A mass spectrometer measures the mass of an isotope relative to that of carbon-12 by analysing the ratio of the ionised isotope’s deflection to the ionised carbon-12’s deflection.

From eq9, we have:

Assume both ions are univalent so that and divide eq11 by eq10:

Therefore,

We can also represent eq13 in the form

where we have replaced *e* with the notation *z*. The output of eq14 is a value with unit of unified atomic mass unit, *u*, since the ratio is unit-less while .

Finally, we divide the output of eq14 by 1*u* to obtain the relative isotopic mass, which is a dimensionless quantity that is defined as the ratio of the mass of an isotope in unified atomic mass unit to one unified atomic mass unit.

###### Question

Is it possible to accurately measure the mass of an atom in *kg* using eq9 without a reference isotope?

###### Answer

No. Due to the limits of precision engineering, measurements of the mass of an atom in *kg* by directly applying eq9 differ from one mass spectrometer to another. We therefore need a reference ‘flight path’ that we can compare with, i.e. using eq14. Since the value of is accurately defined in *u*, the output of eq19 must be in unified atomic mass unit. The value in *kg* is then obtained by the following conversion:

*1u = 1.660539 x 10 ^{-27} kg*