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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)(i). Magnetic moments of Sm³⁺ and Eu³⁺ at 300 K

  • 5 marks
  • Answered
Question

Why do Eu³⁺ and Sm³⁺ not follow the trend of magnetic moment of lanthanides at 300 K? Explain.

Answer in brief

Their first excited J level lies within reach of kT (208 cm⁻¹ at 300 K) and is partly occupied, so the moment exceeds the ground-level value g_J√(J(J+1)) and varies with temperature.

Key points

  • Shielded 4f electrons keep their orbital moment. With only the ground J level occupied, μ=g_J√(J(J+1)), which fits the other Ln³⁺ ions.
  • J=52, g_J=27, μ=0.85 BM; observed 1.54–1.65 BM. Eu³⁺: J=0, μ=0; observed 3.32–3.54 BM.
  • In Eu³⁺ the ⁷F₁ level lies only about 300 cm⁻¹ above ⁷F₀, close to kT=208 cm⁻¹. Boltzmann: N₁/N₀=3 e^(-300/208)=0.71, so many ions are in J=1, which has a moment. In Sm³⁺ the ⁶H_(7/2) level is higher and the effect smaller.
  • With these levels (and the field mixing them into the ground level, Van Vleck) the calculated values become 1.55–1.65 and 3.40–3.51 BM, as observed. The moments depend on temperature.

The full model answer

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

  1. Shielded 4f electrons keep their orbital moment. With only the ground J level occupied, μ=g_J√(J(J+1)), which fits the other Ln³⁺ ions.
  2. Sm³⁺: J=52, g_J=27, μ=0.85 BM; observed 1.54–1.65 BM. Eu³⁺: J=0, μ=0; observed 3.32–3.54 BM.
  3. In Eu³⁺ the ⁷F₁ level lies only about 300 cm⁻¹ above ⁷F₀, close to kT=208 cm⁻¹. Boltzmann: N₁/N₀=3 e^(-300/208)=0.71, so many ions are in J=1, which has a moment. In Sm³⁺ the ⁶H_(7/2) level is higher and the effect smaller.
  4. With these levels (and the field mixing them into the ground level, Van Vleck) the calculated values become 1.55–1.65 and 3.40–3.51 BM, as observed. The moments depend on temperature.

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

All parts of Question 8