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The Bateman equation is a classical master equation where the transition rates are only allowed from one species (i) to the next (i+1) but never in the reverse sense (i+1 to i is forbidden). Bateman found a general explicit formula for the amounts by taking the Laplace transform of the variables. (it can also be expanded with source terms, if ...
Nuclear physics. 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 ...
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.
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, 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 the abundance of ...
In nuclear physics, the Geiger–Nuttall law or Geiger–Nuttall rule relates the decay constant of a radioactive isotope with the energy of the alpha particles emitted. Roughly speaking, it states that short-lived isotopes emit more energetic alpha particles than long-lived ones. The relationship also shows that half-lives are exponentially ...
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: m {\displaystyle P=\Delta {m}\left ( {\frac {A} {M}}\right).}
Decay correction is one way of working out what the radioactivity would have been at the time it was taken, rather than at the time it was tested. For example, the isotope copper-64, commonly used in medical research, has a half-life of 12.7 hours. If you inject a large group of animals at "time zero", but measure the radioactivity in their ...