Half-life (symbol t1⁄2) 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 non-exponential decay. For example, the medical sciences refer to the biological half-life of drugs and other chemicals in the human body. The converse of half-life is doubling time.

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.[1] Rutherford applied the principle of a radioactive element's half-life to studies of age determination of rocks by measuring the decay period of radium to lead-206.

Half-life 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 half-lives elapsed.

Number of
0 11 100
1 12 50
2 14 25
3 18 12 .5
4 116 6 .25
5 132 3 .125
6 164 1 .563
7 1128 0 .781
... ... ...
n 1/2n 100/2n

Probabilistic nature

Simulation of many identical atoms undergoing radioactive decay, starting with either 4 atoms per box (left) or 400 (right). The number at the top is how many half-lives have elapsed. Note the consequence of the law of large numbers: with more atoms, the overall decay is more regular and more predictable.

A half-life usually describes the decay of discrete entities, such as radioactive atoms. 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". 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.

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". In other words, the probability of a radioactive atom decaying within its half-life is 50%.

For example, the image on the right is a simulation of many identical atoms undergoing radioactive decay. 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. 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.

There are various simple exercises that demonstrate probabilistic decay, for example involving flipping coins or running a statistical computer program.[2][3][4]

Formulas for half-life in exponential decay

An exponential decay can be described by any of the following three equivalent formulas:


  • N0 is the initial quantity of the substance 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,
  • t1⁄2 is the half-life 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 t1⁄2, τ, and λ are all directly related in the following way:

where ln(2) is the natural logarithm of 2 (approximately 0.693).

Decay by two or more processes

Some quantities decay by two exponential-decay processes simultaneously. In this case, the actual half-life T1⁄2 can be related to the half-lives t1 and t2 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.


Dice half-life decay
Half life demonstrated using dice in a classroom experiment

There is a half-life describing any exponential-decay process. For example:

  • 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. It varies depending on the atom type and isotope, and is usually determined experimentally. See List of nuclides.
  • 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. For this example the term half time tends to be used, rather than "half life", but they mean the same thing.
  • 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. In a first-order reaction the half-life of the reactant is ln(2)/λ, where λ is the reaction rate constant.

In non-exponential decay

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 decay process that is not even close to exponential, the half-life will change dramatically while the decay is happening. In this situation it is generally uncommon to talk about half-life in the first place, but sometimes people will describe the decay in terms of its "first half-life", "second half-life", etc., where the first half-life is defined as the time required for decay from the initial value to 50%, the second half-life is from 50% to 25%, and so on.[5]

In biology and pharmacology

A biological half-life or elimination half-life is the time it takes for a substance (drug, radioactive nuclide, or other) to lose one-half of its pharmacologic, physiologic, or radiological activity. In a medical context, the half-life may also describe the time that it takes for the concentration of a substance in blood plasma to reach one-half of its steady-state value (the "plasma half-life").

The relationship between the biological and plasma half-lives 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 so-called "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 half-life 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 half-life of caesium in human beings is between one and four months.

The concept of a half-life 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]

See also


  1. ^ John Ayto, 20th Century Words (1989), Cambridge University Press.
  2. ^ Chivers, Sidney (March 16, 2003). "Re: What happens durring half lifes [sic] when there is only one atom left?". MADSCI.org.
  3. ^ "Radioactive-Decay Model". Exploratorium.edu. Retrieved 2012-04-25.
  4. ^ Wallin, John (September 1996). "Assignment #2: Data, Simulations, and Analytic Science in Decay". Astro.GLU.edu. Archived from the original on 2011-09-29.CS1 maint: BOT: original-url status unknown (link)
  5. ^ Jonathan Crowe, Tony Bradshaw (2014). Chemistry for the Biosciences: The Essential Concepts. p. 568. ISBN 9780199662883.CS1 maint: Uses authors parameter (link)
  6. ^ Lin VW; Cardenas DD (2003). Spinal cord medicine. Demos Medical Publishing, LLC. p. 251. ISBN 978-1-888799-61-3.
  7. ^ Pang, Xiao-Feng (2014). Water: Molecular Structure and Properties. New Jersey: World Scientific. p. 451. ISBN 9789814440424.
  8. ^ Australian Pesticides and Veterinary Medicines Authority (31 March 2015). "Tebufenozide in the product Mimic 700 WP Insecticide, Mimic 240 SC Insecticide". Australian Government. Retrieved 30 April 2018.
  9. ^ Fantke, Peter; Gillespie, Brenda W.; Juraske, Ronnie; Jolliet, Olivier (11 July 2014). "Estimating Half-Lives for Pesticide Dissipation from Plants". Environmental Science & Technology. 48 (15): 8588–8602. Bibcode:2014EnST...48.8588F. doi:10.1021/es500434p. PMID 24968074.

