The answer Stefanie Maedler is close to "exactness", but needs to be detailed. (i) "amu" is obsolete, instead "u" must be used (IUPAC rules). (ii) The mass of isotopes is relative to 12-C taken as exactly 12 u ; note that it is the mass of the atom (not of the ion measured in MS) at rest, meaning that relativity effect may be taken into account, for example the bonding energy in molecules (which are very small even with the most precise mass spectrometers). (iii) Relative atomic masses or atomic weight are for elements as the natural isotopic mixture; for example carbon (essentially 99% 12-C and 1% 13-C) is 12.011 u with an uncertainty of about 0.0008 u. There is some variability in natural samples because of isotopic variations (fractionation) in the environment.

See the recent table (2017) : https://www.qmul.ac.uk/sbcs/iupac/AtWt/

Note that most elements have a range of atomic weight. The elements with a single isotope have a very precise atomic weight, and the elements with many isotopes (which are mixtures with slightly variable compositions in nature) have less precise atomic weight.

For the Stefanie examples, 16-O is 15.994915 and oxygen is [15.999 03, 15.999 77] ; 1-H is 1.007825 and hydrogen [1.007 84, 1.008 11] .

(iv) Before the redefinition of the kilogram and mole, the "u" was exactly 1/12 of the mass of 12-C, and also equal to 1 g/mol (also called Dalton, Da).

(iv) There is an additional complication with the recent redefinition of the kilogram and the mole, but this is unimportant if you are nor concerned with relative uncertainties below 10-8. This is another story...

Hope that I did not confuse too much the matter. Please ask if I was too fuzzy...

Not sure, if that answers your question, but first we have to distinguish between the two different units for atomic mass:

The absolute mass of an atom is measured in g or kg. Alternatively, atomic mass can also be measured in atomic mass units (amu), where one amu is equivalent to 1/12 of the atomic mass of the 12-C isotope of carbon.

Example: Hydrogen 1H:

atomic mass in g: 1.661 × 10-24 grams

atomic mass in amu: 1.0080 amu

Example: Oxygen 16O:

2.656 * 10^-23 grams

15.995 amu

Routine mass spectrometers measure in "amu". 1 amu is equivalent to approximately 1 g/mol, i.e. if you take the atomic mass of 1H and multiply it with the Avogadro number, you end up with 1 g/mol.

Thanks Stefanie, isn't 15.995 amu for O based on C-12 by assuming carbon is exactly 12.00000 (ad infinitum). I feel Aston relied more on chemical atomic masses for his calibration- maybe his photographic plates for detection. I cannot find much when I search "absolute atomic mass"

According to the theory of relativity, you can find most of factors are varied (it have not constant values).

The answer Stefanie Maedler is close to "exactness", but needs to be detailed. (i) "amu" is obsolete, instead "u" must be used (IUPAC rules). (ii) The mass of isotopes is relative to 12-C taken as exactly 12 u ; note that it is the mass of the atom (not of the ion measured in MS) at rest, meaning that relativity effect may be taken into account, for example the bonding energy in molecules (which are very small even with the most precise mass spectrometers). (iii) Relative atomic masses or atomic weight are for elements as the natural isotopic mixture; for example carbon (essentially 99% 12-C and 1% 13-C) is 12.011 u with an uncertainty of about 0.0008 u. There is some variability in natural samples because of isotopic variations (fractionation) in the environment.

See the recent table (2017) : https://www.qmul.ac.uk/sbcs/iupac/AtWt/

Note that most elements have a range of atomic weight. The elements with a single isotope have a very precise atomic weight, and the elements with many isotopes (which are mixtures with slightly variable compositions in nature) have less precise atomic weight.

For the Stefanie examples, 16-O is 15.994915 and oxygen is [15.999 03, 15.999 77] ; 1-H is 1.007825 and hydrogen [1.007 84, 1.008 11] .

(iv) Before the redefinition of the kilogram and mole, the "u" was exactly 1/12 of the mass of 12-C, and also equal to 1 g/mol (also called Dalton, Da).

(iv) There is an additional complication with the recent redefinition of the kilogram and the mole, but this is unimportant if you are nor concerned with relative uncertainties below 10-8. This is another story...

Hope that I did not confuse too much the matter. Please ask if I was too fuzzy...

Thanks Dr. Jean. Thanks for your input. I am looking at the problem from a historical of view. This is well before the C-12 suggestion in 1960s or the existence of amu or even u. My first question is can a mass spectrometer give a exact mass of a single isotope in an absolute sense without using any relative scale. What was the need to choosing a relative scale to begin with? Thanks.

