Q68 · CSIR NET Chemistry, December 2017
Paper: CSIR NET December 2017 · Subject: Physical Chemistry · Chapter: Group Theory · Topic: Symmetry Elements Point Groups · Marks: 2 · Difficulty: Medium
$\mathrm{N_2O}$ molecule belongs to the point group
(a)$\mathrm{D}_{\infty \mathrm{h}}$
(b)$\mathrm{C}_{\infty \mathrm{h}}$
(c)$\mathrm{C}_{2 \mathrm{v}}$
(d)$\mathrm{S_2}$ Table 1
| $D_{2h}$ | E | $C_2(z)$ | $C_2(y)$ | $C_2(x)$ | i | $\sigma(xy)$ | $\sigma(xz)$ |
|---|---|---|---|---|---|---|---|
| $A_g$ | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| $B_{1g}$ | 1 | 1 | -1 | -1 | 1 | 1 | -1 |
| $B_{2g}$ | 1 | -1 | 1 | -1 | 1 | -1 | 1 |
| $B_{3g}$ | 1 | -1 | -1 | 1 | 1 | -1 | -1 |
| $A_u$ | 1 | 1 | 1 | 1 | -1 | -1 | -1 |
| $B_{1u}$ | 1 | 1 | -1 | -1 | -1 | -1 | 1 |
| $B_{2u}$ | 1 | -1 | 1 | -1 | -1 | 1 | -1 |
| $B_{3u}$ | 1 | -1 | -1 | 1 | -1 | 1 | 1 |
Answer
Answer: B ✓ checked by 4AB · confidence high
The source book printed no answer; this one was worked out and checked — see the explanation.
Explanation
N₂O is linear but unsymmetrical (N–N–O), so it has a C∞ axis and σ_v planes but no centre of inversion: C∞v.
Study loop for Group Theory