Consider six vibrational modes: symmetric stretching of CO 2, O–H symmetric stretching of H 2O, stretching of HCl, stretching of H 2, N–H symmetric stretching of NH 3, and bending of CO 2. If k modes are IR active but Raman inactive, l are IR inactive but Raman active, and m are both active, k,l,m respectively are

GATE 2024 CY – Question 45

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. · 2 marks · Multiple choice

Consider six vibrational modes: symmetric stretching of $\mathrm{CO_2}$, O–H symmetric stretching of $\mathrm{H_2O}$, stretching of HCl, stretching of $\mathrm{H_2}$, N–H symmetric stretching of $\mathrm{NH_3}$, and bending of $\mathrm{CO_2}$. If k modes are IR active but Raman inactive, l are IR inactive but Raman active, and m are both active, k,l,m respectively are

1, 3, and 2
3, 1, and 2
1, 2, and 3
2, 1, and 3

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Correct answer: (C) 1, 2, and 3

Explanation

A vibration is **IR active** if the dipole moment changes during the vibration, and **Raman active** if the polarisability changes. For molecules with a centre of symmetry the two are mutually exclusive.

Mode	IR	Raman
$CO_2$ symmetric stretch	inactive (no dipole change)	active
$H_2O$ O–H symmetric stretch	active	active
HCl stretch	active	active
$H_2$ stretch	inactive	active
$NH_3$ N–H symmetric stretch	active	active
$CO_2$ bend	active	inactive

IR active but Raman inactive: only the $CO_2$ bend, so $k=1$.
IR inactive but Raman active: the $CO_2$ symmetric stretch and the $H_2$ stretch, so $l=2$.
Both active: $H_2O$, HCl and $NH_3$, so $m=3$.

Answer **(1, 2, 3)** (option C).