Consider the planar X e F 4 X e F 4 molecule described in Problem 13. Assuming

Consider the planar ${XeF}_4$ molecule described in Problem 13. Assuming motion only in the $x-y$ plane, how many nontrivial normal modes are there?

Data from Problem 13

Xenon tetrafluoride, \(\mathrm{XeF}_{4}\), is one the few noble gas compounds. Its molecule is planar, assumed to lie in the \(x-y\) plane. Each F-Xe-F bond angle is \(90^{\circ}\). Model the bonds as four identical springs.

How many displacement coordinates are there? Include possible motion in all three dimensions.

How many nontrivial normal modes are there?

One of the normal modes is a basis function for the identity irreducible representation. Sketch this normal mode.