Chapter 41 - Atomic Physics - Exercises and Problems - Page 1208: 45

The lifetime of the excited state is $~~10~ns$

Let $P$ be the probability that an excited atom will emit a photon. We can find the lifetime of the excited state: $P = \lambda~\Delta t$ $P = (\frac{1}{\tau})~(\Delta t)$ $\tau = \frac{\Delta t}{P}$ $\tau = \frac{0.10~ns}{0.010}$ $\tau = 10~ns$ The lifetime of the excited state is $~~10~ns$