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The basic law of radioactive disintegration in the differential form. A constant of disintegration

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Radioactive disintegration of nucleuses of the same elements happens gradually and has various speed at various elements. Radioactive disintegration - the statistical process, submitting to laws of probability theory. The moment of disintegration of each nucleus cannot be specified in advance, but this theory allows to determine probability of disintegration of one nucleus for the time unit. This probability is characterized by coefficient λ, which is named a constant of disintegration and depends upon nature of element.

The basic law of radioactive disintegration install: The same quantity of nucleuses of the given element breaks up for equal time intervals. The constant of disintegration λ to determine this quantity.

The quantity dN of nucleuses, which are breaking up for a time interval dt, is proportional to quantity of the nucleuses, which have not broken yet to the beginning of the given time interval, and a time interval dt from the law:

(The sign a minus shows decrease of number N during the time).


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