External links


An analgesic or painkiller is any member of the group of drugs used to achieve analgesia, relief from pain.

Analgesic drugs act in various ways on the peripheral and central nervous systems. They are distinct from anesthetics, which temporarily affect, and in some instances completely eliminate, sensation. Analgesics include paracetamol (known in North America as acetaminophen or simply APAP), the nonsteroidal anti-inflammatory drugs (NSAIDs) such as the salicylates, and opioid drugs such as morphine and oxycodone.

When choosing analgesics, the severity and response to other medication determines the choice of agent; the World Health Organization (WHO) pain ladder specifies mild analgesics as its first step.

Analgesic choice is also determined by the type of pain: For neuropathic pain, traditional analgesics are less effective, and there is often benefit from classes of drugs that are not normally considered analgesics, such as tricyclic antidepressants and anticonvulsants.

Biological half-life

The biological half-life of a biological substance is the time it takes for half to be removed by biological processes when the rate of removal is roughly exponential. It is often denoted by the abbreviation . Examples include metabolites, drugs, and signalling molecules. Typically, this refers to the body's cleansing through the function of kidneys and liver in addition to excretion functions to eliminate a substance from the body. In a medical context, half-life may also describe the time it takes for the blood plasma concentration of a substance to halve (plasma half-life) its steady-state. The relationship between the biological and plasma half-lives of a substance can be complex depending on the substance in question, due to factors including accumulation in tissues (protein binding), active metabolites, and receptor interactions.

Combine (Half-Life)

The Combine is a multidimensional empire which serves as the primary antagonistic force in the 2004 video game Half-Life 2, and the subsequent episodes developed by Valve Corporation. The Combine consist of alien, synthetic, and human elements, and dominate Earth. They are encountered throughout Half-Life 2 and its episodic expansions as hostile non-player characters as the player progresses through the games in an effort to overthrow the Combine occupation of Earth.

The Combine are frequently shown as harsh rulers over the citizens of Earth, suppressing dissent with brutality, policing using violence and using invasive surgery to transform humans into either soldiers or slaves. Throughout the games, the player primarily battles transformed humans as well as synthetic and mechanical enemies that are the product of Combine technology. The atmosphere generated by the dystopian Combine state has been praised by reviewers, although the artificial intelligence of the transhuman Combine characters was thought to be inferior to that of other characters in Half-Life 2. In addition to their role within the Half-Life series, the Combine have been adapted for machinima productions and one Combine character type has been made into plush toys by Valve.


Counter-Strike (CS) is a series of multiplayer first-person shooter video games, in which teams of terrorists battle to perpetrate an act of terror (bombing, hostage-taking, assassination) and counter-terrorists try to prevent it (bomb defusal, hostage rescue). The series began on Windows in 1999 with the first game, Counter-Strike. It was initially released as a modification ("mod") for Half-Life and designed by Minh "Gooseman" Le and Jess "Cliffe" Cliffe before the rights to the game's intellectual property were acquired by Valve Corporation, the developers of Half-Life.

That original game was followed by Counter-Strike: Condition Zero, developed by Turtle Rock Studios and released in 2004. In November of that year, Counter-Strike: Source was released by Valve. Released eight months after Condition Zero, Source was a remake of the original Counter-Strike and the first in the series to run on Valve's newly created Source engine. The fourth game in the main series, Counter-Strike: Global Offensive, was released by Valve in 2012 for Windows, OS X, Xbox 360, and PlayStation 3. Hidden Path Entertainment, who also worked on Counter-Strike: Source post-release, helped to develop the game alongside Valve.There have been several community-made spin-off titles created over the years. These include the Online series, Neo, and Nexon: Zombies.


Einsteinium is a synthetic element with symbol Es and atomic number 99. A member of the actinide series, it is the seventh transuranic element.

