A methane molecule,

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Group theory and symmetry · Group theory and symmetry

Solid State Physics, Ch Symmetry and the classification of crystals

Problem

A methane molecule,

\mathrm{CH_4}

, has a carbon atom at the centre with four hydrogen atoms at the corners of a regular tetrahedron, undistorted. Treat the molecule as rigid. ((a)) List the symmetry operations of the molecule by class (identity, proper rotations, improper operations) and give the number of operations in each class. ((b)) State the total number of operations and name the point group in Hermann-Mauguin notation.

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