Radioactive half-life, symbolised as , is a fundamental concept in nuclear physics and radiation safety. It defines the time required for half of the radioactive atoms (nuclei) in a given sample to undergo radioactive decay. This process is entirely statistical; while it is impossible to predict when any single unstable nucleus will decay, for a sufficiently large number of identical nuclei, the decay rate is highly predictable.
Radioactive decay is a spontaneous nuclear process where an unstable atomic nucleus transforms into a more stable form, often emitting radiation in the process. Each specific radionuclide possesses a unique and characteristic half-life, which can range from fractions of a microsecond to billions of years. This decay follows an exponential pattern, meaning that the rate of decay is directly proportional to the number of undecayed nuclei present at any given time.
The mathematical relationship governing radioactive decay and half-life is crucial for its understanding. The number of radioactive nuclei remaining, (N(t)), after a time (t) can be expressed as:
where (N_0) is the initial number of nuclei, and is the decay constant, a unique value for each radionuclide. The decay constant characterises the probability of decay per unit time for a single nucleus.
The half-life is inversely related to the decay constant by the equation:
This relationship highlights that isotopes with a larger decay constant have a shorter half-life, decaying more rapidly. After one half-life, 50% of the original nuclei remain; after two half-lives, 25% remain; and so on, continuing to halve with each subsequent half-life period. The activity of a sample also halves over the same period.
It should be noted that this applies for very large collections of isotopes decaying in a material at the same time. When the number of decays per second is limited, and small variances do not average out consider using the Poisson distribution to determine how many events per second (or minute or hour) you will detect.
Understanding half-life is paramount across numerous scientific and industrial applications:
It is important to note that the half-life of a given radionuclide is an intrinsic nuclear property and is unaffected by external physical or chemical conditions such as temperature, pressure, or chemical bonding. This unique characteristic makes half-life a highly reliable and consistent parameter for characterising radioactive materials.