IMAT Chemistry · Atomic Structure

Isotopes and Relative Atomic Mass

Isotopes are atoms of one element with different numbers of neutrons; the relative atomic mass is the abundance-weighted average of their masses.

All Atomic Structure notes

Why this matters

Isotopes turn up inside the counting questions (an oxygen isotope in 2017, a bromine isotope in 2022), and the 2019 paper asked for the relative atomic mass of a mixture of two hydrogen isotopes.

Concept 1 of 2: Isotopes: same element, different number of neutrons

Chemistry is decided by electrons, and the number of electrons in a neutral atom equals the number of protons. Extra neutrons add mass but no charge, so they change almost nothing chemically. That is why isotopes of an element react in the same way but have different masses.

Definition

Isotopes are atoms with the same atomic number $Z$ but different mass numbers $A$ , so different numbers of neutrons.

Same number of protons and electrons, same electron configuration, same chemical properties.
Different mass, so slightly different physical properties (density, rate of diffusion).
Some isotopes are radioactive (tritium, carbon-14), most are stable.
An isotope is named by its mass number: chlorine-37 or ${}^{37}\mathrm{Cl}$ .

Isotope	Protons	Neutrons	Note
Hydrogen-1 (protium)	1	0	Over 99.9% of natural hydrogen; the only atom with no neutron
Hydrogen-2 (deuterium, D)	1	1	Stable; $\mathrm{D_2O}$ is heavy water
Hydrogen-3 (tritium, T)	1	2	Radioactive (beta emitter)
Carbon-12	6	6	Defines the atomic mass scale: exactly 12
Carbon-14	6	8	Radioactive; used to date once-living material
Chlorine-35	17	18	About 75% of natural chlorine
Chlorine-37	17	20	About 25% of natural chlorine

Practice this conceptself-check · 3 quick reps

Same mass number does not make two atoms isotopes

Isotopes share the atomic number, not the mass number. Carbon-14 and nitrogen-14 have the same mass number but are different elements. Two atoms with the same

Z

and different

A

are isotopes.

Concept 2 of 2: Relative atomic mass from isotope abundances

A sample of an element is a mixture of its isotopes, so its average atom is a weighted mix. Each isotope pulls the average towards its own mass in proportion to how common it is. The result always lies between the lightest and heaviest isotope, closer to the more abundant one.

Definition

The relative atomic mass $A_r$ is the average mass of the atoms of an element, weighted by abundance, on a scale where one atom of carbon-12 is exactly 12.

It has no units (it is a ratio).
It is usually not a whole number, because it averages several isotopes.
For a diatomic gas, the relative molecular mass is twice $A_r$ ( $\mathrm{Cl_2}$ : 71), but $A_r$ itself is per atom.
With two isotopes you can also work backwards: from $A_r$ to the abundances.

Relative atomic mass

A_r = \frac{\sum (\text{isotope mass} \times \%\ \text{abundance})}{100}

isotope massrelative mass of each isotope, close to its mass number
% abundancepercentage of atoms of that isotope in the natural element

Worked example

Natural chlorine is 75% chlorine-35 and 25% chlorine-37. Find its relative atomic mass.

Practice this conceptself-check · 3 quick reps

A simple average ignores abundance

The relative atomic mass is a WEIGHTED average. Only when the two isotopes are equally common does it equal the simple average of their masses. An option exactly halfway between two isotope masses is a trap unless the abundances are equal.

Relative atomic mass is per atom, not per molecule

For hydrogen, chlorine or any diatomic gas, the relative atomic mass refers to one atom. Doubling it gives the relative molecular mass of the gas. Check which one the question asks for before choosing.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Relative atomic mass from isotope abundances
Relative atomic mass
$A_r = \frac{\sum (\text{isotope mass} \times \%\ \text{abundance})}{100}$

Reference tables (1)

Isotopes: same element, different number of neutrons7 rows

Isotope	Protons	Neutrons	Note
Hydrogen-1 (protium)	1	0	Over 99.9% of natural hydrogen; the only atom with no neutron
Hydrogen-2 (deuterium, D)	1	1	Stable; $\mathrm{D_2O}$ is heavy water
Hydrogen-3 (tritium, T)	1	2	Radioactive (beta emitter)
Carbon-12	6	6	Defines the atomic mass scale: exactly 12
Carbon-14	6	8	Radioactive; used to date once-living material
Chlorine-35	17	18	About 75% of natural chlorine
Chlorine-37	17	20	About 25% of natural chlorine

Watch out for (3)

Same mass number does not make two atoms isotopes
→ Isotopes: same element, different number of neutrons
A simple average ignores abundance
→ Relative atomic mass from isotope abundances
Relative atomic mass is per atom, not per molecule
→ Relative atomic mass from isotope abundances

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