GATE 2024 CY – Question 20

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

The molecule $\mathrm{XY_2}$ is microwave active and its vibration-rotation spectrum shows only P and R transitions. In the correct structure,

X is the central atom in linear XY2.
X is the central atom in bent XY2.
Y is the central atom in linear XY2.
Y is the central atom in bent XY2.

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Correct answer: (C) Y is the central atom in linear XY2.

Explanation

Use the two spectroscopic conditions.

**Microwave (pure rotational) activity** requires a **permanent dipole moment**.
**Only P and R branches** in the vibration-rotation spectrum (no Q branch) is typical of a **linear** molecule vibrating along its axis (parallel band, $\Delta J=\pm1$ only).

So $XY_2$ must be linear and polar.

**Y-X-Y (X central):** linear and symmetric, so no dipole moment. Microwave inactive. ✗
**X-Y-Y (Y central):** a linear molecule with two different ends, such as N-N-O, has a permanent dipole. ✓
A bent $XY_2$ would normally also show a Q branch for the bending vibration.

Answer: **Y is the central atom in linear $XY_2$** (option C).