What you'll learn
This revision guide covers isotopes and relative atomic mass, a fundamental topic in CIE IGCSE Chemistry that appears regularly across Paper 2 (Core and Extended) and Paper 4 (Extended). You'll learn how to identify isotopes from atomic notation, calculate relative atomic mass from isotopic abundances, and understand why mass spectrometry data appears in exam questions. This topic connects directly to atomic structure and provides essential skills for quantitative chemistry calculations.
Key terms and definitions
Isotope — atoms of the same element with the same number of protons but different numbers of neutrons, resulting in different mass numbers.
Mass number (A) — the total number of protons and neutrons in the nucleus of an atom.
Atomic number (Z) — the number of protons in the nucleus of an atom, which defines the element and equals the number of electrons in a neutral atom.
Relative atomic mass (Ar) — the weighted average mass of the isotopes of an element compared to 1/12th the mass of a carbon-12 atom, taking into account the abundance of each isotope.
Relative isotopic mass — the mass of a particular isotope of an element compared to 1/12th the mass of a carbon-12 atom.
Abundance — the proportion or percentage of each isotope present in a naturally occurring sample of an element.
Mass spectrometer — an analytical instrument that separates ions according to their mass-to-charge ratio, used to determine isotopic composition and abundance.
Core concepts
Atomic structure and isotope notation
Every atom consists of a nucleus containing protons and neutrons, surrounded by electrons in shells. The atomic number defines which element an atom belongs to because it determines the number of protons. All atoms of carbon have 6 protons; all atoms of chlorine have 17 protons.
Isotopes exist because atoms of the same element can have different numbers of neutrons. Carbon-12 and carbon-14 are both carbon (6 protons) but carbon-12 has 6 neutrons while carbon-14 has 8 neutrons.
Standard isotope notation uses the format:
$$^{A}_{Z}\text{X}$$
Where:
- X is the element symbol
- A is the mass number (protons + neutrons)
- Z is the atomic number (protons)
For example, $^{35}_{17}\text{Cl}$ represents chlorine-35 with 17 protons and 18 neutrons (35 - 17 = 18).
Key points about isotopes:
- Isotopes have identical chemical properties because they have the same number and arrangement of electrons
- Isotopes have different physical properties (such as density and rate of diffusion) because they have different masses
- Most elements exist as a mixture of isotopes in nature
- The isotopes of hydrogen have special names: protium ($^{1}\text{H}$), deuterium ($^{2}\text{H}$), and tritium ($^{3}\text{H}$)
Understanding relative atomic mass
The relative atomic mass does not equal the mass number for most elements because natural samples contain mixtures of isotopes. The Ar value on the periodic table represents a weighted average based on natural abundance.
Take chlorine as a commonly tested example. The periodic table shows Ar(Cl) = 35.5, not a whole number. This is because naturally occurring chlorine contains approximately 75% chlorine-35 and 25% chlorine-37. The relative atomic mass reflects this mixture.
The standard used for comparison is carbon-12, which is assigned a relative mass of exactly 12. All other atomic masses are compared to 1/12th of a carbon-12 atom. This is why relative atomic mass has no units—it's a ratio.
Calculating relative atomic mass from isotopic abundances
CIE IGCSE Chemistry exams regularly test your ability to calculate Ar from given isotopic data. The formula is:
$$\text{Relative atomic mass} = \frac{\sum(\text{isotopic mass} \times \text{abundance})}{\text{total abundance}}$$
When abundances are given as percentages, the total abundance is 100. When given as ratios or actual numbers, you must sum the abundances.
Step-by-step method:
- Multiply each isotopic mass by its abundance
- Add all these products together
- Divide by the total abundance (100 if using percentages)
- Give your answer to an appropriate number of significant figures (usually 1 decimal place)
This calculation appears frequently in Paper 2 Extended and Paper 4, often worth 2-3 marks. Examiners look for clear working and correct mathematical manipulation.
Interpreting mass spectrometry data
Mass spectrometry is the analytical technique used to determine isotopic composition. While detailed knowledge of how a mass spectrometer works is not required for IGCSE, you must be able to interpret mass spectrum data presented in exam questions.
