Uncertainty relationship for rotational spectroscopy

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SUMMARY

The discussion centers on the application of the uncertainty principle in rotational spectroscopy, specifically the relationship ∆E τ ~ ℏ. Participants seek to determine the lifetime of a state corresponding to a line width of 0.1 cm-1 and 100 MHz. The energy terms are clarified using the equations E = hc * (wavenumber) for wavenumbers and E = hf for frequency, with a mention of angular frequency leading to E = ℏω. The discussion emphasizes the importance of understanding these relationships for accurate calculations in spectroscopy.

PREREQUISITES
  • Understanding of the uncertainty principle in quantum mechanics
  • Familiarity with rotational spectroscopy concepts
  • Knowledge of energy equations: E = hf and E = hc * (wavenumber)
  • Basic grasp of angular frequency and its relation to energy
NEXT STEPS
  • Research the implications of the uncertainty principle in quantum mechanics
  • Study the principles of rotational spectroscopy in detail
  • Explore the calculation of lifetimes from line widths in spectroscopy
  • Learn about the relationship between frequency, wavenumber, and energy
USEFUL FOR

Physicists, chemists, and students studying quantum mechanics and spectroscopy, particularly those interested in the mathematical relationships governing energy states and their lifetimes.

jaejoon89
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From uncertainty relationship ∆E τ ~ hbar, what is the lifetime for a state that gives rise to a line of width 0.1 cm^-1? what about for 100 MHz?

How do you get the energy term? I'm really not sure how to do this, would appreciate some insight, thnx.
 
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Reciprocal centimeters are a measure of what?
 
So it's the wavenumber...

1) I just use E=hc*(wavenumber), and here E = ∆E?

2) What about for MHz = s^-1 = f
So I just use E = hf?

Or would it be angular frequency and should I use instead E = hbar omega ?
 

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