What Does FWHM of a Velocity Distribution Reveal?

Click For Summary
SUMMARY

The Full Width at Half Maximum (FWHM) of a velocity distribution quantifies the range of velocities rather than providing a specific velocity. It is essential to distinguish between the most probable velocity, which is the mode, and the mean, as they can differ significantly depending on the distribution shape. In the context of the Maxwell-Boltzmann distribution, the average and most probable velocities can differ by a factor of 2/sqrt(pi), highlighting the importance of understanding the distribution's characteristics.

PREREQUISITES
  • Understanding of statistical distributions, particularly the Maxwell-Boltzmann distribution.
  • Familiarity with the concept of mode versus mean in statistical analysis.
  • Knowledge of FWHM and its application in various scientific fields.
  • Basic grasp of velocity distributions in physics.
NEXT STEPS
  • Research the properties of the Maxwell-Boltzmann distribution in detail.
  • Study the mathematical derivation of FWHM and its implications in different contexts.
  • Explore the differences between mean, median, and mode in statistical distributions.
  • Investigate applications of FWHM in spectroscopy and other scientific measurements.
USEFUL FOR

Physicists, statisticians, and anyone involved in analyzing velocity distributions or applying statistical methods to physical phenomena.

Carnot
Messages
18
Reaction score
0
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
 
Physics news on Phys.org
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).
 

Similar threads

Graduate Deformation in static and transient case
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Average Velocity of gas molecules calculated with a Boltzmann distribution
  • · Replies 7 ·
Replies
7
Views
8K
Undergrad Understanding basic statistical mechanics formulas
  • · Replies 3 ·
Replies
3
Views
2K
High School What is physical significance of the direction of angular velocity?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Velocity Map Imaging: Understanding 3D Reconstruction
  • · Replies 2 ·
Replies
2
Views
6K
Undergrad Recreating Spectral Response from 6-Channel Color Sensor
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Boltzmann distribution and the number of molecules with a certain velocity
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad Spectrometer: bandpass and resolution
  • · Replies 7 ·
Replies
7
Views
4K
Undergrad Confusion about adding angular velocities
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Velocity transformation between frames rotating relative to one another
  • · Replies 1 ·
Replies
1
Views
2K