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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/(2^{n}) 
.^ YouTube: HalfLife 2 Part 10: Welcome to Black Mesa (Time: 7:26) Head downriver. HalfLife 2 Walkthrough 14 January 2010 7:20 UTC www.mahalo.com [Source type: General]
^ YouTube: Half Life 2 Highway 17 Part 3 (Time: 9:48) Continue up the road. HalfLife 2 Walkthrough 14 January 2010 7:20 UTC www.mahalo.com [Source type: General]
^ YouTube: Half Life 2 Highway 17 Part 4 (Time: 9:58) Sandtraps . HalfLife 2 Walkthrough 14 January 2010 7:20 UTC www.mahalo.com [Source type: General]
The name originally
was used to describe a characteristic of unstable atoms (
radioactive
decay), but may apply to any quantity which follows a setrate
decay.
The original term, dating to 1907, was "halflife period", which
was later shortened to "halflife" sometime in the early 1950s.^{[1]}
.^ I am naturally a man who hates deception, and wishes above all things to lead a life with its windows open and shades up, but I have been forced into the very reverse. "Doc." Gordon 2 February 2010 14:49 UTC home.comcast.net [Source type: Original source]
.^ These take place immediately after the end of HalfLife 2. HalfLife 2 Walkthrough 14 January 2010 7:20 UTC www.mahalo.com [Source type: General]
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.
.^ Originally posted by misterdurp Originally posted by Gameloading Originally posted by misterdurp Originally posted by Gameloading Half Life 2 is one of the overrated games of all time. HL2  best game of the decade.  General Gaming  General Discussion  MMORPG.com Forums 14 January 2010 7:20 UTC www.mmorpg.com [Source type: General]
^ Originally posted by Gameloading Originally posted by misterdurp Originally posted by Gameloading Half Life 2 is one of the overrated games of all time. HL2  best game of the decade.  General Gaming  General Discussion  MMORPG.com Forums 14 January 2010 7:20 UTC www.mmorpg.com [Source type: General]
^ YouTube: Half Life 2 Highway 17 Part 4 (Time: 9:58) Sandtraps . HalfLife 2 Walkthrough 14 January 2010 7:20 UTC www.mahalo.com [Source type: General]
The table at right shows the reduction of a quantity in terms of
the number of halflives elapsed.
Probabilistic nature of
halflife
.^ Using a grenade in a game like Half Life 2 is such a chore. HL2  best game of the decade.  General Gaming  General Discussion  MMORPG.com Forums 14 January 2010 7:20 UTC www.mmorpg.com [Source type: General]
.^ There is a ramp just to the left of it. HalfLife 2 Walkthrough 14 January 2010 7:20 UTC www.mahalo.com [Source type: General]
^ When we look at the amount of impact a game like Halo had when compared to Half Life 2 both culturally and in the genre, its clear that Halo has done more for the genre than Half Life 2 did, not that I'm suggesting that Halo should be game of the decade, I just used it as an example because it also happens to be an FPS. If Half Life 2 is an old school and plays it safe, that's fine. HL2  best game of the decade.  General Gaming  General Discussion  MMORPG.com Forums 14 January 2010 7:20 UTC www.mmorpg.com [Source type: General]
^ No complaints there, but from a gameplay perspective, Half Life 2 did nothing that pushed the genre forward. HL2  best game of the decade.  General Gaming  General Discussion  MMORPG.com Forums 14 January 2010 7:20 UTC www.mmorpg.com [Source type: General]
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.
.^ YouTube: Half Life 2 Highway 17 Part 4 (Time: 9:58) Sandtraps . HalfLife 2 Walkthrough 14 January 2010 7:20 UTC www.mahalo.com [Source type: General]
^ YouTube: Half Life 2 A Red Letter Day (Time: 9:27) Follow Alyx into the lab. HalfLife 2 Walkthrough 14 January 2010 7:20 UTC www.mahalo.com [Source type: General]
^ YouTube: Half Life 2 Point Insertion (Time: 8:37) Move forward. HalfLife 2 Walkthrough 14 January 2010 7:20 UTC www.mahalo.com [Source type: General]
.^ Besides the firelight there was only one great bronze lamp to illuminate the room. "Doc." Gordon 2 February 2010 14:49 UTC home.comcast.net [Source type: Original source]
^ There is only one consolation which I have with regard to him; unless my diagnosis was entirely at fault, he would have had that attack of erysipelas anyway. "Doc." Gordon 2 February 2010 14:49 UTC home.comcast.net [Source type: Original source]
^ I dare say there was no danger this time, only he came up behind like a cat, and —” . "Doc." Gordon 2 February 2010 14:49 UTC home.comcast.net [Source type: Original source]
.^ HLstatsX  Realtime Player Statistics for HalfLife 1 and HalfLife 2! HLstatsX  Realtime Player Statistics for HalfLife 1 and HalfLife 2!  Global Ranking 14 January 2010 7:20 UTC www.hlstatsx.com [Source type: General]
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].
Formulae for
halflife in exponential decay
An exponential decay process can be described by any of the
following three equivalent formulae:
where

 N_{0} is the
initial quantity of the thing that will decay (this quantity may be
measured in grams, moles, number of atoms, etc.),
 N_{t} is
the quantity that still remains and has not yet decayed after a
time t,
 t_{1 / 2} is the
halflife of the decaying quantity,
 τ
is a positive number
called the mean lifetime of the decaying
quantity,
 λ is a
positive number called the decay constant of
the decaying quantity.
The three parameters t_{1 /
2}, τ, and λ are all
directly related in the following way:

Click "show" to see a detailed derivation of the relationship
between halflife, decay time, and decay constant. 
Start with the three equations
 N_{t} =
N_{0}e ^{− t /
τ}
 N_{t} =
N_{0}e ^{−
λt}
We want to find a relationship between 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 condition:
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 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
 N_{t} =
N_{0} at t=0 (as expected—this is
the definition of "initial quantity")

at t = t_{1 /
2} (as expected—this is the definition of
halflife)
 N_{t}
approaches zero when t approaches infinity (as
expected—the longer we wait, the less remains).
Decay by two or more
processes
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:
Examples

There is a halflife describing any exponentialdecay process.
For example:
 The current flowing through an RC circuit or RL circuit decays with a halflife of RCln(2) or ln(2)L / R,
respectively.
 In a firstorder chemical reaction, the halflife of
the reactant is ln(2) / λ, where λ is
the reaction rate constant.
 In radioactive decay, the halflife is
the length of time after which there is a 50% chance that an atom
will have undergone nuclear decay. It varies depending on
the atom type and isotope,
and is usually determined experimentally.
Halflife in
nonexponential decay
Main article:
Rate equation
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. A quantity of carbon14 will decay to half of its
original amount (on average) after 5730 years, regardless of how
big or small the original quantity was. After 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.
.^ You yourself know how many men I have seen here, and you know I never see men at Annie's.’ There is no one else. "Doc." Gordon 2 February 2010 14:49 UTC home.comcast.net [Source type: Original source]
^ He said to himself that he did not care if she were old enough to be his mother, his grandmother even, there was no one in the whole world like her. "Doc." Gordon 2 February 2010 14:49 UTC home.comcast.net [Source type: Original source]
^ He, in fact, began to consider that the day was waning, and what a wildgoose chase it would probably be for him to attempt to follow the man. "Doc." Gordon 2 February 2010 14:49 UTC home.comcast.net [Source type: Original source]
This is an example where the halflife reduces as time
goes on. (In other nonexponential decays, it can increase
instead.)
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.
See also
References
 ^
John Ayto, "20th Century Words" (1989), Cambridge University
Press.
External
links