What is the relationship between Q factor and spectral emmision line width?

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SUMMARY

The relationship between the Q factor and spectral emission line width is established through the formula Γ = 2πν/Q, where ν represents the frequency of the emitted light. In this discussion, the wavelength of the emitted light is given as 0.6 x 10^-6 meters, which corresponds to a frequency calculated using the speed of light. The Q factor is specified as 5 x 10^7, leading to a precise determination of the spectral line width based on these parameters. The discussion highlights the connection between amplitude and Q factor, emphasizing that for large Q, A^2 approximates Q^2.

PREREQUISITES
  • Understanding of quantum mechanics and atomic behavior
  • Familiarity with the concepts of Q factor and its implications in oscillatory systems
  • Knowledge of spectral emission and wavelength-frequency relationships
  • Basic grasp of harmonic motion and energy relationships in physics
NEXT STEPS
  • Study the derivation of the formula Γ = 2πν/Q in detail
  • Explore the relationship between amplitude and Q factor in damped harmonic oscillators
  • Learn about the implications of spectral line width in quantum mechanics
  • Investigate the calculation of frequency from wavelength using the speed of light
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Physicists, students of quantum mechanics, and anyone interested in the principles of spectral emission and harmonic motion will benefit from this discussion.

silverdiesel
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I have no ideal where to begin on this question.

Light of wavelength 0.6x10^-6 meters is emmited by an electron in an atom behaving as a lightly damped SHM with a Q factor of 5x10^7. Determine the width of the spectral emmision line.

I am thinking E=hv=A^2

where A^2=Q^2 for large Q.

but, in all realality, I am just pulling these relationships from the text. I don't intuitivly understand why Amplitute and the Q value would roughly be the same, nor do I understand why Energy would equal just A^2, as opposed to A^2cos^2(wt).
 
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[itex]\Gamma=2\pi\nu/Q[/itex].
 

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