(a) The structures of cis- and trans-N₂F₂ were shown in worked example 3.1. Give an appropriate hybridization scheme for the N atoms in each isomer. 

(b) What hybridization scheme is appropriate for the O atoms in H₂O₂ (Fig. 2.1)?

Figure 2.1

Data from Example 3.1

How do the rotation axes and planes of symmetry in cis- and trans-N₂F₂ differ? 

First draw the structures of cis- and trans-N₂F₂; both are planar molecules.

1. The identity operator E applies to each isomer.

2. Each isomer possesses a plane of symmetry which contains the molecular framework. However, their labels differ (see point 5 below).

3. The cis-isomer contains a C₂ axis which lies in the plane of the molecule, but the trans-isomer contains a C₂ axis which bisects the N—N bond and is perpendicular to the plane of the molecule.

4. The cis- (but not the trans-) isomer contains a mirror plane, σ_v, lying perpendicular to the plane of the molecule and bisecting the N—N bond:

5. The consequence of the different types of C₂ axes, and the presence of the σ_v plane in the cis-isomer, is that the symmetry planes containing the cis- and trans-N₂F₂ molecular frameworks are labelled σ_v' and σ_h respectively.