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 N is the quantity and λ (lambda) is a positive rate called the exponential decay constant, disintegration constant, rate constant, or transformation constant:
The solution to this equation (see derivation below) is:
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Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is considered radioactive. Three of the most common types of decay are alpha, beta, and gamma decay. The weak force is the mechanism that is responsible for beta decay, while the other two are governed by the electromagnetic and nuclear forces.
Radioactive decay is a random process at the level of single atoms. According to quantum theory, it is impossible to predict when a particular atom will decay, regardless of how long the atom has existed. However, for a significant number of identical atoms, the overall decay rate can be expressed as a decay constant or as a half-life. The half-lives of radioactive atoms have a huge range: from nearly instantaneous to far longer than the age of the universe.
View the full Wikipedia page for Radioactive decayIn particle physics and nuclear physics, the branching fraction (or branching ratio) for a decay is the fraction of particles which decay by an individual decay mode or with respect to the total number of particles which decay. It applies to either the radioactive decay of atoms or the decay of elementary particles. It is equal to the ratio of the partial decay constant of the decay mode to the overall decay constant. Sometimes a partial half-life is given, but this term is misleading; due to competing modes, it is not true that half of the particles will decay through a particular decay mode after its partial half-life. The partial half-life is merely an alternate way to specify the partial decay constant λ, the two being related through:
For example, for decays of Cs, 98.13% are ε (electron capture) or β (positron) decays, and 1.87% are β (electron) decays. The half-life of this isotope is 6.480 days, which corresponds to a total decay constant of 0.1070 d. Then the partial decay constants, as computed from the branching fractions, are 0.1050 d for ε/β decays, and 2.001×10 d for β decays. Their respective partial half-lives are 6.603 d and 347 d.
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