Explain why the atomic radius of potassium is greater than that of both sodium and chlorine, with reference to nuclear charge and electron shielding.

IB DP Chemistry Higher Level (2023 syllabus) — S3.1 The periodic table: classification of elements · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

Model answer (4 marks)

Potassium has a larger atomic radius than sodium because it has an extra electron shell (n=4 vs. n=3). The valence electrons are therefore further from the nucleus. The additional shell also means more inner‑shell electrons, which shield the valence electron from the nucleus, reducing the effective nuclear charge and allowing the electron cloud to expand.

Chlorine has a smaller radius than potassium because its valence electrons are in the same n=3 shell as sodium but it has 17 protons compared with 11 in sodium. The much larger nuclear charge gives a higher effective nuclear charge on the valence electrons, pulling them closer to the nucleus and contracting the radius.

Thus the extra shell and shielding in potassium outweigh the higher nuclear charge of chlorine, giving potassium the largest radius of the three.

Examiner tips

  • State the extra shell in K and its effect on radius. Explain shielding and effective nuclear charge. Compare Cl’s higher nuclear charge to K’s. Use correct terminology: electron shell, shielding, effective nuclear charge.

Common mistakes

  • Confusing period numbers (saying K and Cl are in the same period). Forgetting to mention shielding by inner electrons. Using vague terms like ‘more protons’ without linking to effective nuclear charge.

Mark scheme (4 marks)

  1. Potassium has more electron shells (energy levels) than sodium, so valence electrons are further from the nucleus.
  2. Greater shielding by inner electrons in potassium reduces the effective nuclear charge experienced by the valence electron, increasing atomic radius compared to sodium.
  3. Potassium and chlorine are in the same period (period 3 / period 4 comparison is not relevant here — both K and Cl are compared: chlorine has a greater nuclear charge than potassium for the same principal quantum shell would be incorrect; the correct point is that chlorine has a much higher nuclear charge than potassium while both have valence electrons in period 3 — actually K is period 4 and Cl is period 3, so K is larger due to the additional shell, but comparing within-period: chlorine has more protons than sodium with the same number of shells, so greater nuclear charge pulls electrons closer). Corrected point: Chlorine has a higher nuclear charge (17 protons) than potassium's valence shell shielding scenario — the key point is that chlorine's valence electrons are in the same shell (n = 3) as sodium but experience a greater effective nuclear charge (more protons, similar shielding), pulling electrons closer and reducing radius.
  4. Therefore potassium has the largest atomic radius of the three because the additional electron shell effect outweighs nuclear charge, while chlorine's high effective nuclear charge contracts its electron cloud more than sodium's.

Key terms in this question

atomic radius · nuclear charge · electron shielding

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