Isotopes and Relative Atomic Mass
Carbon dating tells archaeologists whether a bone is 500 years old or 50,000 years old. It works because carbon has isotopes — atoms of carbon with different numbers of neutrons. ¹⁴C is slightly unstable and decays at a known rate; ¹²C is stable. The ratio of ¹⁴C to ¹²C in organic material decreases predictably over time. Without isotopes, there would be no carbon dating, no nuclear medicine, no PET scans. Understanding isotopes is also the key to understanding why chlorine's atomic mass is 35.5 — not a whole number.
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Chlorine has two naturally occurring isotopes: chlorine-35 and chlorine-37. Both are chlorine atoms, but one is slightly heavier than the other. If you look up chlorine on the periodic table, its relative atomic mass is listed as 35.45 — not a whole number. Why isn't it simply 35 or 37?
Before reading on, write your best answer. What would need to be true for the relative atomic mass to be exactly 36 (halfway between 35 and 37)?
📚 Know
- Definition of isotope and how isotopes differ
- How to write nuclide notation for isotopes
- Definition and meaning of relative atomic mass (Ar)
🔗 Understand
- Why isotopes of the same element have identical chemical properties
- How mass spectrometry data gives isotopic abundance
- How to calculate Ar from isotopic masses and percentage abundances
✅ Can Do
- Write nuclide notation and identify differences between isotopes
- Calculate relative atomic mass from isotopic abundance data
- Interpret mass spectrometry data for an element
Key Definitions
Core Content
Misconceptions to Fix
Wrong: Isotopes have different chemical properties because they have different masses.
Right: Isotopes have identical chemical properties because chemistry is determined by electron configuration, which is the same for all isotopes of an element. Isotopes differ in physical properties (density, boiling point) and nuclear stability due to different neutron numbers.
Isotopes: Same Element, Different Mass
Isotopes of the same element share the same number of protons (Z) but differ in neutron number. Since chemical behaviour is determined by the number and arrangement of electrons (which equals protons in neutral atoms), isotopes have identical chemical properties. They do differ in:
- Physical properties: slightly different mass → slightly different density, melting/boiling points, reaction rates (kinetic isotope effect)
- Nuclear stability: some isotopes are radioactive (unstable nucleus) while others are stable
| Isotope | Protons (Z) | Neutrons (A−Z) | Mass number (A) | Stability | Natural abundance |
|---|---|---|---|---|---|
| ¹H (protium) | 1 | 0 | 1 | Stable | 99.985% |
| ²H (deuterium) | 1 | 1 | 2 | Stable | 0.015% |
| ³H (tritium) | 1 | 2 | 3 | Radioactive | Trace (artificial) |
| ¹²C | 6 | 6 | 12 | Stable | 98.89% |
| ¹³C | 6 | 7 | 13 | Stable | 1.11% |
| ¹⁴C | 6 | 8 | 14 | Radioactive (t½ = 5730 yr) | Trace |
| ³⁵Cl | 17 | 18 | 35 | Stable | 75.77% |
| ³⁷Cl | 17 | 20 | 37 | Stable | 24.23% |
Calculating Relative Atomic Mass
The relative atomic mass (Ar) is the weighted average of all isotopic masses, weighted by their fractional abundance. The standard reference is ¹²C = exactly 12.
Ar = Σ (isotopic mass × fractional abundance)
= (m₁ × f₁) + (m₂ × f₂) + (m₃ × f₃) + ...
where fractional abundance = percentage ÷ 100
Mass Spectrometry and Isotope Data
A mass spectrometer ionises atoms and accelerates them through a magnetic field. Heavier ions deflect less, lighter ions more — they separate by mass. A detector measures the relative number of ions at each mass value, producing a mass spectrum showing peaks at each isotope's mass, with peak height proportional to abundance.
Mass Spectrum of Chlorine
Worked Examples
Worked Example 1 — Annotated: Calculate Ar from mass spectrum data
Worked Example 2 — Annotated: Find isotopic abundance from Ar
Common Mistakes
📓 Copy Into Your Books
▼⚛️ Isotopes
- Same Z (protons), different A (neutrons)
- Same chemical properties (same electrons)
- Different physical properties (different mass)
- Notation: mass A top, atomic Z bottom
- Example: ³⁵Cl and ³⁷Cl — both chlorine
⚖️ Relative Atomic Mass
- Ar = Σ(isotopic mass × fractional abundance)
- Fractional abundance = % ÷ 100
- All fractions must sum to 1.000
- Reference: ¹²C = exactly 12
- Ar is a decimal, not a whole number
📊 Mass Spectrometry
- Separates ions by mass-to-charge ratio (m/z)
- Peak mass = isotope mass number
- Peak height ∝ relative abundance
- Used to determine Ar and identify isotopes
⚠️ Exam Traps
- Use fractions (not %) in Ar calculation
- Ar pulled toward most abundant isotope
- Isotopes ≠ different chemical properties
- Mass number (A) is always a whole number
Activities
1 Magnesium has three isotopes: ²⁴Mg (78.99%), ²⁵Mg (10.00%), ²⁶Mg (11.01%). Calculate the relative atomic mass of magnesium. Show full working.
2 Copper has two stable isotopes: ⁶³Cu and ⁶⁵Cu. If Ar(Cu) = 63.55, calculate the percentage abundance of each isotope. Show working.
