 (NA) 
Genre  FPS 
Mode(s)  Single player, 132 Players Online 
Age rating(s)  ESRB: M 
Platform(s)  PC, Playstation 2 
Media  CD(PC) DVD(PS2) 
Credits  Soundtrack  Codes  Walkthrough 
Contents 
HalfLife series 

HalfLife  Opposing Force  Blue Shift  Decay HalfLife 2  Deathmatch  The Lost Coast HalfLife 2: Episode One  Episode Two  Episode Three 
Compilations 
The Orange Box 
Related Games 
Portal  Team Fortress Classic  Team Fortress 2 
Miscellaneous 
HalfLife Fact File 
Half life can mean different things:
Here are sentences from other pages on HalfLife 2, which are similar to those in the above article.
