WACE Chemistry
Isotopes and Relative Atomic Mass: What Every WACE Chemistry Student Needs to Know
Relative atomic mass is one of those topics where students lose marks not because the chemistry is hard, but because they mix up mass number with atomic mass, or forget to use fractional abundances instead of percentages. WACE markers see these slips constantly, and they cost points in what should be straightforward calculation questions. Getting the fundamentals locked in early makes every subsequent Unit 1 topic easier.
What the syllabus asks
For the ATAR course examination, you need to be able to:
- Describe what isotopes are and explain why they share the same electron configuration.
- Write and interpret isotope notation in both the nuclide symbol format and hyphen notation.
- Define relative atomic mass (Ar) and explain what it means as a ratio.
- Calculate Ar from isotopic composition, and work backwards to find isotopic abundances when Ar is given.
The idea, explained
What are isotopes?
Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons. Because the number of protons defines the element (the atomic number, Z), isotopes sit in exactly the same position on the periodic table. A neutral atom has the same number of electrons as protons, so all isotopes of an element share an identical electron configuration.
Because chemical behaviour is controlled by electron configuration, isotopes of the same element react in the same ways. Their physical properties, however, differ because their mass numbers differ (mass number A = protons + neutrons). Different masses mean different densities, different rates of diffusion and effusion, and, in some cases, radioactive instability.
Writing isotope notation
There are two equivalent ways to write a specific isotope:
- Nuclide symbol: the mass number A appears at the top left and the atomic number Z at the bottom left of the element symbol. For example, carbon-12 is written as 12 over 6, then C (often shown as ¹²₆C).
- Hyphen notation: simply the element symbol followed by a hyphen and the mass number, for example C-12, C-13, or U-235.
Carbon has three naturally occurring isotopes, C-12, C-13, and C-14. All three have Z = 6 protons and 6 electrons. Their neutron counts are 6, 7, and 8 respectively (calculated as A minus Z). C-12 and C-13 are stable; C-14 is radioactive.
Relative atomic mass (Ar)
The relative atomic mass of an element is the ratio of the average mass of an atom of that element to one-twelfth the mass of a carbon-12 atom. Because it is a ratio, Ar has no units. The values printed on your periodic table are these weighted averages, which is why they are almost never whole numbers.
The formula is:
Ar = sum of (isotope mass × fractional abundance)
Fractional abundance is the percentage divided by 100. Always convert percentages before substituting into the formula.
Worked example 1: calculating Ar
Chlorine has two naturally occurring isotopes: Cl-35 (mass 34.969, abundance 75.78%) and Cl-37 (mass 36.966, abundance 24.22%).
Ar(Cl) = (34.969 × 0.7578) + (36.966 × 0.2422) = 26.501 + 8.953 = 35.45
This matches the periodic table value of approximately 35.5. Notice that Ar sits much closer to 35 than to 37, reflecting the roughly 3:1 dominance of Cl-35.
Worked example 2: finding abundances from Ar
Boron has two isotopes, B-10 (mass 10.013) and B-11 (mass 11.009). The relative atomic mass of boron is 10.81. Find the percentage abundance of each isotope.
Let x = fractional abundance of B-10, so (1 - x) = fractional abundance of B-11.
10.81 = (10.013 × x) + (11.009 × (1 - x)) 10.81 = 10.013x + 11.009 - 11.009x 10.81 - 11.009 = -0.996x -0.199 = -0.996x x = 0.1998, so B-10 is approximately 19.98% 1 - x = 0.8002, so B-11 is approximately 80.02%
The heavier isotope dominates, which is why Ar at 10.81 sits much closer to 11 than to 10.
What the exam asks
In the ATAR course examination, Ar questions typically fall into two types. The first gives you isotope masses and percentage abundances and asks you to calculate Ar. The second gives you Ar and the mass of each isotope, then asks you to find the percentage abundance of one or both isotopes. Both types require the same formula, just rearranged. You may also be asked to explain why isotopes have the same chemical properties (same electron configuration) or why Ar is not a whole number (it is a weighted average over multiple isotopes).
Common mistakes
- Using percentage abundances directly instead of fractional abundances. Dividing by 100 is essential before multiplying by isotope mass. Forgetting this step gives an answer roughly 100 times too large.
- Confusing mass number with relative atomic mass. Mass number (A) is always a whole number and refers to one specific isotope. Ar is a weighted average and is almost never a whole number.
- Forgetting that neutrons = A minus Z. When a question asks how many neutrons an isotope contains, subtract the atomic number from the mass number, not the other way around.
- Stating that isotopes have different chemical properties. Isotopes share identical electron configurations and therefore identical chemical behaviour. Different physical properties (mass, density, radioactivity) are fair game, but chemical properties are the same.
- Leaving units on Ar. Because relative atomic mass is a ratio, it is dimensionless. Writing "g/mol" or "amu" after your answer will cost marks.
If you want to work through practice problems on this topic with immediate, personalised feedback, Avocado's AI-native tutoring service has a dedicated lesson ready for you: Isotopes and Relative Atomic Mass.