What Does FWHM of a Velocity Distribution Reveal?

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Discussion Overview

The discussion centers on the interpretation of the full width at half maximum (FWHM) in the context of velocity distributions, particularly regarding its relationship to the most probable velocity and the characteristics of different types of distributions.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant inquires whether FWHM indicates the most probable velocity of a velocity distribution.
  • Another participant clarifies that FWHM represents a range of velocities and is a measure of the spread of a distribution, not a specific velocity.
  • A claim is made that the most probable velocity is typically the mean, which is challenged by another participant who states that it is actually the mode.
  • It is noted that the interpretation of FWHM may depend on the symmetry of the distribution being considered.
  • A reference to the Maxwell-Boltzmann distribution is made, highlighting that it is not perfectly symmetrical and that the average and most probable velocities can differ significantly.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between FWHM, the most probable velocity, and the mean. There is no consensus on whether FWHM indicates the most probable velocity, and the discussion remains unresolved regarding the implications of distribution symmetry.

Contextual Notes

Participants mention the dependence of interpretations on the type of distribution, particularly noting the asymmetry in the Maxwell-Boltzmann distribution. The discussion does not resolve the implications of these characteristics on the relationship between FWHM and velocity measures.

Carnot
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Hi

FWHM on a velocity distribution provides me with a specific velocity. What does FWHM say about the velocity distribution, I mean, does FWHM give me the most probable velocity of the distribution or something like that?

Thanks
 
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Simon Bridge said:
The most probable velocity is usually the mean, like you'd expect.

No, that's the mode. It might or might not be anywhere near the mean.
 
Depends on the distribution aye - I'm used to FWHM being used for pretty symmetrical distributions though.
 
Consider the Maxwell-Boltzmann distribution - surely a common (if not the most common) velocity distribution. It's not all that symmetrical - there's a long tail to the right, and thus the average and most probable velocities differ by a factor of 2/sqrt(pi).
 

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