41. If N is the number of undecayed nuclei present at time t ,then dN dt = R − λN where R is the rate of production by the cyclotron and λ is the disintegration constant. The second term gives the rate of decay. Rearrange the equation slightly and integrate: Z N N0 dN R − λN = Z t0 dt where N0 is the number of undecayed nuclei present at time t = 0. This yields − 1 λ ln R − λN R − λN0 = t. We solve for
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