We have seen in the previous unit that atoms can be described by their atomic number (Z) and their mass number (A).

It is possible, however, for the number of nucleons present in the nucleus to differ in atoms of the same element.

An atom of a particular element is identified by the number of protons in its nucleus, ie its atomic number (Z). This means that the difference in the number of nucleons must be caused by a different number of neutrons being present in the nucleus.

Such atoms are still chemically identical but will differ in their mass numbers, due to the different numbers of neutrons in the nucleus.

These atoms are called isotopes.

Isotopes of a substance are defined as atoms of the same element which contain the same number of protons, but a varying number of neutrons.

Another way of describing isotopes is as follows:

Isotopes are atoms with the same atomic number, but with a different mass number.


Example 1

Hydrogen (symbol H) has three isotopes:


H 2 H 3 H
1 1 1

Isotopes of hydrogen

In the first isotope of hydrogen (noH) there is only one proton in the nucleus.

In the second isotope of hydrogen (noH), there is one proton but one neutron in the nucleus as well.

This isotope of hydrogen is known as hydrogen-2 or deuterium. The name is derived from the fact that there are two nuclear particles in the nucleus.

The third isotope of hydrogen (noH) contains one proton and two neutrons.

This isotope of hydrogen is known as hydrogen-3 or tritium. The name is derived from the fact that there are three nuclear particles in the nucleus.

Example 2

Chlorine (symbol Cl) has two isotopes - one with a mass number of 35, the other with a mass number of 37:


Cl 37 Cl    
17 17  

17 electrons           17 electrons

35 nucleons            37 nucleons

Isotopes of chlorine

Both of these atoms are found to behave in exactly the same way in a chemical reaction. The only difference is the different numbers of neutrons in the nucleus of each isotope.

In noCl the number of neutrons present is 18, calculated from the equation:

number of neutrons

= mass number (A) - atomic number (Z)

= 35 - 17

= 18 neutrons

An important fact to note is the proportions in which the isotopes of elements occur in nature. In chlorine, the proportion of noCl present to noCl is approximately 3 to 1.

The ratio will vary from substance to substance.

For example sodium (symbol Na) has three naturally occurring isotopes:


Na 23 Na 24 Na
11 11 11

The proportions in which these isotopes are found is as follows:


Na 23 Na 24 Na
11 11 11

        10 %

      85 %

  5 %

Another important question to consider is which isotope must be dealt with when speaking of chlorine or sodium? To answer this equation, we must look at relative atomic mass.

Relative atomic mass

Due to the fact that atoms have such little actual mass, scientists had to find alternative methods of expressing the mass of an atom.

They chose the carbon-12 (noC) isotope as a standard and stated that masses of all other atoms would be expressed relative to this standard.

In other words, if C has mass number (A) of 12, then carbon-12 has mass of 12. Thus hydrogen (A = 1) will have mass of 1. Magnesium (A = 24) will have mass of 24.

The masses of atoms relative to the carbon-12 isotope (noC) are called the relative atomic masses.

Relative atomic mass has the symbol     Ar.

It is defined as the number of times the "average" atom of an element is heavier than 1/12th of the mass of a carbon-12 isotope.

Note that relative atomic mass has no units. It is simply a comparison.

The effect of isotopes on relative atomic mass

The presence of isotopes of a particular element has an effect on the value of the relative atomic mass.

Isotopes occur in various proportions depending on what element is being considered, as seen previously.The ratio of isotopes present must be considered when calculating the relative atomic mass of an element.

Consider the following examples.

Example 1

Isotopes of hydrogen

The ratio of the three isotopes of hydrogen found naturally is:

noH = 97 %

noH = 2 %

noH = 1 %

To calculate the relative atomic mass of hydrogen, we do the following calculation:

Relative atomic mass
=(no x 1) + (no x 2) + (no x 3)  ie % of the isotope found naturally multiplied by its mass number
= 0,97 + 0,04 + 0,03
= 1,04 mass units

This is only an approximate value as the percentages are not exact. This calculation allows for an "average" relative atomic mass to be calculated for hydrogen, based on all the isotopes present according to their naturally occurring ratio.

When the relative atomic mass of an element is used as a mass number, the relative atomic mass is rounded off to the nearest whole number.

Example 2

Naturally occurring magnesium (symbol Mg) has three stable isotopes:


Mg 25 Mg 26 Mg
12 12 12

Their relative abundance is:

          79 %

       10,5 %

   10,5 %

Relative atomic mass



= (no x 24) + (no x 25) + (no+ 26)

= 18,96 + 2,625 + 2,73

= 24,315 mass units

Thus, Ar for magnesium is equal to 24,315.

Test yourself
Gallium consist of 60 % gallium 69 and 40 % gallium 71. What is the relative atomic mass of gallium? Fill in the missing numbers in the following calculation. Fill in all answers before checking.

Relative molecular mass and formula mass

Click here for a periodic table.

The relative molecular mass (Mr) is the mass of a molecule compared to one-twelfth of the mass of an atom of carbon-12.

It is found by adding together the relative atomic masses of the atoms in the molecule.


Mr (H2O) = 2 x 1 + 16 = 18

Mr (CO2) = 12 + 2 x 16 = 44

The term "relative molecular mass" should only be used for molecules. Giant structures like crystals are represented by formulae which show the simplest ratio of atoms or ions in the structure. In this case, the term "relative formula mass" should be used.

Relative formula mass is the mass of the formula of a compound compared to one-twelfth of the mass of an atom of carbon-12.


Relative formula mass (CuSO4) = 63,5 + 32 + 4 x 16 = 159,5

Test yourself
Using the values from the periodic table, link the following formulae with the appropriate molecular or formula mass.
Drag the number from column 3 to column 2.

© learnthings Ltd 2003