Einsteinium was discovered as a component of the debris of the first hydrogen bomb explosion in 1952, and named after Albert Einstein. Its most common isotope einsteinium-253 (half-life 20.47 days) is produced artificially from decay of californium-253 in a few dedicated high-power nuclear reactors with a total yield on the order of one milligram per year. The reactor synthesis is followed by a complex process of separating einsteinium-253 from other actinides and products of their decay. Other isotopes are synthesized in various laboratories, but at much smaller amounts, by bombarding heavy actinide elements with light ions. Owing to the small amounts of produced einsteinium and the short half-life of its most easily produced isotope, there are currently almost no practical applications for it outside basic scientific research. In particular, einsteinium was used to synthesize, for the first time, 17 atoms of the new element mendelevium in 1955.

Einsteinium is a soft, silvery, paramagnetic metal. Its chemistry is typical of the late actinides, with a preponderance of the +3 oxidation state; the +2 oxidation state is also accessible, especially in solids. The high radioactivity of einsteinium-253 produces a visible glow and rapidly damages its crystalline metal lattice, with released heat of about 1000 watts per gram. Difficulty in studying its properties is due to einsteinium-253's decay to berkelium-249 and then californium-249 at a rate of about 3% per day. The isotope of einsteinium with the longest half-life, einsteinium-252 (half-life 471.7 days) would be more suitable for investigation of physical properties, but it has proven far more difficult to produce and is available only in minute quantities, and not in bulk. Einsteinium is the element with the highest atomic number which has been observed in macroscopic quantities in its pure form, and this was the common short-lived isotope einsteinium-253.Like all synthetic transuranic elements, isotopes of einsteinium are very radioactive and are considered highly dangerous to health on ingestion.

Exponential decay

A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where N is the quantity and λ (lambda) is a positive rate called the exponential decay constant:

The solution to this equation (see derivation below) is:

where N(t) is the quantity at time t, and N0 = N(0) is the initial quantity, i.e. the quantity at time t = 0.

Half-Life (series)

Half-Life (stylized HλLF-LIFE) is a series of first-person shooter games developed and published by Valve. The major installments feature protagonist Gordon Freeman, a physicist who battles an alien invasion. Half-Life (1998) and Half-Life 2 (2004) are full-length games, while Half-Life 2: Episode One (2006) and Half-Life 2: Episode Two (2007) are shorter, episodic games. A third episode, Half-Life 2: Episode Three, was scheduled for release by Christmas 2007, but is now described as vaporware.

The first game in the Portal series, set in the same universe as Half-Life, was released in 2007.

Half-Life (video game)

Half-Life (stylized as HλLF-LIFE) is a first-person shooter video game developed by Valve and published by Sierra Studios for Microsoft Windows in 1998. It was Valve's debut product and the first in the Half-Life series. Players assume the role of Dr. Gordon Freeman, who must fight his way out of the Black Mesa research facility after an experiment goes wrong, fighting enemies and solving puzzles.

Unlike many other games at the time, the player has almost complete uninterrupted control of Freeman, and the story is told mostly through scripted sequences seen through his eyes. Valve co-founder Gabe Newell said the team aimed to create an immersive world rather than a "shooting gallery". The game's engine, GoldSrc, is a heavily modified version of the Quake engine licensed from id Software.

Half-Life received acclaim for its graphics, realistic gameplay, and seamless narrative. It won over fifty PC "Game of the Year" awards and is considered one of the greatest video games of all time. It influenced first-person shooters for years after its release.

Half-Life had sold eight million copies by November 16, 2004, and 9.3 million copies by December 2008. It was ported to the PlayStation 2 in 2001, and OS X and Linux in 2013. It was followed in 2004 by Half-Life 2.

Half-Life 2

Half-Life 2 (stylized as HλLF-LIFE2) is a first-person shooter video game developed and published by Valve Corporation. It is the sequel to 1998's Half-Life and was released in November 2004 following a five-year $40 million development. During development, a substantial part of the project was leaked and distributed on the Internet. The game was developed alongside Valve's Steam software and the Source engine.

Taking place some years after the events of Half-Life, protagonist Gordon Freeman is awakened by the enigmatic G-Man to find the world has been taken over by the alien Combine. Joined by allies including resistance fighter Alyx Vance, Gordon searches for a way to free humanity using a variety of weapons, including the object-manipulating Gravity Gun.

