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Indian Forest Service (Mains)

Chemistry optional

  • 2 papers
  • 200 marks each
  • 3 h per paper

Paper I covers physical and inorganic chemistry.

Indian Forest Service (Mains), Chemistry optional · 2025 · Paper I

Q3(c). Three-state nuclear-spin partition function

Question

A nitrogen nucleus has energies 0, ±γ_N ℏB. Derive its partition function and mean energy and sketch their dependence on B. Find relative populations at 298 K and B = 20.0 T. Given γ_N ℏ = 2.04 × 10⁻²⁷ J/T.

Answer in brief

With x = γ_N ℏB/(kB T), q = 1 + 2 cosh x and ⟨E⟩ = −2γ_N ℏB sinh x/(1 + 2 cosh x); the three room-temperature populations are almost equal.

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Topic notes: statistical thermodynamics, the Boltzmann distribution, partition functions and the Sackur–Tetrode equation, with every Civil Services, IFoS and Geo-Scientist PYQ →

Coverspartition functionnuclear spin statesBoltzmann distributionmean energystatistical thermodynamics

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