Determining the life time of a excited state.

AI Thread Summary
The discussion focuses on estimating the lifetime of excited states in atoms using the uncertainty in emitted light frequency, which is given as 8 MHz. The user considers applying the energy-time uncertainty principle, ΔE Δt ≥ ħ/2, but is unsure how to relate the frequency uncertainty to energy. They reference the energy levels of the hydrogen atom and the relationship E = hf to connect frequency and energy. Clarification is sought on whether the frequency uncertainty can be used as the uncertainty in energy for this principle. The conversation emphasizes the need for a clear understanding of these quantum mechanics concepts.
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
 
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