Explaining and how to calculate the relative atomic mass RAM or Ar of
How to calculate relative atomic mass
- Every atom has its own unique relative atomic
mass (RAM) 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
(amu = relative atomic mass unit).
The relative atomic
mass scale is now based on an isotope of carbon, namely, carbon-12,
which is given the value of 12.0000 amu.
- The unit 'amu' is now being replaced by a
lower case u, where u is the symbol for the unified atomic mass
- Therefore one atom of carbon, isotopic mass
12, equals 12 u, or,
- 1 u = 1/12th the
mass of one atom of the carbon-12 isotope.
- Note that for the standard nuclide notation,
, the top
left number is the mass number (12) and the bottom left number is the
atomic/proton number (6).
- 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!
- Examples are shown in the Periodic Table
- (i) Because of the presence of
neutrons in the nucleus, the relative atomic mass is usually at least double
the atomic/proton number because there are usually more neutrons than
protons in the nucleus (mass proton = 1, neutron = 1). Just scan the
periodic table above and examine the pairs of numbers.
- You should also notice that generally
speaking the numerical difference between the atomic/proton number and the
relative atomic mass tends to increase with increasing atomic number. This
has consequences for nuclear
- (ii) For many calculation
purposes, relative atomic masses are usually quoted and used at this
academic level to zero or one decimal place eg.
- e.g. hydrogen H = 1.0 or ~1, calcium Ca= 40.0 or
~40, chlorine Cl = 35.5, copper Cu = 63.6 or ~64, silver Ag 107.9 or ~108
- At A level, values of relative
atomic masses may be quoted to one or two decimal places.
- Many atomic masses are known to an accuracy
of four decimal places, but for some elements, isotopic composition varies
depending on the mineralogical source, so four decimal places isn't
necessarily more accurate!
- 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 never whole integer numbers.
- Isotopes are atoms of the same element with different
masses due to different numbers of neutrons. The very accurate relative 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.
the nuclide notation for 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 the average mass of all the
isotopic atoms present in the element compared to 1/12th
the mass of a carbon-12 atom (relative isotopic mass of 12.0000).
- So, in calculating relative atomic mass you
must take into account the
different isotopic masses of the same elements, but also their %
abundance in the element.
- Therefore you need to know the
percentage (%) of each isotope of an element in order to accurately
calculate the element's relative atomic mass.
- For approximate calculations of relative
atomic mass you can just use the mass numbers of the isotopes, which are
obviously all integers ('whole numbers'!) e.g. in the two calculations
- To the nearest whole number, isotopic
mass = mass number for a specific isotope.
Examples of relative atomic mass calculations
for GCSE/IGCSE/AS level students
How do I calculate relative atomic mass?
Example 1.1 Calculating the relative atomic mass of bromine
- bromine consists of
two isotopes, 50% 79Br and 50% 81Br, calculate the Ar of bromine
from the mass numbers (top left numbers).
- Ar = [ (50 x 79) + (50
x 81) ] /100 = 80
- So the relative atomic mass of
bromine is 80 or RAM or Ar(Br) = 80
- 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.
- The element bromine is the only case I know where averaging
the isotopic masses actually works! so beware!
Example 1.2 Calculating the relative atomic mass of chlorine
- chlorine consists of
two isotopes, 75% chlorine-35 and 25% chlorine-37, so using
these two mass numbers ...
- ... think of the data based on 100
atoms, so 75 have a mass of 35 and 25 atoms have a mass of 37.
- The average mass = [ (75 x 35) +
(25 x 37) ] / 100 = 35.5
- So the relative atomic mass of
chlorine is 35.5 or RAM or Ar(Cl) = 35.5
- 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.
Examples for Advanced Level Chemistry students only
How to calculate relative atomic mass with accurate relative
Using data from modern very accurate mass spectrometers
Accurate calculation of relative atomic mass
(need to know and define what relative isotopic mass is)
is defined as 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 relative isotopic mass of the cobalt-5
This definition of relative isotopic mass is
a completely different from the definition of relative atomic mass, except
both are based on the same international standard of atomic mass i.e. 1 unit
= 1/12th the mass of a carbon-12 isotope (12C).
If we were to redo the calculation of the
relative atomic mass of chlorine (example
1.1 above), which is quite adequate for GCSE purposes (and maybe A level too),
but more accurately at A
level, we might 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!)
Mass Spectrometer and isotope analysis
on the GCSE-AS(basic) Atomic Structure Notes, with further RAM calculations.
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
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 from chemical analysis of reacting
masses but now
mass spectrometers can sort
out all of the isotopes present and their relative abundance.
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
data books actually quote 18.7 and 81.3, but we didn't use the very accurate
relative isotopic masses mentioned above!)
On other pages
Atomic structure and Relative Formula
type in answer
Honly or multiple choice
OTHER CALCULATION PAGES
What is relative atomic mass?,
relative isotopic mass & calculating relative atomic mass
formula/molecular mass of a compound or element molecule
Law of Conservation of Mass and simple reacting mass calculations
Composition by percentage mass of elements
in a compound
Empirical formula and formula mass of a compound from reacting masses
(easy start, not using moles)
Reacting mass ratio calculations of reactants and products
moles) and brief mention of actual percent % yield and theoretical yield,
and formula mass determination
Introducing moles: The connection between moles, mass and formula mass - the basis of reacting mole ratio calculations
(relating reacting masses and formula
moles to calculate empirical formula and deduce molecular formula of a compound/molecule
(starting with reacting masses or % composition)
Moles and the molar volume of a gas, Avogadro's Law
Reacting gas volume
ratios, Avogadro's Law
and Gay-Lussac's Law (ratio of gaseous
Molarity, volumes and solution
concentrations (and diagrams of apparatus)
How to do acid-alkali
titration calculations, diagrams of apparatus, details of procedures
Electrolysis products calculations (negative cathode and positive anode products)
e.g. % purity, % percentage & theoretical yield, dilution of solutions
(and diagrams of apparatus), water of crystallisation, quantity of reactants
required, atom economy
Energy transfers in physical/chemical changes,
Gas calculations involving PVT relationships,
Boyle's and Charles Laws
Radioactivity & half-life calculations including
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