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Half-life (symbol t) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential (or, rarely, 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 (in exponential growth) 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 in studies of age determination of rocks by measuring the decay period of radium to lead-206.

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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.

A half-life often 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%.[2]

For example, the accompanying image 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.

In second order reactions, the rate of reaction is proportional to the square of the concentration. By integrating this rate, it can be shown that the concentration [A] of the reactant decreases following this formula:

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.[7]

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").

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,[9] though this can be altered by behavior and 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,[10] and certain authors maintain that pesticide risk and impact assessment models rely on and are sensitive to information describing dissipation from plants.[11]

In epidemiology, the concept of half-life can refer to the length of time for the number of incident cases in a disease outbreak to drop by half, particularly if the dynamics of the outbreak can be modeled exponentially.[12][13]

Half-Life is a 1998 first-person shooter game developed by Valve Corporation and published by Sierra Studios for Windows. It was Valve's debut product and the first game in the Half-Life series. The player assumes the role of Gordon Freeman, a scientist who must escape from the Black Mesa Research Facility after it is invaded by aliens following a disastrous scientific experiment. The gameplay consists of combat, exploration and puzzles.

Valve was disappointed with the lack of innovation in the FPS genre, and aimed to create an immersive world rather than a "shooting gallery". Unlike other games at the time, the player has almost uninterrupted control of the player character; the story is mostly experienced through scripted sequences rather than cutscenes. Valve developed the game using GoldSrc, a heavily-modified version of the Quake engine, licensed from id Software. The science fiction novelist Marc Laidlaw was hired to craft the plot and assist with design.

Half-Life is a first-person shooter (FPS) that requires the player to perform combat tasks and puzzle solving to advance through the game. Unlike most first-person shooters at the time, which relied on cut-scene intermissions to detail their plotlines, Half-Life's story is told mostly using scripted sequences (bar one short cutscene), keeping the player in control of the first-person viewpoint. In line with this, the player rarely loses the ability to control the player character, Gordon Freeman, who never speaks and is never actually seen in the game; the player sees "through his eyes" for the entire length of the game. Half-Life has no levels; it instead divides the game into chapters, whose titles briefly appear on screen as the player progresses through the game. With the exception of short loading pauses, progression throughout the game is continuous, with each map directly connecting to the next, with the exception of levels involving teleportation.[4]

The game regularly integrates puzzles, such as navigating a maze of conveyor belts or using nearby boxes to build a small staircase to the next area the player must travel to. Some puzzles involve using the environment to kill an enemy, like turning a valve to spray hot steam at their enemies. There are few bosses in the conventional sense, where the player defeats a superior opponent by direct confrontation. Instead, such organisms occasionally define chapters, and the player is generally expected to use the terrain, rather than firepower, to kill the boss. Late in the game, the player receives a "long jump module" for the HEV suit, which allows the player to increase the horizontal distance and speed of jumps by crouching before jumping. The player must rely on this ability to navigate various platformer-style jumping puzzles in Xen toward the end of the game.[4]

The player battles alone for the majority of the game, but is occasionally assisted by non-player characters; specifically security guards and scientists who help the player. The guards will fight alongside the player, and both guards and scientists can assist in reaching new areas and pass on relevant plot information. An array of alien enemies populate the game, including headcrabs, bullsquids, vortigaunts, and headcrab zombies. The player also faces human opponents in the Hazardous Environment Combat Unit (a fictional special forces unit of the United States Marine Corps), and Black Ops assassins.

Half-Life includes online multiplayer support for both individual and team-based deathmatch modes.[5] It was one of the first mainstream games to use the WASD keys as the default control scheme.[6]

Theoretical physicist Gordon Freeman arrives late for work at the Black Mesa Research Facility. As part of a scientific experiment, he pushes an unusual crystal of alien origin into a machine known as the anti-mass spectrometer. The spectrometer explodes, creating a "resonance cascade" that severely damages the facility and opens a portal to an alien dimension, Xen. The surviving scientists urge Gordon to travel to the surface, where he defends himself against hostile Xen creatures and the Hazardous Environmental Combat Unit (HECU), a special forces unit of the United States Marine Corps dispatched to eliminate the Xen creatures as well as all surviving Black Mesa personnel to cover up the incident.

Gordon learns that scientists from the Lambda Complex may have found a way to close the portal. Gordon travels to the other end of the facility to assist them. Along the way, he activates a rocket engine test facility to destroy a giant tentacled creature and uses a disused railway system to reach and launch a satellite rocket, with the purpose of attempting to close the portal via satellite, which ultimately fails. Freeman is captured by HECU marines and left to be killed in a garbage compactor, but escapes and makes his way to an older part of the facility. There, he discovers Xen specimens collected before the incident.

Overwhelmed by the alien forces, the HECU pulls out of Black Mesa and begin airstrikes. Scaling cliffs, navigating destroyed buildings, and traversing through underground water channels, Gordon arrives at the Lambda Complex, where scientists learn the portal is being forced open on the other side by a large entity. They have developed teleportation technology that allows Gordon to travel to Xen, where he is tasked with stopping the entity.

In Xen, Gordon encounters the remains of researchers who ventured there before him, and Gordon defeats the Gonarch, a large egg-laying headcrab. At an alien factory manufacturing alien soldiers, he enters a portal that sends him to a vast cave. There, Gordon confronts the Nihilanth, the entity maintaining the rift, and destroys it. Gordon is summoned by the mysterious G-Man, who has been watching his progress in Black Mesa. The G-Man commends him and explains that his "employers" wish to employ Gordon. If Gordon refuses, he is teleported to an area full of alien soldiers to be killed immediately. If Gordon accepts, the G-Man congratulates him and places him into stasis to await his next assignment.