Explaining and how to calculate the relative atomic mass RAM or
Ar of an element
Introduction

Every atom has its own unique atomic mass based on a standard comparison or
relative scale e.g. it has been based on hydrogen H = 1 amu and oxygen O = 16 amu in the
past.

The relative atomic mass scale is now based on an isotope of carbon, carbon-12,
which is given the value of 12.0000 amu.

In other words the relative atomic mass of an element is now based on the arbitrary value
of the carbon-12 isotope being assigned a mass of 12.0000 by international agreement!
,
o
Examples are shown in the Periodic Table diagram above.
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Note that because of the presence of neutrons in the nucleus, the relative atomic
mass is usually at least double the atomic/proton number because there usually at
the number of neutrons as protons in the nucleus (mass proton = 1, neutron = 1).
o
Also note, that for many calculations purposes, relative atomic masses are usually
quoted and used at this academic level to one decimal place eg.
o
hydrogen H = 1.0 or 1, calcium Ca= 40.0 or 40, chlorine Cl = 35.5, copper Cu = 63.6,
silver Ag 108 or 107.9 at A level etc.
o
Sometimes at A level, values of relative atomic masses to two decimal places may be
quoted.

In using the symbol Ar for RAM you should bear in mind that the letter A on its own usually
means the mass number of a particular isotope and amu is the acronym shorthand
for atomic mass units)

However there are complications due to isotopes and so very accurate atomic masses are
not whole numbers.

Isotopes are atoms of the same element with different masses due to different numbers of
neutrons. The very accurate atomic mass scale is based on a specific isotope of carbon,
carbon-12, 12C = 12.0000 units exactly, for most purposes C = 12 is used for simplicity.

For example
,
and
are the three isotopes of hydrogen, though the vast
majority of hydrogen atoms have a mass of 1. When their accurate isotopic masses, and
their % abundance are taken into account the average accurate relative mass for hydrogen
= 1.008, but for most purposes H = 1 is good enough!

The strict definition of relative atomic mass (Ar) is that it equals average mass of all the
isotopic atoms present in the element compared to 1/12th the mass of a carbon-12 atom.
o
So, you are taking into account the different isotopic masses of the same elements,
but also their % abundance in the element.
o
Therefore you need to know the percentage (%) of each isotope of an element in
order to accurately calculate the element's relative atomic mass.
Examples of relative atomic mass calculations for GCSE/IGCSE/AS level students



and
Example 1.1: bromine consists of 50% 79Br and 50% 81Br, calculate the Ar of bromine.
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Ar = [ (50 x 79) + (50 x 81) ] /100 = 80
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So the relative atomic mass of bromine is 80 or RAM or Ar(Br) = 80
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Note the full working shown. Yes, ok, you can do it in your head BUT many students
ignore the %'s and just average all the isotopic masses (mass numbers) given, in this
case bromine-79 and bromine-81.
and


Example 1.2: chlorine consists of 75% chlorine-35 and 25% chlorine-37.
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Think of the data based on 100 atoms, so 75 have a mass of 35 and 25 atoms have a
mass of 37.
o
The average mass = [ (75 x 35) + (25 x 37) ] / 100 = 35.5
o
So the relative atomic mass of chlorine is 35.5 or RAM or Ar(Cl) = 35.5
o
Note: 35Cl and 37Cl are the most common isotopes of chlorine, but, there are tiny
percentages of other chlorine isotopes which are usually ignored at GCSE/IGCSE and
Advanced GCE AS/A2 A level.
Example 1.3:
The mass number for any isotope is the sum of the protons and neutrons in the nucleus, and is
always an integer i.e. a whole number.
Examples for Advanced Level Chemistry students only
(a) Calculation of relative atomic mass
Relative isotopic mass = the accurate mass of a single isotope of an element compared to 1/12th the
mass of a carbon-12 atom e.g. the accurate mass of
is58.9332 !
If we were to redo the chlorine example 1.1 above, which is quite adequate for GCSE purposes, more
accurately at A level, we would do ....
chlorine is 75.77% 35Cl of isotopic mass 34.9689 and 24.23% 37Cl of isotopic mass 36.9658
so Ar(Cl) = [(75.77 x 34.9689) + (24.23 x 36.9658)] / 100 = 35.4527 (but 35.5 is usually ok in
calculations pre-university!)
See also Mass Spectrometer and isotope analysis on the GCSE-AS(basic) Atomic Structure Notes,
with further RAM calculations.
(b) Calculations of % composition of isotopes
It is possible to do the reverse of a relative atomic mass calculation if you know the Ar and which
isotopes are present.
It involves a little bit of arithmetical algebra.
The Ar of boron is 10.81 and consists of only two isotopes, boron-10 and boron-11
The relative atomic mass of boron was obtained accurately in the past and mass spectrometers can
sort out the isotopes present.
If you let X = % of boron 10, then 100-X is equal to % of boron-11
Therefore Ar(B) = (X x 10) + [(100-X) x 11) / 100 = 10.81
so, 10X -11X +1100 =100 x 10.81
-X + 1100 = 1081, 1100 - 1081 = X (change sides change sign!)
therefore X = 19
so naturally occurring boron consists of 19% 10B and 81% 11B (the data books quote 18.7 and 81.3)