# Resolution (mass spectrometry)

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Obsolete Template

## Gold Book

(energy): By analogy with the peak width definition for mass resolution, a peak showing the number of ions as a function of their translational energy should be used to give a value for the energy resolution.

(10 per cent valley definition): Let two peaks of equal height in a mass spectrum at masses m and m - Δm be separated by a valley which at its lowest point is just 10 per cent of the height of either peak. For similar peaks at a mass exceeding m, let the height of the valley at its lowest point be more (by any amount) than ten per cent of either peak height. Then the resolution (10 per cent valley definition) is m/Δm. It is usually a function of m. The ratio m/Δm should be given for a number of values of .

(peak width definition): For a single peak made up of singly charged ions at mass in a mass spectrum, the resolution may be expressed as where 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 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.

Source: PAC, 1991, 63, 1541 (Recommendations for nomenclature and symbolism for mass spectroscopy (including an appendix of terms used in vacuum technology). (Recommendations 1991)) on page 1554

Orange Book, p. 203

## Orange Book

Let two peaks of equal height in a mass spectrum at masses m and m - Δm be separated by a valley which at its lowest point is just 10% of the height of either peak. For similar peaks at a mass exceeding m , let the height of the valley at its lowest point be more (by any amount) than 10% of either peak. Then the resolution (10% valley definition) is m / Δm. The ratio m /Δm should be given for a number of values of m.

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. (Note that 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 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 (FWHM) height.

## 1997 ASMS Poster

From the ASMS Terms and Definitions Poster:

Resolution of the Confusion on Peak Separation

Mass resolving power and mass resolution have been used interchangeably throughout the literature, so the confusion surrounding their exact meaning is understandable. In his forthcoming book, "Guide to Mass Spectrometry," Ken Busch advocates definitions that are consistent these proposed terminologies for mass resolution and mass resolving power. In most disciplines, resolution is understood to be the smallest observable change in a quantity, whereas resolving power, i.e. the ability to distinguish two closely spaced quantities, is inversely proportional to resolution.

Proposed definitions:

mass resolution - the mass (actually, m/z) difference, Dmx that exists between two adjacent peaks in a mass spectrum that are of equal size and shape (Gaussian, Lorentzian, triangular) with a specified amount of overlap, where the subscript "x" denotes the overlap criterion (10% valley, Full Width at Half Height [FWHH], etc.) See Usage Note for mass resolving power and theoretical mass resolving power

mass resolving power - m/Dmx, where Dmx is the mass resolution See Usage Note for theoretical mass resolving power

Usage note: Although the definition of mass resolution is contingent upon two adjacent, mass spectral peaks of equal size and shape, which is almost never the case experimentally, it is acceptable to calculate the mass resolving power or mass resolution from a single peak. An assumption is made about the peak shape, whereby the peak width at 5% height for a single peak would be approximately equivalent to the distance between the apexes of two peaks with a 10% valley between them. This assumption is not unreasonable for most common peak shapes encountered in mass spectrometry. Therefore, the mass resolving power that is obtained by dividing the mass (m/z) value at the apex of a peak by the peak width at 5% of the peak height could be indicated as m/Dm10%V theoretical mass resolving power -

Usage note: Theoretical mass resolving power is useful for determining the relative difficulty in separating two peaks in a mass spectrum. The "masses" are actually m/z values, and the subscript "d" indicates that the criterion used to determine Dm is simply the difference in mass between the two peaks. One should be careful to notice the subtle distinction between Dmd, a quantity that is independent of instrumental performance, and Dmx, a quantity that is determined by instrumental performance. It is important to realize that the theoretical mass resolving power makes no peak shape assumptions. Therefore, the choice of overlap criterion, i.e., 10% valley, full width half height, etc. is the link between the theoretical mass resolving power and the experimentally measured "mass resolving power." For an instrument to be capable of separating two particular ions, the instrument must possess a mass resolving power (over the range m + Dm) that is greater than the theoretical mass resolving power calculated for the ions in question. For example, if it is desired to determine whether or not a particular mass spectrometer is capable of resolving 41K+ from 40Ar1H+, determine the theoretical mass resolving power:

Next, the instrumental mass resolving power of the instrument at m/z = 41 is compared with the theoretical mass resolving power. For a quadrupole based instrument, a 10% valley overlap would correspond to a Dm of approximately 1 Da, assuming typical scan rates are used. For a peak at m/z = 41, this corresponds to a "mass resolving power" = 41. Therefore, this particular instrument does not possess mass resolving power capable of separating these two species. >From the preceding discussion, it is apparent that even greater mass resolving power would be required for a separation if two adjacent peaks if the peaks are not of equal size and shape. The lesser peak could be lost in the "wings" of the larger peak.

Another comment: Note that resolving power is dimensionless, but when defined as peakwidth, it usually has units of "parts-per-million" (of mass). Thus, a resolution of 10,000 corresponds to 100 ppm.