How to find the lifetime of sodium atoms in the 3p using information on the spectral line width?
Half the fwhm has to be added/subtracted  to the central wavelength and then this change in wavelength converted to an energy. Thus the limits on the wavelength are $\lambda \pm \Delta \lambda /2) $ and the energy change $\Delta E=hc/(\lambda - \Delta \lambda /2)-hc/(\lambda + \Delta \lambda /2)$ Joules with $c$ in m/s and $h$ in J s. Plugging in the numbers gives a lifetime of $\approx 10^{-9}$, i.e. $1$ ns.  

As a rule of thumb, lifetimes of excited electronic states are rarely less than $10^{-12} $s and if the transition is allowed, as in this case often of the order of nanoseconds to microseconds. If transitions are forbidden then the lifetimes can extend from microseconds to seconds.