Lectures on Physics has been derived from Benjamin Crowell's Light and Matter series of free introductory textbooks on physics. See the editorial for more information.... 
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Probability distribution for radioactive decayHere is a rigorous justification for the statement in section 2.4 that the probability distribution for radioactive decay is found by substituting N(0) = 1 into the equation for the rate of decay. We know that the probability distribution must be of the form
where k is a constant that we need to determine. The atom is guaranteed to decay eventually, so normalization gives us
The integral is most easily evaluated by converting the function into an exponential with e as the base
which gives an integral of the familiar form R ecxdx = (1/c)ecx . We thus have
which gives the desired result:


Home Modern Physics Rules of Randomness Examples Probability distribution for radioactive decay 