Pyridine and pyrimidine are both aromatic compounds, how many electrons does each nitrogen atom contribute to the electron cloud of each compound?

Okay, let's see.

This is asking you to consider which of nitrogen's valence electrons count towards the `2n+2` rule (Hückel's Rule) when it comes to aromaticity.

The only ones that are delocalized within the `pi` electron cloud are the ones in the ring, i.e. not in an orbital perpendicular to the `2p_z` (vertical) orbitals of each carbon in the ring.

There are only three electron groups around each nitrogen, indicating a trigonal planar electron geometry.

Since the `sp^2` orbitals are in the same plane as the rest of the molecule, and since the `z` axis is vertical and the `xy`-plane is horizontal, the `xy`-plane is perpendicular to the `z` axis; so, the `sp^2` orbital of nitrogen is perpendicular to the `2p_z` of each carbon.

Hence, the `sp^2` orbital does not contribute its lone pair into the ring, and nitrogen only contributes electrons into the ring that are already bonding.

Each nitrogen therefore contributes approximately three `pi` electrons to the aromatic ring. If we assume the electronegativities of carbon and nitrogen are similar enough, then there would be three `pi` electrons per nitrogen.