QB_PH_SEC6_007: Molecular Spectroscopy

Which of the following molecules exhibits a pure rotational Raman spectrum?

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Governing Selection Rule**: Pure rotational Raman activity requires the molecular polarizability to change as the molecule rotates in space, which occurs if and only if the molecular polarizability is **anisotropic** (non-spherical polarizability ellipsoid). 2. **Molecular Symmetry Analysis**: - $\text{CH}_4$: Tetrahedral ($T_d$), spherical top molecule $\implies$ polarizability ellipsoid is spherical (isotropic) $\implies$ Raman inactive for pure rotation. - $\text{SF}_6$: Octahedral ($O_h$), spherical top $\implies$ Raman inactive for pure rotation. - $\text{CCl}_4$: Tetrahedral ($T_d$), spherical top $\implies$ Raman inactive for pure rotation. - $\text{H}_2$: Linear homonuclear diatomic $\implies$ cylindrical polarizability ellipsoid (anisotropic, $\alpha_\parallel \neq \alpha_\perp$) $\implies$ pure rotational Raman active with selection rule $\Delta J = 0, \pm 2$. 3. **Conclusion**: $\text{H}_2$ exhibits a pure rotational Raman spectrum. Option (B) is correct.