Explain the degrees of freedom for polyatomic molecules.

Polyatomic molecules possess multiple degrees of freedom, which are essentially independent motions that molecules can undergo. These degrees of freedom include translational, rotational, and vibrational motions.

1. Translational degrees of freedom: These refer to the movement of the entire molecule through space. For a polyatomic molecule composed of \( N \) atoms, there are three translational degrees of freedom corresponding to motion along the x, y, and z axes. However, for a molecule in _______ ___ ____ _____ ___ _________ ______ _____.
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