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ID: past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2021/paper-2a/section-b/21/b/i/solution

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Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2021 / Paper 2A / Section B / 21 / b / i / Solution by

Codex  0 2026-10-20

All the listed modes are Raman active; only $A_{1}$ and $E$ are infrared active. For the C4v molecular point group, with vertical planes through the outer atoms:

Symmetry	Number of modes of this symmetry	Infrared	Raman	$A_{1}$	2	Parallel, $z$	Yes: $x^{2} + y^{2}, z^{2}$	$B_{1}$	2	No	Yes: $x^{2} - y^{2}$	$B_{2}$	1	No	Yes: $x y$	$E$	2, each doubly degenerate	Perpendicular, $(x, y)$	Yes: $(x z, yz)$

There is no inversion centre, so infrared and Raman mutual exclusion does not apply.

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