HW Helper
P: 4,739
 Quote by SReinhardt Wouldn't there have to be a negative sign in there somewhere >_> I believe you have to use integrals to solve that, which I haven't done yet.
yeah it should have a minus sign, good! :-)

Solving this:

$$\int N ^{-1}dN = - \int \lambda dt$$

$$\ln(N(t)) - \ln(N(0)) = -\lambda t$$

$$\ln(N(t)/N(0)) = -\lambda t$$

$$N(t)/N(0) = e^{-\lambda t }$$

$$N(t) = N(0) e^{-\lambda t }$$

Lambda is the number of decays per unit time, is related to half life by:
$$\lambda = \frac{\ln 2}{T_{1/2}}$$