A half-life is the time required for half of the unstable radioactive nuclei in a sample to undergo radioactive decay, or more generally the time required for a radioactive quantity governed by the same exponential decay law to fall to half its initial value. It is one of the fundamental quantities used to describe radioactive materials.
If a sample initially contains a large number of identical radioactive nuclei, approximately half will remain undecayed after one half-life, one quarter after two half-lives, one eighth after three half-lives, and so on. The process is statistical rather than deterministic for individual nuclei. It is not possible in ordinary radioactive decay to predict exactly when a particular unstable nucleus will decay, but the probability that it will decay during a given interval can be described precisely. Half-life is therefore a population level characteristic rather than a countdown clock assigned to individual atoms. It is commonly represented by the notation T half in scientific writing and is directly related to the decay constant that appears in the mathematical radioactive decay law.
Radioactive decay follows an exponential law when the decay probability remains constant over time. If N zero is the initial number of radioactive nuclei and N is the number remaining after time t, the relationship can be expressed as N equals N zero multiplied by e raised to the negative lambda t, where lambda is the decay constant. The half-life is related to the decay constant by T half equals the natural logarithm of two divided by lambda.
This means that a short half-life corresponds to a large decay constant and a high probability of decay per unit time, while a long half-life corresponds to a small decay constant. The activity of the sample, measured in becquerels, also decreases exponentially because activity is proportional to the number of undecayed nuclei. The half-life therefore determines the characteristic timescale over which both the number of radioactive nuclei and the activity decline. The exact behaviour can become more complicated when a radionuclide is produced continuously, when daughter products are themselves radioactive, or when environmental processes change the amount of material present.
Half-life does not mean that all radioactive material disappears after one half-life. After one half-life, approximately fifty percent of the original radioactive nuclei remain. After two half-lives, approximately twenty five percent remain. After ten half-lives, approximately one thousandth remains. Mathematically, the quantity approaches zero asymptotically rather than reaching exactly zero after a finite number of half-lives. Practical discussions may describe a radionuclide as effectively decayed after many half-lives when the remaining activity becomes sufficiently small for the purpose under consideration.
The relevant number of half-lives depends on the required radiation level, regulatory standard, detection capability and physical application. A short lived radionuclide can therefore become negligible relatively quickly, while a long lived radionuclide may remain detectable for very long periods. The phrase radioactive persistence must consequently be interpreted in relation to both half-life and the initial quantity of material.
Different radionuclides have enormously different half-lives. Some radioactive nuclear states have half-lives measured in fractions of a second, while others have half-lives extending over billions of years. Carbon 14 has a half-life of approximately 5730 years and is used in radiocarbon dating. Iodine 131 has a half-life of approximately eight days and is used in some medical applications where relatively rapid decay is desirable.
Cesium 137 has a half-life of approximately thirty years and is important in environmental and radiation protection contexts. Uranium 238 has a half-life of approximately 4.5 billion years, comparable with the age of the Earth. These differences arise from nuclear structure and the probability of particular decay modes. Half-life is therefore not a property that follows a simple relationship with atomic mass alone. Nuclear stability depends on factors including proton number, neutron number, nuclear energy levels, angular momentum and the available decay pathways.
Half-life is central to radiometric dating because the predictable decay of certain isotopes provides a natural clock. If a geological or archaeological material contains a radioactive parent isotope and its decay products remain appropriately related to the original system, measurements of parent and daughter quantities can provide information about elapsed time. Carbon 14 dating applies to relatively recent organic material because carbon 14 has a suitable half-life and is incorporated into living organisms through the carbon cycle.
Other isotope systems are used for much older rocks and minerals. Accurate dating requires assumptions about the initial conditions and subsequent isolation of the system. Researchers therefore consider contamination, loss or gain of parent or daughter isotopes and geological alteration. Half-life alone does not establish an age. It provides the decay timescale that becomes useful for dating when combined with measurements and a valid model of the material's history.
Half-life also matters greatly in medicine and radiation protection. Medical radionuclides are selected partly according to how rapidly they decay, because a diagnostic or therapeutic application may require activity to persist long enough to perform the procedure but decline sufficiently quickly afterwards. A patient receiving a radioactive substance may therefore experience decreasing activity over time due to both physical radioactive decay and biological elimination. The combination is sometimes described through an effective half-life.
In environmental protection, half-life helps estimate how the activity of a radioactive contaminant changes over time, but physical decay is only one process. Weathering, groundwater movement, biological uptake, erosion and human remediation can alter the amount of material present at a particular location. Consequently, the radiological behaviour of an environmental contaminant cannot always be inferred from its physical half-life alone.
The concept of half-life is also useful for understanding radioactive decay chains. A parent radionuclide may decay into a daughter radionuclide that is itself radioactive, creating a sequence of transformations. If the daughter has a much shorter half-life than the parent, its activity can approach a state related to the rate at which the parent produces it. In other circumstances, both parent and daughter activities change significantly over time.
Nuclear decay chains are important in uranium and thorium series, in which many radioactive isotopes occur between long lived parent nuclei and stable final products. The existence of decay chains means that a radioactive material can produce radiation from several different radionuclides rather than only from the original isotope. Radiation monitoring therefore often requires identifying multiple radionuclides and their characteristic emissions rather than relying on a single half-life measurement.
The term half-life can also be used outside radioactive decay for any process exhibiting an exponential reduction, including some biological, chemical and pharmacological processes, but the underlying meaning should not be confused across contexts. In nuclear physics, radioactive half-life is a property of a specific unstable nuclear state under ordinary conditions and is generally unaffected by temperature, pressure or chemical form, although specialised nuclear processes can have unusual environmental dependencies.
Electron capture can sometimes be influenced by the electron environment to a very small degree because the process involves orbital electrons, but ordinary radioactive decay is fundamentally governed by nuclear properties. Half-life therefore provides a powerful quantitative description of nuclear instability. It does not mean that individual atoms have a predetermined lifespan, does not directly measure radiation dose, and does not by itself indicate how hazardous a radionuclide is. Hazard depends additionally on activity, radiation type, energy, exposure pathway, chemical behaviour and biological effects.
