Q97 · CSIR NET Chemistry, December 2013
Paper: CSIR NET December 2013 · Subject: Physical Chemistry · Chapter: Group Theory · Topic: Character Tables · Marks: 2 · Difficulty: Medium
The transition that is allowed by x-polarized light in trans-butadiene is (The character table for $\mathrm{C_{2h}}$ is given below)
| $\mathrm{C_{2h}}$ | E | $\mathrm{C_2}$ | i | $\sigma_h$ | |
|---|---|---|---|---|---|
| $\mathrm{A_g}$ | 1 | 1 | 1 | 1 | $R_z, x^2, y^2, z^2, xy$ |
| $\mathrm{B_g}$ | 1 | -1 | 1 | -1 | $R_x, R_y, xz, yz$ |
| $\mathrm{A_u}$ | 1 | 1 | -1 | -1 | z |
| $\mathrm{B_u}$ | 1 | -1 | -1 | 1 | x, y |
(a)${ }^{1} \mathrm{A}_{\mathrm{u}} \leftrightarrow{ }^{1} \mathrm{A}_{\mathrm{u}}$
(b)${ }^{1} \mathrm{A}_{\mathrm{u}} \leftrightarrow{ }^{1} \mathrm{B}_{\mathrm{g}}$
(c)${ }^{1} \mathrm{B}_{\mathrm{u}} \leftrightarrow{ }^{1} \mathrm{B}_{\mathrm{g}}$
(d)${ }^{3} \mathrm{B}_{\mathrm{g}} \leftrightarrow{ }^{1} \mathrm{A}_{\mathrm{g}}$
Answer
Answer: B ✓ checked by 4AB · confidence high
Explanation
In C₂h, x transforms as B_u. A transition is x-allowed if Γ_i × B_u × Γ_f contains A_g: A_u × B_u × B_g = A_g, so ¹A_u → ¹B_g is allowed (b); the others give A_u, B_u or a spin change.
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