1.
Explaining and how to calculate the relative atomic mass RAM or A_{r} of
an element
(a)
Introduction  defining relative atomic mass  carbon12 scale
 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 of an element takes into
account the different masses of the isotopes of that element and the
abundance of the isotopes in the naturally occurring element (meaning the
percentage of each isotope present).
 Relative atomic mass is defined and explained below,
and examples of how to calculate it from data.

The relative atomic
mass scale is now based on an isotope of carbon, namely, carbon12,
nuclide symbol
,
which is given the arbitrary value of 12.0000 amu by international agreement.
 The unit 'amu' is now being replaced by a
lower case u, where u is the symbol for the unified atomic mass
unit.
 Therefore one atom of carbon, isotopic mass
12, equals 12 u, or,
 1 u = ^{1}/_{12}th the
mass of one atom of the carbon12 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).
 Since the relative atomic mass of an element is now
based on the carbon12 isotope
it can now be defined as ...
 ...
relative atomic mass equals the average mass of all the atoms in an element
compared to ^{1}/_{12}th the mass of a carbon12 atom
(carbon12 isotope).
 Examples are shown in the Periodic Table
diagram above.
 Note
 (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
stability.
 (ii) For many calculation
purposes, relative atomic masses are usually quoted and used at this
academic level (GCSE/IGCSE/O level) to zero or one decimal place eg.
 hydrogen H = 1.008 or ~1; calcium
Ca = 40.08 or
~40.0; chlorine Cl = 35.45 ~35.5, copper Cu =
63.55 or ~63.5/64, silver Ag = 107.9 or ~108
etc.
 At Advanced 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!
 Note that in the case of carbon, there are three
isotopes carbon12 ^{12}C the most abundant and small amounts
of carbon13 ^{13}C and carbon14 ^{14}C. The average
calculated mass of the atoms compared to carbon 12 is 12.01, but for
most purposes at preuniversity level, 12.0 is sufficient accuracy.
 In using the symbol A_{r} 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, carbon12, ^{12}C = 12.0000
units exactly, for most purposes C = 12 is used for simplicity.
 For
example
hydrogen1,
hydrogen2, and
hydrogen3, are
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!

See
also GCSE/IGCSE/AS Atomic Structure Notes
 Therefore, a stricter definition of
relative atomic mass (A_{r}) is that it equals the average mass of all the
isotopic atoms present in the element compared to ^{1}/_{12}th
the mass of a carbon12 atom.
 AND, the relative isotopic mass of carbon12 is
assigned a numerical value 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
below.
 To the nearest whole number, isotopic
mass = mass number for a specific isotope.
 If an element only has one isotope, relative
atomic mass = relative mass of this isotope.
 A good example is fluorine.
 All fluorine
atoms have a mass of 19 (^{19}F), therefore its
relative atomic mass is 19 and no calculation is needed.
Above is typical periodic table used in GCSE sciencechemistry specifications
and I've 'usually' used these values in my exemplar calculations to cover most
syllabuses
TOP OF PAGE
and subindex
(b) Examples of relative atomic mass calculations
for GCSE 91/IGCSE/AS/A level chemistry students
How do I calculate relative atomic mass?
You
can calculate relative atomic mass from isotopic abundances
 For accurate chemical calculations relative atomic
mass must be used and not an individual mass number.
 Therefore relative atomic mass takes into account all
the different 'stable' isotopes of an element which are naturally present.
 The relative atomic mass is the average mass and is
quite easily calculated from the percentage composition (% abundance).
 The presence of isotopes accounts for why some
relative atomic masses are not even close to a whole number.
 Some relative atomic masses are nearly whole numbers
due to coincidence of % isotopes, others because one isotope might dominate
the composition with only tiny amounts of lighter or heavier isotopes.

Example 1.1 Calculating the relative atomic mass of bromine
and
 bromine consists of
two isotopes, 50% ^{79}Br and 50% ^{81}Br, calculate the A_{r} of bromine
from the mass numbers (top left numbers).
 Think of the calculation in terms of '100 atoms'
 A_{r} = [ (50 x 79) + (50
x 81) ] /100 = 80
 So the relative atomic mass of
bromine is 80 or RAM or A_{r}(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
bromine79 and bromine81.
 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
based on the
and
isotopes
 Chlorine consists of
two isotopes, 75% chlorine35 and 25% chlorine37, so using
these two mass numbers ...
 ... again 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 A_{r}(Cl) =
35.5
 Note: ^{35}Cl and ^{37}Cl 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: Calculating the relative atomic
mass of copper from its isotopic composition (isotope abundance)
 Naturally occurring copper consists of 69.2% copper63
(^{63}Cu) and 30.8% copper65 (^{65}Cu)
 Still think in terms of 100 atoms and don't be put
off by decimal fractions, it still works out correctly because 69.2 + 30.8 =
100!
 average mass = relative atomic mass of copper
= {(63 x 69.2) + (65 x 30.8)} / 100 =
63.6
 
 Example 1.4: Silver atoms consist of 51.4% of
the isotope ^{107}Ag and 48.6% of the isotope ^{109}Ag
 Calculate the relative atomic mass of silver.



