THE MASS SPECTRA OF ELEMENTS

THE MASS SPECTRA OF ELEMENTS This page looks at the information you can get from the mass spectrum of an element. It shows how you can find out the masses and relative abundances of the various isotopes of the element and use that information to calculate the relative atomic mass of the element. It also looks at the problems thrown up by elements with diatomic molecules - like chlorine, Cl2. The mass spectrum of monatomic elements Monatomic elements include all those except for things like chlorine, Cl2, with molecules containing more than one atom. The mass spectrum for boron
	Note:  If you need to know how this diagram is obtained, you should read the page describing how a mass spectrometer works.
The number of isotopes The two peaks in the mass spectrum shows that there are 2 isotopes of boron - with relative isotopic masses of 10 and 11 on the 12C scale.
	Notes:  Isotopes are atoms of the same element (and so with the same number of protons), but with different masses due to having different numbers of neutrons. We are assuming (and shall do all through this page) that all the ions recorded have a charge of 1+. That means that the mass/charge ratio (m/z) gives you the mass of the isotope directly. The carbon-12 scale is a scale on which the mass of the 12C isotope weighs exactly 12 units.
The abundance of the isotopes The relative sizes of the peaks gives you a direct measure of the relative abundances of the isotopes. The tallest peak is often given an arbitrary height of 100 - but you may find all sorts of other scales used. It doesn't matter in the least. You can find the relative abundances by measuring the lines on the stick diagram. In this case, the two isotopes (with their relative abundances) are: boron-10 23 boron-11 100 Working out the relative atomic mass The relative atomic mass (RAM) of an element is given the symbol Ar and is defined as: The relative atomic mass of an element is the weighted average of the masses of the isotopes on a scale on which a carbon-12 atom has a mass of exactly 12 units. A "weighted average" allows for the fact that there won't be equal amounts of the various isotopes. The example coming up should make that clear. Suppose you had 123 typical atoms of boron. 23 of these would be 10B and 100 would be 11B. The total mass of these would be (23 x 10) + (100 x 11) = 1330 The average mass of these 123 atoms would be 1330 / 123 = 10.8 (to 3 significant figures). 10.8 is the relative atomic mass of boron. Notice the effect of the "weighted" average. A simple average of 10 and 11 is, of course, 10.5. Our answer of 10.8 allows for the fact that there are a lot more of the heavier isotope of boron - and so the "weighted" average ought to be closer to that. The mass spectrum for zirconium The number of isotopes The 5 peaks in the mass spectrum shows that there are 5 isotopes of zirconium - with relative isotopic masses of 90, 91, 92, 94 and 96 on the 12C scale. The abundance of the isotopes This time, the relative abundances are given as percentages. Again you can find these relative abundances by measuring the lines on the stick diagram. In this case, the 5 isotopes (with their relative percentage abundances) are: zirconium-90 51.5 zirconium-91 11.2 zirconium-92 17.1 zirconium-94 17.4 zirconium-96 2.8
	Note:  You almost certainly wouldn't be able to measure these peaks to this degree of accuracy, but your examiners may well give you the data in number form anyway. We'll do the sum with the more accurate figures.
Working out the relative atomic mass Suppose you had 100 typical atoms of zirconium. 51.5 of these would be 90Zr, 11.2 would be 91Zr and so on.
	Note:  If you object to the idea of having 51.5 atoms or 11.2 atoms and so on, just assume you've got 1000 atoms instead of 100. That way you will have 515 atoms, 112 atoms, etc. Most people don't get in a sweat over this, and just use the numbers as they are!
The total mass of these 100 typical atoms would be (51.5 x 90) + (11.2 x 91) + (17.1 x 92) + (17.4 x 94) + (2.8 x 96) = 9131.8 The average mass of these 100 atoms would be 9131.8 / 100 = 91.3 (to 3 significant figures). 91.3 is the relative atomic mass of zirconium.