A mass spectrum displays:
- x-axis: mass-to-charge ratio (m/z), which equals the mass number for singly charged ions
- y-axis: abundance (either as a percentage or relative height)
Exam questions provide mass spectrum peaks and ask you to:
- Identify isotopes present (from x-axis values)
- Determine abundances (from y-axis values)
- Calculate relative atomic mass from the spectrum
The number of peaks shows how many isotopes exist. For example, a bromine mass spectrum shows two peaks of similar height at m/z = 79 and m/z = 81, indicating two isotopes in approximately equal amounts.
Real examples of isotopes in CIE papers
Chlorine: Two isotopes, $^{35}\text{Cl}$ (75%) and $^{37}\text{Cl}$ (25%), giving Ar = 35.5. This example appears across multiple past papers because the non-whole-number Ar requires explanation.
Copper: Two isotopes, $^{63}\text{Cu}$ (69%) and $^{65}\text{Cu}$ (31%), giving Ar = 63.6. Copper provides a good example where the Ar is closer to one isotope because of its greater abundance.
Bromine: Two isotopes, $^{79}\text{Br}$ (51%) and $^{81}\text{Br}$ (49%), giving Ar ≈ 80. The approximately equal abundance makes bromine straightforward for calculations.
Boron: Two isotopes, $^{10}\text{B}$ (20%) and $^{11}\text{B}$ (80%), giving Ar = 10.8. Boron demonstrates how a heavily dominant isotope pulls the Ar close to its own mass.
Carbon: While carbon-12 is the standard, naturally occurring carbon also contains trace amounts of carbon-13 and radioactive carbon-14. The Ar is 12.01 due to the small proportion of carbon-13.
Applications and significance
Understanding isotopes matters beyond exam calculations:
- Radiocarbon dating uses the radioactive isotope carbon-14 to date archaeological specimens
- Medical imaging employs radioactive isotopes as tracers
- Nuclear power depends on uranium-235, a specific isotope of uranium
- Chemical analysis uses mass spectrometry routinely in forensics and pharmaceutical testing
For CIE IGCSE Chemistry, focus remains on identifying isotopes, explaining their properties, and performing Ar calculations rather than these applications.
Worked examples
Example 1: Calculating relative atomic mass from percentages
Question: Magnesium has three naturally occurring isotopes. The table shows their mass numbers and abundances.
| Isotope | Mass number | Percentage abundance |
|---|---|---|
| Mg-24 | 24 | 78.6 |
| Mg-25 | 25 | 10.1 |
| Mg-26 | 26 | 11.3 |
Calculate the relative atomic mass of magnesium. Show your working.
Solution:
Step 1: Multiply each mass by its abundance:
- (24 × 78.6) = 1886.4
- (25 × 10.1) = 252.5
- (26 × 11.3) = 293.8
Step 2: Add the products: 1886.4 + 252.5 + 293.8 = 2432.7
Step 3: Divide by total percentage: 2432.7 ÷ 100 = 24.327
Step 4: Round appropriately: Ar(Mg) = 24.3
[3 marks: 1 mark for correct method, 1 mark for calculation, 1 mark for answer to 1 d.p.]
Example 2: Working backwards from relative atomic mass
Question: Naturally occurring copper consists of two isotopes, $^{63}\text{Cu}$ and $^{65}\text{Cu}$. The relative atomic mass of copper is 63.6.
Calculate the percentage abundance of $^{63}\text{Cu}$. [3 marks]
Solution:
Let x = percentage of $^{63}\text{Cu}$
Then (100 - x) = percentage of $^{65}\text{Cu}$
Using the Ar formula:
$$\frac{63x + 65(100-x)}{100} = 63.6$$
Multiply both sides by 100:
63x + 6500 - 65x = 6360
-2x + 6500 = 6360
-2x = -140
x = 70
Percentage of $^{63}\text{Cu}$ = 70%
(Therefore $^{65}\text{Cu}$ = 30%)
[Method mark for setting up equation, calculation mark, answer mark]
Example 3: Interpreting mass spectrum data
Question: The mass spectrum of neon shows three peaks at m/z values of 20, 21, and 22 with relative heights of 90.5, 0.3, and 9.2 respectively.
