Determining the life time of a excited state.

Elekko
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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.
 
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Recall the general relation E = hf.
 
TSny said:
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)
 
Need to mention that of course f = 8 MHz
 
To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.
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