(51.4 x 107) +
(48.6 x 109) 
5499.8 + 5297.4 

A_{r}(Ag)

= 
 
=
 
= 108.0 


100 
100 

 The relative atomic mass of silver is 108.0 (to 1
decimal place)
 
 Example 1.5: Europium atoms consist of 47.8%
Eu151 and 52.2% of Eu153
 Calculate the relative atomic mass of europium.



(47.8 x 151) +
(52.2 x 153) 
7217.8 + 7986.6 

A_{r}(Eu)

= 
 
=
 
= 152.0 


100 
100 

 The relative atomic mass of europium is 152.0 (to 1
decimal place)
 
 Example 1.6: Atoms of the element silicon
consist of 92.2% silicon28, 4.7% silicon29 and 3.1% of silicon30.
 Calculate the relative atomic mass of silicon.



(92.2 x 28) + (4.7
x 29) + (3.1 x 30) 
2581.6 + 136.3 + 93.0 

A_{r}(Si)

= 
 
=
 
= 28.1 


100 
100 

 The relative atomic mass of silicon is 28.1 (to 1
decimal place or 3 significant figures)
 
 See below and
mass Spectrometer and isotope analysis
on the GCSEAdvanced A Level (basic) Atomic Structure Notes, with further
relative atomic mass calculations.
(c) Examples for Advanced A Level Chemistry students only
How to calculate relative atomic mass with accurate relative
isotopic masses
Using data from modern very accurate mass spectrometers
(1)
Very accurate calculation of relative atomic mass
(need to know and define what relative isotopic mass is)
Relative
isotopic mass
is defined as the accurate mass of a single isotope of
an element compared to ^{1}/_{12}th the mass of a
carbon12 atom e.g. the accurate relative isotopic mass of the cobalt5
is 58.9332
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 u)
= 1/12th the mass of a carbon12 isotope (^{12}C).
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% ^{35}Cl of
isotopic mass 34.9689 and 24.23% ^{37}Cl of isotopic mass 36.9658
so A_{r}(Cl) = [(75.77 x
34.9689) + (24.23 x 36.9658)] / 100
=
35.4527
(but 35.5 is usually ok in calculations preuniversity!)
See also
Mass Spectrometer and isotope analysis
on the GCSE/A level Atomic Structure Notes, with further RAM calculations.
(2)
Calculations of % composition of isotopes
It is possible to do the reverse
of a relative atomic mass calculation if you know the A_{r} and
which isotopes are present.
It involves a little bit of
arithmetical algebra.
The A_{r} of boron is
10.81 and consists of only two isotopes, boron10 and boron11
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 100X is equal to % of boron11
Therefore A_{r}(B) = (X
x 10) + [(100X) 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% ^{10}B and
81% ^{11}B
(the
data books actually quote 18.7 and 81.3, but we didn't use the very accurate
relative isotopic masses mentioned above!)
TOP OF PAGE
and subindex
On other pages
on
Atomic structure and
Relative Formula
Mass
Selfassessment Quizzes on relative atomic mass
type in answer
QUIZ or
multiple choice
QUIZ
APPENDIX 1. A typical periodic table used in preuniversity examinations
Above is typical periodic table used in GCSE sciencechemistry specifications in
doing chemical calculations,
and I've 'usually' used these values in my exemplar calculations to cover most
syllabuses
TOP OF PAGE
and subindex
(d)
APPENDIX 2. Table of relative atomic masses for elements 1 to 92
Notes on
the relative atomic mass data:
(i) The list of relative atomic mass are in
alphabetical order by element name, together with chemical symbol and
proton/atomic number from 1 to 92.
(ii) The relative atomic masses are quoted to two decimal
places, though it is essential to be aware that values in preuniversity
examinations might be rounded to the nearest integer or one decimal place.
(iii) Transuranium elements have been eliminated because
their isotopic composition varies depending on the source e.g. cyclotron,
nuclear reactor etc. AND all their isotopes are highly radioactive and most are
very unstable (so your relative atomic mass changes all the time!)
(iv) * radioactive, mass number of most stable isotope
quoted
Chemical Symbol

