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

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In summary, The question discusses the emission of light by an electron in an atom in the form of lightly damped SHM with a Q factor of 5x10^7. The width of the spectral emission line is determined by the relationship E=hv=A^2, where A^2=Q^2 for large Q. However, the understanding of why amplitude and Q value are roughly the same and why energy is equal to A^2 is not clear. The equation for width of the spectral emission line is \Gamma=2\pi\nu/Q.
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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].
 

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

What is spectral emission line width?

Spectral emission line width refers to the width of a spectral line in a spectrum. It is a measure of the range of wavelengths present in the emission line and is typically measured in units of wavelength, such as nanometers or Angstroms.

How is spectral emission line width related to the energy levels of atoms?

The spectral emission line width is directly related to the energy levels of atoms. When an atom emits light, it does so at specific wavelengths corresponding to the energy difference between its energy levels. The width of the emission line is determined by the uncertainty principle, which states that the more precisely the energy is known, the less precisely the time of the emission can be known. This results in a broadening of the spectral line.

What factors can affect the spectral emission line width?

Several factors can affect the spectral emission line width, including temperature, pressure, and the presence of external magnetic or electric fields. These factors can cause the energy levels of the atoms to shift, resulting in a broader or narrower emission line.

Why is spectral emission line width important in spectroscopy?

Spectral emission line width is important in spectroscopy because it can provide information about the physical conditions of the emitting source. By measuring the width of the spectral lines, scientists can determine the temperature, density, and other properties of the source.

How is spectral emission line width measured?

Spectral emission line width is typically measured using a spectrometer, which separates light into its component wavelengths. The width of the emission line can then be determined by measuring the full width at half maximum (FWHM), which is the distance between the two points on the spectrum where the intensity is half of the maximum intensity.

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