Half time is the time taken by a quantity to reach one half of its extremal value, where the rate of change is proportional to the difference between the present value and the extremal value (i.e. in

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 is the quantity and (lambda Lambda (; uppe ...

processes). It is synonymous with

half-life Half-life is a mathematical and scientific description of exponential or gradual decay. Half-life, half life or halflife may also refer to: Film * Half-Life (film), ''Half-Life'' (film), a 2008 independent film by Jennifer Phang * ''Half Life: ...

, but used in slightly different contexts. The diagram shows the increase in the quantity (red) in response to a step-change in the motive force that changes it (blue). The time-axis is in multiples of the half time. It can be seen that the quantity increases to one-half of its final value after one half time, to three-quarters after two half times, to seven-eighths after three half times, and so on. The relationship between the quantity (''Q'') and time (''t'') is described by the mathematical formula: :

Q(t) = Q_\mathrm(1 - e^)

where ''Q''_f is the extremal value and ''λ'' is a constant, approximately equal to 0.69 divided by the half time – more precisely: ln (2) / (half time). Where the quantity decreases in response to a step-decrease in the motive force that changes it, the curve is mirrored in the time-axis and may be referred to as

. The concept of half time is used in

diving Diving most often refers to: * Diving (sport), the sport of jumping into deep water * Underwater diving, human activity underwater for recreational or occupational purposes Diving or Dive may also refer to: Sports * Dive (American football), ...

physiology where body tissues take up and release

inert gases An inert gas is a gas that does not readily undergo chemical reactions with other chemical substances and therefore does not readily form chemical compounds. Though inert gases have a variety of applications, they are generally used to prevent u ...

(usually

nitrogen Nitrogen is a chemical element; it has Symbol (chemistry), symbol N and atomic number 7. Nitrogen is a Nonmetal (chemistry), nonmetal and the lightest member of pnictogen, group 15 of the periodic table, often called the Pnictogen, pnictogens. ...

) following changes in depth. Different tissue types have different half times for a given inert gas, and modelling the uptake and release of gases by the tissues is important to avoid

decompression sickness Decompression sickness (DCS; also called divers' disease, the bends, aerobullosis, and caisson disease) is a medical condition caused by dissolved gases emerging from Solution (chemistry), solution as bubbles inside the body tissues during D ...

Examples

In electronics, when a

capacitor In electrical engineering, a capacitor is a device that stores electrical energy by accumulating electric charges on two closely spaced surfaces that are insulated from each other. The capacitor was originally known as the condenser, a term st ...

is charged or discharged via a

resistor A resistor is a passive two-terminal electronic component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active e ...

, the voltage on the capacitor follows the above formula, with the half time approximately equal to 0.69 times the

time constant In physics and engineering, the time constant, usually denoted by the Greek language, Greek letter (tau), is the parameter characterizing the response to a step input of a first-order, LTI system theory, linear time-invariant (LTI) system.Concre ...

, which is equal to the product of the resistance and the capacitance. *The first models of nitrogen uptake and release in the body of a diver used five parallel compartments with half times from 5 minutes to 75 minutes. Later models refined this by considering more compartments and a wider range of half times. The U.S. Navy tables used six compartments with half times of 5, 10, 20, 40, 80 and 120 minutes. The Bühlmann tables use twelve of the sixteen compartments in the ZH-L₁₆ algorithm, which uses half times from 4 to 635 minutes.

References

{{Reflist Temporal exponentials

Examples

See also

References