Half-Life 2 received critical acclaim. It was praised for its advanced physics, animation, sound, AI, graphics, and narrative. The game won 39 "Game of the Year" awards and the title of "Game of the Decade" at the 2012 Spike Video Game Awards, and is widely considered to be one of the greatest games of all time. Over 6.5 million copies of Half-Life 2 were sold at retail by December 2008 (not including Steam sales). By February 2011, Half-Life 2 had sold over 12 million copies. It was followed by the sequels Episode One (2006) and Episode Two (2007).

Impact factor

The impact factor (IF) or journal impact factor (JIF) of an academic journal is a measure reflecting the yearly average number of citations to recent articles published in that journal. It is frequently used as a proxy for the relative importance of a journal within its field; journals with higher impact factors are often deemed to be more important than those with lower ones. The impact factor was devised by Eugene Garfield, the founder of the Institute for Scientific Information. Impact factors are calculated yearly starting from 1975 for journals listed in the Journal Citation Reports.

Isotopes of hydrogen

Hydrogen (1H) has three naturally occurring isotopes, sometimes denoted 1H, 2H, and 3H. The first two of these are stable, while 3H has a half-life of 12.32 years. All heavier isotopes are synthetic and have a half-life less than one zeptosecond (10−21 second). Of these, 5H is the most stable, and 7H is the least.Hydrogen is the only element whose isotopes have different names that are in common use today. The 2H (or hydrogen-2) isotope is usually called deuterium, while the 3H (or hydrogen-3) isotope is usually called tritium. The symbols D and T are sometimes used for deuterium and tritium. The IUPAC accepts the D and T symbols, but recommends instead using standard isotopic symbols (2H and 3H) to avoid confusion in the alphabetic sorting of chemical formulas. The ordinary isotope of hydrogen, with no neutrons, is sometimes called "protium". (During the early study of radioactivity, some other heavy radioactive isotopes were given names, but such names are rarely used today.)

Radioactive decay

Radioactive decay (also known as nuclear decay, radioactivity or nuclear radiation) is the process by which an unstable atomic nucleus loses energy (in terms of mass in its rest frame) by emitting radiation, such as an alpha particle, beta particle with neutrino or only a neutrino in the case of electron capture, or a gamma ray or electron in the case of internal conversion. A material containing such unstable nuclei is considered radioactive. Certain highly excited short-lived nuclear states can decay through neutron emission, or more rarely, proton emission.

Radioactive decay is a stochastic (i.e. random) process at the level of single atoms. According to quantum theory, it is impossible to predict when a particular atom will decay, regardless of how long the atom has existed. However, for a collection of atoms, the collection's expected decay rate is characterized in terms of their measured decay constants or half-lives. This is the basis of radiometric dating. The half-lives of radioactive atoms have no known upper limit, spanning a time range of over 55 orders of magnitude, from nearly instantaneous to far longer than the age of the universe.

A radioactive nucleus with zero spin can have no defined orientation, and hence emits the total momentum of its decay products isotropically (all directions and without bias). If there are multiple particles produced during a single decay, as in beta decay, their relative angular distribution, or spin directions may not be isotropic. Decay products from a nucleus with spin may be distributed non-isotropically with respect to that spin direction, either because of an external influence such as an electromagnetic field, or because the nucleus was produced in a dynamic process that constrained the direction of its spin. Such a parent process could be a previous decay, or a nuclear reaction.The decaying nucleus is called the parent radionuclide (or parent radioisotope), and the process produces at least one daughter nuclide. Except for gamma decay or internal conversion from a nuclear excited state, the decay is a nuclear transmutation resulting in a daughter containing a different number of protons or neutrons (or both). When the number of protons changes, an atom of a different chemical element is created.

The first decay processes to be discovered were alpha decay, beta decay, and gamma decay. Alpha decay occurs when the nucleus ejects an alpha particle (helium nucleus). This is the most common process of emitting nucleons, but highly excited nuclei can eject single nucleons, or in the case of cluster decay, specific light nuclei of other elements. Beta decay occurs in two ways:

(i) beta-minus decay, when the nucleus emits an electron and an antineutrino in a process that changes a neutron to a proton, or

(ii) beta-plus decay, when the nucleus emits a positron and a neutrino in a process that changes a proton to a neutron.

