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The resolving power in MS is often defined as $m / \Delta m$, or the reciprocal of the smallest discernible mass difference $\Delta m$ normalized to average mass $m$.

I wonder why the normalization to the average mass $m$ makes sense. Is there a physical reason, or a mathematical or sociologic reason? Is 1 at 100 really same as 2 at 200, does this resolving power scale like that or is that just copied from optics? In optics I would accept that resolution depends on wavelength, but how so for mass?

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$m / \Delta m$, or the reciprocal of the smallest discernible mass difference $\Delta m$ normalized to average mass $m$.

Good question because the resolution in mass spectrometry and chromatography have been misused and there is an element of inadequacy if we look deeply. I don't know where you got this definition, but whoever wrote it has the notion of $m$ wrong. It is not normalized to average mass. It is the single mass of your analyte or molecule of interest. There is an entire 2022 article in a leading journal dedicated to your query.

Resolution and Resolving Power in Mass Spectrometry Kermit K. Murray in J. Am. Soc. Mass Spectrom. 2022, 33, 12

The proper definition is as follows, in case there is a problem in accessing it.

For a single peak made up of singly charged ions at mass m in a mass spectrum, the resolution may be expressed as m/Δm, where Δm is the width of the peak at a height which is a specified fraction of the maximum peak height. It is recommended that one of three values 50%, 5%, or 0.5% should always be used. For an isolated symmetrical peak recorded with a system which is linear in the range between 5% and 10% levels of the peak, the 5% peak width definition is technically equivalent to the 10% valley definition. A common standard is the definition of resolution based upon Δm being Full Width of the peak at Half its Maximum height, sometimes abbreviated "fwhm". This acronym should preferably be defined the first time it is used.

Nowhere it says, average mass! $m$ is a single mass of your interest, and its width is $\Delta m$.

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    $\begingroup$ Thanks so much! However, the main question is how the normalization makes sense.. How would you interpret the choice of the definition? I understand why a resolution would use the reciprocal of the smallest discernible difference. But why divide by the mass? $\endgroup$
    – Selenimoon
    Mar 20 at 9:36
  • $\begingroup$ Welcome, that is just a human definition of resolution. There is no right or wrong. $\endgroup$
    – AChem
    Mar 20 at 17:47

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