(a) State what the three peaks represent. [1]
(b) Calculate the relative atomic mass of neon from this data. [2]
Solution:
(a) The three peaks represent the three isotopes of neon: $^{20}\text{Ne}$, $^{21}\text{Ne}$, and $^{22}\text{Ne}$ [1 mark]
(b) $$\text{Ar} = \frac{(20 \times 90.5) + (21 \times 0.3) + (22 \times 9.2)}{90.5 + 0.3 + 9.2}$$
$$= \frac{1810 + 6.3 + 202.4}{100}$$
$$= \frac{2018.7}{100}$$
Ar(Ne) = 20.2 [2 marks: 1 for method, 1 for answer]
Common mistakes and how to avoid them
Mistake: Confusing mass number with relative atomic mass and thinking they're the same thing. Correction: Mass number is the count of protons plus neutrons in one specific atom (always a whole number). Relative atomic mass is the weighted average for an element considering all its isotopes (usually not a whole number). Check the periodic table—most Ar values aren't whole numbers.
Mistake: Stating that isotopes have different numbers of protons. Correction: Isotopes have the same number of protons (same atomic number) but different numbers of neutrons. If the number of protons changes, it becomes a different element entirely. Always emphasize "same protons, different neutrons."
Mistake: Forgetting to divide by total abundance when calculating Ar, especially when abundances aren't given as percentages adding to 100. Correction: If abundances are given as ratios (e.g., 3:1) or actual numbers, you must calculate the total and divide by it. Practice identifying whether you're given percentages or other formats.
Mistake: Rounding too early in multi-step calculations, leading to inaccurate final answers. Correction: Keep full calculator values throughout the calculation and only round your final answer to 1 decimal place (or as instructed). Premature rounding accumulates errors that lose marks.
Mistake: Writing that isotopes have different chemical properties because of their different masses. Correction: Isotopes have identical chemical properties because chemical reactions depend on electron arrangement, which is the same for all isotopes of an element. Only physical properties (like density, diffusion rate) differ due to mass differences.
Mistake: Misreading mass spectrum axes or confusing the peak height with the mass number. Correction: Always check axis labels carefully. The x-axis shows m/z (the mass), while the y-axis shows abundance (how much of that isotope exists). The height of the peak indicates abundance, not mass.
Exam technique for Isotopes and relative atomic mass
Command word recognition: "Calculate" questions about relative atomic mass typically carry 2-3 marks and require full working. Show each step: multiply masses by abundances, sum the products, divide by total abundance, and give a final answer. Even if your arithmetic is wrong, method marks can be earned. "Explain" questions about isotopes need you to clearly state both the similarity (same protons/atomic number) and difference (different neutrons/mass number).
Show your working: For calculation questions, examiners award marks for method even if the final answer is incorrect. Write out the formula, substitute values clearly, and show each arithmetic step. Don't just write the answer—CIE mark schemes allocate separate marks for setting up the calculation and for the numerical answer.
Significant figures and decimal places: Unless specified otherwise, give relative atomic mass answers to 1 decimal place. CIE mark schemes typically accept answers within a small range (e.g., 24.3 ± 0.1), but excessive rounding or too many decimal places can lose the accuracy mark.
Using data from the periodic table: The Data Sheet provided in exams includes Ar values. If a question doesn't provide isotopic data but asks you to explain why chlorine has Ar = 35.5, you must explain the existence of two isotopes with their approximate abundances. Practice explaining non-whole-number Ar values from the periodic table.
Quick revision summary
Isotopes are atoms of the same element with identical atomic numbers (protons) but different mass numbers (neutrons). They have the same chemical properties but different physical properties. Relative atomic mass (Ar) is the weighted average of all isotopic masses, calculated by summing (isotopic mass × abundance) and dividing by total abundance. This explains why most elements have non-whole-number Ar values on the periodic table. Mass spectrometry separates isotopes and shows their abundances as peaks. Calculate Ar by multiplying each peak's m/z value by its height, totaling these products, and dividing by the sum of all heights.