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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.
alpha decay; The decay energy is the mass difference Δm between the parent and the daughter atom and particles. It is equal to the energy of radiation E. If A is the radioactive activity, i.e. the number of transforming atoms per time, M the molar mass, then the radiation power P is: = (). or
the gamma function, a generalization of the factorial; the upper incomplete gamma function; the modular group, the group of fractional linear transformations; the gamma distribution, a continuous probability distribution defined using the gamma function; second-order sensitivity to price in mathematical finance
The following apply for the nuclear reaction: a + b ↔ R → c in the centre of mass frame , where a and b are the initial species about to collide, c is the final species, and R is the resonant state .
Alpha decay or α-decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle (helium nucleus) and thereby transforms or "decays" into a different atomic nucleus, with a mass number that is reduced by four and an atomic number that is reduced by two.
The four most common modes of radioactive decay are: alpha decay, beta decay, inverse beta decay (considered as both positron emission and electron capture), and isomeric transition. Of these decay processes, only alpha decay (fission of a helium-4 nucleus) changes the atomic mass number ( A ) of the nucleus, and always decreases it by four.
This is because the mass–energy is a convex function of atomic number, so all nuclides on an odd isobaric chain except one have a lower-energy neighbor to which they can decay by beta decay. See Mattauch isobar rule. (123 Te is expected to decay to 123 Sb, but the half-life appears to be so long that the decay has never been observed.)
The decay scheme of a radioactive substance is a graphical presentation of all the transitions occurring in a decay, and of their relationships. Examples are shown below. It is useful to think of the decay scheme as placed in a coordinate system, where the vertical axis is energy, increasing from bottom to top, and the horizontal axis is the proton number, increasing from left to right.