Simple Nature - Light and Matter

j / Calibration of the 14 C dating method using tree rings and artifactswhose ages were known from other methods. Redrawn from EmilioSegrè, Nuclei and Particles, 1965.Rate of decayIf you want to find how many radioactive decays occur within atime interval lasting from time t to time t + ∆t, the most straightforwardapproach is to calculate it like this:(number of decays between t and t + ∆t)= N(t) − N(t + ∆t)Usually we’re interested in the case where ∆t is small compared tot 1/2 , and in this limiting case the calculation starts to look exactlylike the limit that goes into the definition of the derivative dN/ dt. Itis therefore more convenient to talk about the rate of decay − dN/ dtrather than the number of decays in some finite time interval. Doingcalculus on the function e x is also easier than with 0.5 x , so we rewritethe function N(t) asN = N(0)e −t/τ ,where τ = t 1/2 / ln 2 is shown in example 6 on p. 835 to be theaverage time of survival. The rate of decay is then− dNdt = N(0) e −t/τ .τ832 Chapter 13 Quantum Physics