A mass spectrum of an unknown element X shows three peaks:
A Calculate the relative atomic mass of element X. Show full working.
B Use the calculated Ar to identify the element (refer to the periodic table). State how many isotopes this element has.
Look back at what you wrote in the Think First section. What has changed? What did you get right? What surprised you?
Multiple Choice
Multiple Choice
5 random questions from a replayable lesson bank — feedback shown immediately
Short Answer
Short Answer Questions
6. Carbon-12 (¹²C) and carbon-14 (¹⁴C) are isotopes of carbon. (a) State one similarity and two differences between these isotopes. (b) Explain why both isotopes react identically with oxygen to form CO₂. 4 MARKS
7. The Ar of neon is 20.18. Neon has three isotopes: ²⁰Ne (90.48%), ²¹Ne (0.27%), and ²²Ne (9.25%). Using the Ar formula, verify that these abundances are consistent with Ar = 20.18. Show full working. 3 MARKS
✅ Comprehensive Answers
▼⚖️ Activity 1
1. Fractions: ²⁴Mg = 78.99÷100 = 0.7899, ²⁵Mg = 0.1000, ²⁶Mg = 0.1101. Sum = 1.0000 ✓. Ar = (24 × 0.7899) + (25 × 0.1000) + (26 × 0.1101) = 18.958 + 2.500 + 2.863 = 24.321 ≈ 24.32. (Compare to periodic table: Ar(Mg) = 24.31 ✓).
2. Let x = fractional abundance of ⁶³Cu. Then (1−x) = fractional abundance of ⁶⁵Cu. Ar = (63×x) + (65×(1−x)) = 63.55. 63x + 65 − 65x = 63.55. −2x = 63.55 − 65 = −1.45. x = 0.725. ⁶³Cu = 72.5%; ⁶⁵Cu = 27.5%. Verify: (63×0.725) + (65×0.275) = 45.675 + 17.875 = 63.55 ✓.
📊 Activity 2
A: Check: 1.4 + 24.1 + 22.1 + 52.4 = 100.0% ✓. Fractions: 204→0.014, 206→0.241, 207→0.221, 208→0.524. Ar = (204×0.014) + (206×0.241) + (207×0.221) + (208×0.524) = 2.856 + 49.646 + 45.747 + 108.992 = 207.24 ≈ 207.2.
B: Element X is Lead (Pb), Ar ≈ 207.2 (matches periodic table value of 207.2). Lead has 4 naturally occurring isotopes: ²⁰⁴Pb, ²⁰⁶Pb, ²⁰⁷Pb, ²⁰⁸Pb.
❓ Multiple Choice
1. C — Isotopes: same Z (protons), different A (neutrons count differs). Same element means same Z always.
2. B — Ar = (79 × 0.5069) + (81 × 0.4931) = 40.045 + 39.941 = 79.986 ≈ 79.99. Almost exactly 80 because the abundances are nearly equal.
3. D — Ar = 6.94, very close to 6. The lighter isotope dominates. If x = fraction of mass 6: 6x + 7(1−x) = 6.94 → −x = −0.06 → x = 0.94 = 94% mass-6 (this is lithium: ⁶Li 7.5%, ⁷Li 92.5% — the question uses hypothetical values).
4. A — Same protons → same electrons → same electron configuration → identical chemical behaviour. Neutrons don't participate in bonding.
5. C — Ar = (107 × 0.52) + (109 × 0.48) = 55.64 + 52.32 = 107.96. (This is silver, Ag.)
📝 Short Answer Model Answers
Q6 (4 marks): (a) Similarity: both have 6 protons (atomic number Z = 6) and 6 electrons (1 mark). Differences: (1) ¹²C has 6 neutrons, ¹⁴C has 8 neutrons (1 mark). (2) ¹²C is stable; ¹⁴C is radioactive (unstable nucleus) (1 mark). (b) Both react identically with oxygen because chemical behaviour is determined by electron configuration. ¹²C and ¹⁴C both have 6 protons → 6 electrons in a neutral atom → identical electron arrangement → same bonding behaviour → both form 2 C=O bonds with 2 oxygen atoms to give CO₂ (1 mark).
Q7 (3 marks): Fractions: ²⁰Ne = 90.48÷100 = 0.9048, ²¹Ne = 0.0027, ²²Ne = 0.0925. Sum = 0.9048 + 0.0027 + 0.0925 = 1.0000 ✓ (1 mark). Ar = (20 × 0.9048) + (21 × 0.0027) + (22 × 0.0925) (1 mark) = 18.096 + 0.0567 + 2.035 = 20.188 ≈ 20.18 ✓ (1 mark). The calculated value matches the stated Ar, confirming the abundances are consistent.
Revisit Your Thinking
Return to your Think First response. You should now be able to explain the 35.45 value precisely:
- Relative atomic mass is a weighted average. It accounts for both the mass of each isotope AND its natural abundance.
- Chlorine-35 is about three times more abundant (~75%) than chlorine-37 (~25%). Because the lighter isotope is more common, the weighted average is pulled closer to 35 than to 37.
- For the average to be exactly 36, both isotopes would need to be present in equal amounts (50% each). Since they are not, the average is 35.45.
Consolidation Game
Isotopes and Relative Atomic Mass
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