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UPSC Combined Geo-Scientist

Chemist

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

Mains Paper II covers physical chemistry.

UPSC Combined Geo-Scientist, Mains · 2022 · Mains Paper II

Q1(c). Temperature coefficient of conductivity: metal and semiconductor

Question

A temperature variation study of conductivity can distinguish between a metallic conductor and a semiconductor — Explain.

Answer in brief

Metal: σ falls slowly as T rises (more lattice scattering); intrinsic semiconductor: σ rises exponentially (more carriers across the gap); the sign of dσ/dT is the test.

Key points

  • Metal: partly filled (overlapping) bands; carrier number n is large (10²⁸–10²⁹ m⁻³) and independent of T.
  • Rising T ⇒ stronger lattice vibrations (phonons) ⇒ more electron scattering ⇒ mobility μ falls ⇒ σ falls; Cu, 300 → 310 K: σ drops by about 4%.
  • Semiconductor: filled valence band, empty conduction band, small band gap Eg; carriers are made thermally, n ∝ exp(−Eg/2kBT), and this rise outweighs the small fall in μ.
  • Si, 300 → 310 K: σ310/σ300 = 2.01, the conductivity doubles.
  • Metals show a positive temperature coefficient of resistance, semiconductors a negative one (thermistors); ln σ against 1/T has slope −Eg/2kB, which gives Eg.

The full model answer

As written for the answer booklet: the diagram carries the working, the lines stay short. Read here only; it is not offered as a download.

Model answer to Q1(c), 2022 Mains Paper II: solution pages 5 and 6
Solution pages 5 and 6 of 37
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Topic notes: defects, non-stoichiometry and semiconductors, with every Civil Services, IFoS and Geo-Scientist PYQ →

Coversband theorysemiconductormetallic conductorband gaptemperature coefficient of resistanceelectrical conductivity

All parts of Question 1