Isotopes and Relative Atomic Mass

GCSE Chemistry · Atomic Structure

Isotopes

Isotopes are atoms of the same element that have the same number of protons but a different number of neutrons. Because they have the same number of protons (and therefore electrons), isotopes have identical chemical properties. However, they differ in mass.

For example, chlorine has two naturally occurring isotopes:

Chlorine-35 (¹⁷Cl): 17 protons, 18 neutrons
Chlorine-37 (¹⁷Cl): 17 protons, 20 neutrons

Both isotopes react in exactly the same way because chemical reactions depend on electrons, not neutrons.

Mass Number and Atomic Number

Every atom is described by two numbers:

Atomic number (bottom number): the number of protons in the nucleus. This defines the element.
Mass number (top number): the total number of protons + neutrons in the nucleus.

Number of neutrons = mass number − atomic number

For example, carbon-14 has atomic number 6 and mass number 14, so it contains 6 protons and 8 neutrons.

Relative Atomic Mass (Ar)

The relative atomic mass (Ar) of an element is the weighted average mass of all its naturally occurring isotopes, taking into account their relative abundances. It is measured relative to carbon-12, which is defined as exactly 12.

Because it is a ratio, relative atomic mass has no units.

Calculating Relative Atomic Mass

To calculate Ar, you use the formula:

Ar = Σ (isotope mass × percentage abundance) ÷ 100

Worked Example: Chlorine

Chlorine exists as 75% chlorine-35 and 25% chlorine-37.

Ar = (35 × 75 + 37 × 25) ÷ 100

Ar = (2625 + 925) ÷ 100

Ar = 3550 ÷ 100

Ar = 35.5

This is why chlorine's relative atomic mass on the periodic table is 35.5, not a whole number.

Worked Example: Boron

Boron has two isotopes: boron-10 (20%) and boron-11 (80%).

Ar = (10 × 20 + 11 × 80) ÷ 100

Ar = (200 + 880) ÷ 100

Ar = 10.8

Working Backwards

You may be asked to calculate the percentage abundance of isotopes given the Ar. For two isotopes, if one has abundance x%, the other has (100 − x)%.

Example

Copper has Ar = 63.5. Its isotopes are Cu-63 and Cu-65. Find the abundance of each.

Let abundance of Cu-63 = x%

63x + 65(100 − x) = 63.5 × 100

63x + 6500 − 65x = 6350

−2x = −150

x = 75

So copper is 75% Cu-63 and 25% Cu-65.

Key Exam Points

Isotopes have the same chemical properties but different physical properties (e.g. density, rate of diffusion)
The Ar on the periodic table is an average, which is why it is often not a whole number
You must be comfortable calculating Ar from abundances and working backwards
Isotopes are important in medicine (radioactive tracers), dating rocks (carbon-14), and nuclear energy (uranium-235 vs uranium-238)