Lifetime an atom can spend in an excited state

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SUMMARY

The discussion centers on the relationship between the Einstein Aij coefficients and the lifetime an atom spends in an excited state, as described by the Heisenberg Uncertainty Principle. Specifically, large values of Aij correspond to shorter lifetimes, resulting in broader line profiles characterized by larger wavelengths (lambda). The principle states that the product of the uncertainties in energy and time is approximately equal to the reduced Planck constant (ħ), which is crucial for understanding this relationship.

PREREQUISITES
  • Understanding of Einstein Aij coefficients
  • Familiarity with Heisenberg's Uncertainty Principle
  • Basic knowledge of quantum mechanics
  • Concept of atomic excited states
NEXT STEPS
  • Study the derivation of the Einstein Aij coefficients
  • Explore the implications of Heisenberg's Uncertainty Principle in quantum mechanics
  • Investigate the relationship between energy and wavelength in quantum systems
  • Examine line broadening effects in spectroscopy
USEFUL FOR

Students and researchers in quantum mechanics, physicists studying atomic transitions, and anyone interested in the principles of spectroscopy and atomic behavior.

randa177
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Can you please give me a hint to start this problem?

The Einstein Aij coefficients are related to the lifetime an atom can spend in an excited state i before going to state j. Using Heisenberg’s Uncertainty Principle, show that large values of Aij lead to line profiles with large values of (lamda)

Thanks
 
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Heisenberg uncertainty principle: \Delta E \cdot \Delta t \sim \hbar

Let delta-t be the lifetime of the state. How is E related to lambda?
 
Last edited:
Oh, thanks a lot! That is very easy now!
Thanks
Randa
 

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