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Exponential decay. A quantity undergoing exponential decay. Larger decay constants make the quantity vanish much more rapidly. This plot shows decay for decay constant ( λ) of 25, 5, 1, 1/5, and 1/25 for x from 0 to 5. A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.
Rates. The decay rate, or activity, of a radioactive substance is characterized by the following time-independent parameters: The half-life, t 1/2, is the time taken for the activity of a given amount of a radioactive substance to decay to half of its initial value.
The lifetime of a particle is given by the inverse of its decay rate, , the probability per unit time that the particle will decay. For a particle of a mass M and four-momentum P decaying into particles with momenta p i {\displaystyle p_{i}} , the differential decay rate is given by the general formula (expressing Fermi's golden rule )
Exponential growth. Exponential growth is a process that increases quantity over time at an ever-increasing rate. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a quantity undergoing exponential growth is an exponential ...
Spontaneous emission is the process in which a quantum mechanical system (such as a molecule, an atom or a subatomic particle) transits from an excited energy state to a lower energy state (e.g., its ground state) and emits a quantized amount of energy in the form of a photon. Spontaneous emission is ultimately responsible for most of the light ...
Half-life (symbol t½) 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 ...
Radiometric dating. Radiometric dating, radioactive dating or radioisotope dating is a technique which is used to date materials such as rocks or carbon, in which trace radioactive impurities were selectively incorporated when they were formed. The method compares the abundance of a naturally occurring radioactive isotope within the material to ...
Orbital decay is a gradual decrease of the distance between ... Having an equation for the rate of change of orbital energy with respect to both radial distance and ...