Element name

Atomic No. Z

Relative atomic mass 
Ac 
Actinium 
89 
227.03 
Al 
Aluminium 
13 
26.98 
Sb 
Antimony 
51 
121.75 
Ar 
Argon 
18 
39.95 
As 
Arsenic 
33 
74.92 
At 
Astatine 
85 
210
* 
Ba 
Barium 
56 
137.33 
Be 
Beryllium 
4 
9.01 
Bi 
Bismuth 
83 
208.98 
B 
Boron 
5 
10.81 
Br 
Bromine 
35 
79.90 
Cd 
Cadmium 
48 
112.41 
Cs 
Caesium 
55 
132.91 
Ca 
Calcium 
20 
40.08 
C 
Carbon 
6 
12.01 
Ce 
Cerium 
58 
140.12 
Cl 
Chlorine 
17 
35.45 
Cr 
Chromium 
24 
52.00 
Co 
Cobalt 
27 
58.93 
Cu 
Copper 
29 
63.55 
Dy 
Dysprosium 
66 
162.50 
Er 
Erbium 
68 
167.26 
Eu 
Europium 
63 
151.97 
F 
Fluorine 
9 
19.00 
Fr 
Francium 
87 
223
* 
Gd 
Gadolinium 
64 
157.25 
Ga 
Gallium 
31 
69.72 
Ge 
Germanium 
32 
72.60 
Au 
Gold 
79 
196.97 
Hf 
Hafnium 
72 
178.49 
He 
Helium 
2 
4.00 
Ho 
Holmium 
67 
164.93 
H 
Hydrogen 
1 
1.01 
In 
Indium 
49 
114.82 
I 
Iodine 
53 
126.90 
Ir 
Iridium 
77 
192.22 
Fe 
Iron 
26 
55.85 
Kr 
Krypton 
36 
83.80 
La 
Lanthanum 
57 
138.91 
Pb 
Lead 
82 
207.20 
Li 
Lithium 
3 
6.94 
Lu 
Lutetium 
71 
174.97 
Mg 
Magnesium 
12 
24.31 
Mn 
Manganese 
25 
54.94 
Hg 
Mercury 
80 
200.59 





Chemical Symbol

Element name

Atomic No.
Z

Relative atomic mass 
Mo 
Molybdenum 
42 
95.94 
Nd 
Neodymium 
60 
144.24 
Ne 
Neon 
10 
20.18 
Ni 
Nickel 
28 
58.69 
Nb 
Niobium 
41 
92.91 
N 
Nitrogen 
7 
14.01 
Os 
Osmium 
76 
190.20 
O 
Oxygen 
8 
16.00 
Pd 
Palladium 
46 
106.42 
P 
Phosphorus 
15 
30.97 
Pt 
Platinum 
78 
195.08 
Po 
Polonium 
84 
209
* 
K 
Potassium 
19 
39.10 
Pr 
Praseodymium 
59 
140.91 
Pm 
Promethium 
61 
145
* 
Pa 
Protactinium 
91 
231.04 
Ra 
Radium 
88 
226.03 
Rn 
Radon 
86 
222
* 
Re 
Rhenium 
75 
186.21 
Rh 
Rhodium 
45 
102.91 
Rb 
Rubidium 
37 
85.47 
Ru 
Ruthenium 
44 
101.07 
Sm 
Samarium 
62 
150.36 
Sc 
Scandium 
21 
44.96 
Se 
Selenium 
34 
78.96 
Si 
Silicon 
14 
28.09 
Ag 
Silver 
47 
107.87 
Na 
Sodium 
11 
23.00 
Sr 
Strontium 
38 
87.62 
S 
Sulfur 
16 
32.07 
Ta 
Tantalum 
73 
180.95 
Tc 
Technetium 
43 
98.91 
Te 
Tellurium 
52 
127.60 
Tb 
Terbium 
65 
158.93 
Tl 
Thallium 
81 
204.38 
Th 
Thorium 
90 
232.04 
Tm 
Thulium 
69 
168.93 
Sn 
Tin 
50 
118.71 
Ti 
Titanium 
22 
47.88 
W 
Tungsten 
74 
183.85 
U 
Uranium 
92 
238.03 
V 
Vanadium 
23 
50.94 
Xe 
Xenon 
54 
131.29 
Yb 
Ytterbium 
70 
173.04 
Y 
Yttrium 
39 
88.91 
Zn 
Zinc 
30 
65.39 
Zr 
Zirconium 
40 
91.22 

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Website content © Dr
Phil Brown 2000+. All copyrights reserved on revision notes, images,
quizzes, worksheets etc. Copying of website material is NOT
permitted. Exam revision summaries & references to science course specifications
are unofficial. 
Alphabetical order of the
elements of the periodic table symbol name atomic number: relative atomic
mass of Ac Actinium 89, relative atomic mass of Al Aluminium 13, relative
atomic mass of Sb Antimony 51, relative atomic mass of Ar Argon 18, relative
atomic mass of As Arsenic 33, relative atomic mass of At Astatine 85,
relative atomic mass of Ba Barium 56, relative atomic mass of Be Beryllium 4,
relative atomic mass of Bi Bismuth 83, relative atomic mass of B Boron 5,
relative atomic mass of Br Bromine 35, relative atomic mass of Cd Cadmium 48,
relative atomic mass of Cs Caesium 55, relative atomic mass of Ca Calcium 20,
relative atomic mass of C Carbon 6, relative atomic mass of Ce Cerium 