Question

An excited state in an atom has a life time of 3.0×10⁻⁷ s. Calculate the line width of the emitted photon, when the atom decays spontaneously to its ground state.

Answer 1

Given:

$\Delta t=3.0*10^{-7}\:\rm s$

The line width is given by

$$\Delta \nu=\frac{1}{2\pi\Delta t}=\frac{1}{2\pi*3.0*10^{-7}\:\rm s}=5.3*10^5\:\rm Hz$$