Statistical Nature of Radiation Emission

The emission of atomic and nuclear radiation obeys the rules of quantum theory. As a result of this, one can only talk about the probability that a reaction will take place or that a particle will be emitted. If one attempts to measure the number of particles emitted by a nuclear reaction, that number is not constant in time it has a statistical uncertainty because of the probabilistic nature of the phenomenon under study. 

Consider a radioactive source emitting electrons and assume that one attempts to measure the number of electrons per unit time emitted by the source. For every atom of the source there is a probability, not a certainty, that an electron will be emitted during the next unit of time. One can never measure the exact number. The number of particles emitted per unit time is different for successive units of time. Therefore, one can only determine the average number of particles emitted. That average, like any average, carries with it an uncertainty, an error. The determination of this error is an integral part of any radiation measurement. 

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