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GATE 2022 CY – Question 21

Physical Chemistry · Spectroscopy: Atomic spectroscopy; Russell-Saunders coupling; Term symbols and spectral details; origin of selection rules. Rotational, Vibrational, Electronic and Raman spectroscopy of diatomic and simple polyatomic molecules. Line broadening and line widths; simple properties of Gaussian and Lorentzian line shapes. Molecular spectroscopy: Absorbance, Beer- Lambert’s law, Einstein’s coefficient, Jablonski diagram. Relationship of transition moment integral with molar extinction coefficient and oscillator strength. Basic principles of Nuclear Magnetic Resonance: Gyromagnetic ratio; Chemical shift, nuclear coupling. · 1 mark · Multiple choice

A hypothetical diatomic molecule shows three pure-vibrational peaks. Intensities (arbitrary units) at 300, 600, 900 K are:

I: 1.0, 1.0, 1.0

II: 0.1, 0.1, 0.1

III: 0.02, 0.04, 0.06

Which statement is correct?

  1. Peak I appears at the lowest energy
  2. Peak II appears at the lowest energy
  3. Peak III appears at the lowest energy
  4. Peak I appears at the highest energy

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Correct answer: (C) Peak III appears at the lowest energy

Explanation

Peak III grows with temperature, indicating a hot-band transition from a thermally populated vibrational excited state. For an anharmonic oscillator, spacing decreases as v increases, so a hot band lies below the fundamental and overtones.

Thus **III is lowest, C**; constant weak intensity alone does not imply a hot band.