To consider the masses of atoms measured in grams, for example, would be to deal inconveniently with extremely small numbers. Rather, the mass of an atom is compared with that of an atom of carbon-12. The relative atomic mass of carbon-12 is taken to be 12. Relative masses have no units because they have cancelled in their calculation.
Some elements have isotopes. In calculating the relative atomic mass of an element with isotopes, the relative mass and proportion of each is taken into account. For example, naturally occurring chlorine consists of atoms of relative isotopic masses 35 (75%) and 37 (25%). Its relative atomic mass is 35.5.
Ar = (75/100 x 35) + (25/100 x 37) = 35.5
The relative masses of atoms are measured using an instrument called a mass spectrometer, invented by the English physicist Francis William Aston (1877-1945) when he was working in Cambridge with J. J. Thomson. It was in his use of this instrument that the existence of isotopes of elements was discovered. Aston eventually discovered many of the naturally occurring isotopes of non-radioactive elements. He was awarded the Nobel Prize for Chemistry in 1922.
Briefly, the mass spectrometer works by bombarding gaseous atoms with fast-moving electrons which knock out an electron from the atom. The cations formed are brought down on to a detector in turn according to their mass. The instrument provides a measure of the relative mass (compared to 12C) and the relative number of each isotope.
The diagrams below represent the mass spectrum of naturally occurring chlorine.
The above right spectrum has been represented so that the most abundant isotope has a relative abundance of 100%, with the other mass peaks scaled in relation to this. The relative atomic mass of chlorine is now calculated as shown below:
Ar = (100/133 x 35) + (33/133 x 37) = 35.5
See also The Mole | Relative Molecular Mass | Isotope.