Determining the life time of a excited state.

[Elekko]

Homework Statement

The smallest uncertainty in the frequency of emitted light when excited atoms return to ground state for molecules is estimated to be 8 MHz. Use this information to estimate the lifetime of the excited states.
I would like to know if I'm thinking correct.

Homework Equations

Well here, it is a question we can take in general by having an uncertainty of the frequency at f = MHz.
I took the hydrogen atom in which the energy levels in general can be written as

$E_n=\frac{-13.6eV}{n^2}$ where I then calculate the difference in energy for instance between state n = 1 and n = 2.

The Attempt at a Solution

Can I then apply the energy-time uncertainty principle $\Delta E \Delta t \ge \frac{\hbar}{2}$ ?
I'm not sure about this, science we have an uncertainty in FREQUENCY which makes me stuck.

Appreciate for help.

 

[TSny]

Recall the general relation E = hf.

 

[Elekko]

Recall the general relation E = hf.

Can this be used as the uncertainty in energy in the energy-time uncertainty principle?
(Im not very sure about this, science I don't have a solution for this)

 

[Elekko]

Need to mention that of course f = 8 MHz