Given the matrices for C₃ and σh below C₃= -1/2 -(√(3))/2 0 (√(3))/2 -1/2 0 0 0 1 σh= 1 0 0 0 1 0 0 0 1 the trace of the matrix representing for S₃² is

(a) 0. Explanation: S₃² = C₃²; trace = 1 + 2cos 240° = 0.

Q127 · CSIR-NET Chemistry, December 2019

Paper: CSIR-NET December 2019 · Subject: Physical Chemistry · Chapter: Group Theory · Topic: Group Theory – General · Marks: 2 · Difficulty: Medium

Given the matrices for $\mathrm{C_3}$ and $\sigma_h$ below

\[ C_{3}=\begin{bmatrix} -\dfrac{1}{2} & -\dfrac{\sqrt{3}}{2} & 0 \\ \dfrac{\sqrt{3}}{2} & -\dfrac{1}{2} & 0 \\ 0 & 0 & 1 \end{bmatrix} \quad \sigma_{h}=\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \]

the trace of the matrix representing for $\mathrm{S_3^2}$ is

(a)0

(b)-2

(c)1

(d)-1

Answer

Answer: A ✓ checked by 4AB · confidence high

Explanation

S₃² = C₃²; trace = 1 + 2cos 240° = 0.

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