Radionuclides disintegration probability

The decay rate of a given radionuclide is generally constant and independent of the past history of the nuclide and of the P, T (at least below 10 K), and chemistry of the system. The probability fP of the radionuclide disintegrating over time At is... 

The Poisson distribution describes the probability P t) that, in a time interval t, Ndiscrete events (such as radionuclide disintegrations, openings of a individual ion channels, or photon detections) will have taken place. That probability is... 

The decay of a radionuclide is a statistical process in the sense that it is not possible to predict exactly when a particular nucleus will disintegrate. One may, however, ascribe a probability that a nucleus will decay in unit time. This probability is known as the radioactive decay constant (transformation constant), X, of the radionuclide. The number of atoms of a radioactive substance disintegrating per unit time, 6N/dt, which is referred to as the activity of the substance, is proportional to the total number, N, of radioactive atoms present at time t, the constant of proportionality being X. 

Symmetric fission, in which the or Pu nuclei disintegrate into two products of equal mass number, has a low probability. For this reason, their products do not play a significant role in the radionuclide composition of irradiated fuel. 

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