Highly excited neutron-rich nuclei, formed as the product of other types of decay, occasionally lose energy by way of neutron emission, resulting in a change from one isotope to another of the same element. The nucleus may capture an orbiting electron, causing a proton to convert into a neutron in a process called electron capture. All of these processes result in a well-defined nuclear transmutation.

By contrast, there are radioactive decay processes that do not result in a nuclear transmutation. The energy of an excited nucleus may be emitted as a gamma ray in a process called gamma decay, or that energy may be lost when the nucleus interacts with an orbital electron causing its ejection from the atom, in a process called internal conversion.

Another type of radioactive decay results in products that vary, appearing as two or more "fragments" of the original nucleus with a range of possible masses. This decay, called spontaneous fission, happens when a large unstable nucleus spontaneously splits into two (or occasionally three) smaller daughter nuclei, and generally leads to the emission of gamma rays, neutrons, or other particles from those products.

For a summary table showing the number of stable and radioactive nuclides in each category, see radionuclide. There are 28 naturally occurring chemical elements on Earth that are radioactive, consisting of 33 radionuclides (5 elements have 2 different radionuclides) that date before the time of formation of the solar system. These 33 are known as primordial nuclides. Well-known examples are uranium and thorium, but also included are naturally occurring long-lived radioisotopes, such as potassium-40. Another 50 or so shorter-lived radionuclides, such as radium and radon, found on Earth, are the products of decay chains that began with the primordial nuclides, or are the product of ongoing cosmogenic processes, such as the production of carbon-14 from nitrogen-14 in the atmosphere by cosmic rays. Radionuclides may also be produced artificially in particle accelerators or nuclear reactors, resulting in 650 of these with half-lives of over an hour, and several thousand more with even shorter half-lives. (See List of nuclides for a list of these sorted by half-life.)

Source (game engine)

Source is a 3D video game engine developed by Valve Corporation. It debuted as the successor to GoldSrc with Counter-Strike: Source in June 2004, followed shortly by Half-Life 2 in November, and has been in active development since. Source does not have a concise version numbering scheme; instead, it is designed in constant incremental updates. The successor, Source 2, was officially announced in March 2015, with the first game to use it being Dota 2, which was ported over from Source later that year.

The Orange Box

The Orange Box is a video game compilation containing five games developed by Valve Corporation. Two of the games included, Half-Life 2 and its first stand-alone expansion, Episode One, had previously been released as separate products. Three new games were also included in the compilation: the second stand-alone expansion, Half-Life 2: Episode Two, the puzzle game Portal, and Team Fortress 2, the multiplayer game sequel to Team Fortress Classic. Valve also released a soundtrack containing music from the games within the compilation. A separate product entitled The Black Box was planned, which would have included only the new games, but was later cancelled.

The Orange Box was first released for Microsoft Windows and Xbox 360 on October 10, 2007, while the PlayStation 3 version, developed by EA UK was released in December 11, 2007. A digital Orange Box pack, containing the five games, was released on May 27, 2010 for OS X following the release of Steam for the platform, while a similar version for Linux followed after the Steam's clients release for Linux in early 2013.

The Orange Box received critical acclaim, with Portal being recognized as a surprise favorite of the package. The PlayStation 3 version of The Orange Box was noted for several technical shortcomings that were not present in the other versions, only a few of which were fixed through a single patch.

Valve Corporation

Valve Corporation is an American video game developer, publisher and digital distribution company headquartered in Bellevue, Washington. It is the developer of the software distribution platform Steam and the Half-Life, Counter-Strike, Portal, Day of Defeat, Team Fortress, Left 4 Dead, and Dota 2 games.

Valve was founded in 1996 by former Microsoft employees Gabe Newell and Mike Harrington. Their debut product, the PC first-person shooter Half-Life, was released in 1998 to critical acclaim and commercial success, after which Harrington left the company. In 2003, Valve launched Steam, which accounted for around half of digital PC game sales by 2011. By 2012, Valve employed around 250 people and was reportedly worth over US$3 billion, making it the most profitable company per employee in the United States. In 2015, Valve entered the game hardware market with the Steam Machine, a line of third-party built gaming PCs running Valve's SteamOS operating system.

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