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UPSC Civil Services (Mains)

Chemistry optional

  • 2 papers
  • 250 marks each
  • 3 h per paper
  • 5 of 8 questions, Q1 and Q5 compulsory

Paper I covers physical and inorganic chemistry.

UPSC Civil Services (Mains), Chemistry optional · 2026 · Paper I

Q8(c)(ii). Metallic radii from La to Lu, and the exceptions Eu and Yb

  • 5 marks
  • Answered
Question

Why do the metallic radii decrease from La to Lu except at Eu and Yb?

Answer in brief

4f electrons shield the rising nuclear charge poorly (lanthanide contraction). Eu and Yb keep stable 4f⁷ and 4f¹⁴ shells in the metal and give only two electrons, not three, to the metallic bond, so their atoms are larger.

Key points

  • From La to Lu the nuclear charge rises by one at each step while the new electron enters the inner 4f subshell.
  • 4f orbitals are diffuse and shield poorly, so Z_(eff) on the outer electrons rises steadily and the atom shrinks: the lanthanide contraction. Ln³⁺ falls from 116 pm (La) to 98 pm (Lu) for CN 8.
  • Most of the metals are Ln³⁺ cores with three conduction electrons each. Eu and Yb instead keep the half-filled 4f⁷ and full 4f¹⁴ shells: divalent metals, M²⁺ cores with only 6s² in the conduction band.
  • Fewer bonding electrons and a larger core (Eu²⁺ 125 against Eu³⁺ 107 pm; Yb²⁺ 114 against 99 pm, CN 8) give weaker bonding, a larger radius, and lower density and melting point.

The full model answer

Written out in full, as it should go in the answer booklet. The solution page with its diagrams follows it.

The steady decrease (3 marks)

  1. From La to Lu the nuclear charge rises by one at each step while the new electron enters the inner 4f subshell.
  2. 4f orbitals are diffuse and shield poorly, so Z_(eff) on the outer electrons rises steadily and the atom shrinks: the lanthanide contraction. Ln³⁺ falls from 116 pm (La) to 98 pm (Lu) for CN 8.

The exceptions Eu and Yb (2 marks)

  1. Most of the metals are Ln³⁺ cores with three conduction electrons each. Eu and Yb instead keep the half-filled 4f⁷ and full 4f¹⁴ shells: divalent metals, M²⁺ cores with only 6s² in the conduction band.
  2. Fewer bonding electrons and a larger core (Eu²⁺ 125 against Eu³⁺ 107 pm; Yb²⁺ 114 against 99 pm, CN 8) give weaker bonding, a larger radius, and lower density and melting point.

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Model answer to Q8(c)(ii), 2026 Paper I: solution page 53
Solution page 53 of 55
Read the whole 2026 solution2026 question paper

All parts of Question 8