Determining the life time of a excited state.

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SUMMARY

The discussion centers on estimating the lifetime of excited states in atoms using the uncertainty principle. The smallest uncertainty in the frequency of emitted light is given as 8 MHz, which directly relates to the energy-time uncertainty principle, expressed as ΔEΔt ≥ ħ/2. Participants confirm that the frequency uncertainty can be converted to energy uncertainty using the relation E = hf, allowing for the calculation of the excited state lifetime. The hydrogen atom's energy levels, defined by E_n = -13.6 eV/n², serve as a basis for these calculations.

PREREQUISITES
  • Understanding of quantum mechanics principles, specifically the energy-time uncertainty principle.
  • Familiarity with the relationship between energy and frequency, expressed as E = hf.
  • Basic knowledge of atomic structure, particularly hydrogen atom energy levels.
  • Ability to perform calculations involving energy differences between quantum states.
NEXT STEPS
  • Study the energy-time uncertainty principle in detail, including its implications in quantum mechanics.
  • Learn how to convert frequency uncertainty to energy uncertainty using E = hf.
  • Explore the energy level calculations for hydrogen and other atoms to understand quantum transitions.
  • Investigate practical applications of uncertainty principles in spectroscopy and quantum state analysis.
USEFUL FOR

Students and researchers in quantum mechanics, physicists studying atomic transitions, and anyone interested in the implications of uncertainty principles in quantum systems.

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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