In current use, a mass spectrometer must be calibrated using several ions with known m/z ratios. In this regard the m/z measurements are relative. Even the highly precise masses of the element isotopes were mostly measured by sector instruments, then by Penning trap (ICR) using known elements as references. Mass differences can be measured with high accuracy. The current isotope masses are given with about 9 or 11 significant digits.

In principle, absolute mass (or m/z) can be measured if you know all parameters of the instrument. Aston and Thomson estimated the masses of ions this way, I suppose. The history of isotopes and MS is summarized in chapter 1 of the book "Measuring Mass" by M. A. Grayson, 2002. I can tell about FTICR because it it the instrument I know well. Using the simple cyclotron equation, you just need the magnetic field strength and the resonant frequency, but many second order effects change this frequency. This is the reason we can measure highly accurate differences but not absolute values by mass spectrometry. You may look at IUPAC literature, they maintain historical archives on atomic weight measurements.

Historical aspects are in the attached papers.

From an instrumental performance point of view, there are a number of factors which enter in to the measuremetn of mass by mass spectrometry that impact the measured mass of an ion.

Given an input voltage to an ion lens or an electric sector energy dispersive element, it is assumed that the electric field is uniform and precisely known. However, the presence of non-ideal conductors and field effects the electric field will not be ideal and exactly known. This is particularly problematic in the case of static electric fields, as compared to alternating or RF fields. If one contaminates the lenses in an ion source, and then evaluates the ion transmission or instrument sensitivity in terms of current per unit of pressure of the systems, and then cleans the source lenses, there can be orders of magnitude in sensitivity difference. This is due to the change in the effective electric field at teh lenses.

For a magnetic field, it is again assumed that the field is entirely uniform and precisely defined. If one looks at the tuning of an NMR instrument magnetic field, at least in non-super conducting magnet systems, in spite of having very carefully designed magnets, it is generally necessary to provide additional tuning of the magnetic field uniformity and strength, and this is also impacted by other magnetic material or fields within the field of the magnet, which extends at various field strength gradients to nearly infinity in all directions.

At the small fractional mass level, there is also the question of the mass defect, which has to do with the energy of the combination of the electrons, protons and neutrons and the energy released during the formation of the atom. At a much finer level of detail, the kinetic energy of the ion can also result in some perturbation of the exact mass.

This leaves the question of how to verify the veracity of the assumptions of the performance of the instrument during operation. One needs a standard, for the verification. The simplest answer is to select a known mass to charge ion and then define it as a number. Initially, the choice was oxygen, which was defined as exactly 16. Later the standard was changed to carbon-12 being exactly 12. I would assume that this change was largely due to the number of potential interferences in measuring 16, for which there are a larger number of ions that can add up to approximately 16, than there are ions that add up to 12. In any case, having a readily available standard which can be used to define the mass to charge scale is much more appropriate than trying to verify the assumptions of ideal ion selection behavior on a daily basis. What standards would one have to verify the exact behavior of the ion selection system to base the measured mass strictly on the input of all of the electric, magnetic and/or RF fields?

Having one universally available defined standard makes a lot more sense. Alternatively, what would the impact of having to go through extreme precision measurements of all of the system that impact the separation of the ions and result in the mass measurement?

Thanks for providing those references Dr. Jean-Francois and Dr. Canham. It seems that in principle one can determine the "absolute" masses provided all other instrumental parameters are exactly known. Hence absolute calibration is difficult. However atomic mass of an isotope should be a fundamental constant as well like subatomic particle masses. By that I mean physicists can measure mass of electron and proton without reference to anything else so why atomic masses?

I was thinking to this analogy: If we had a hypothetical atomic balance, which could weigh atoms, currently we have calibrated that balance by asking it to read the weight of a C-12 atom as 12.00000000 units (as many digits as the balance can read to infinity). All atoms are then weighed on this balance. Although we know that the weight of C-12 atom is not exactly 12.0000000000000000000000000 units. It looks very artificial.

John Canham the reason for switching from O-16 to C-12 was that there were two scales before the 1960s. One was a chemical atomic weight and the other was physical atomic weight. Chemists did not take oxygen isotopes into account and all their atomic weights were off by "somewhat" constant factor by the physicist's atomic weight because the latter took pure O-16 into account. Physics took over the accuracy from a chemist's hands who had no control over isotopic measurements in the 1940s.