Explaining the pattern of first ionization energies across Period 3

First ionization energy is dependent on four factors:

• the charge on the nucleus;
• the distance of the outer electron from the nucleus;
• the amount of screening by inner electrons;
• whether the electron is alone in an orbital or one of a pair.

The upward trend: In the whole of period 3, the outer electrons are in 3-level orbitals. These electrons are at approximately the same distance from the nucleus, and are screened by corresponding electrons in orbitals with principal atomic numbers n=1 and n=2. The determining factor in the increase in energy is the increasing number of protons in the nucleus from sodium across to argon. This creates greater attraction between the nucleus and the electrons and thus increases the ionization energies. The increasing nuclear charge also pulls the outer electrons toward the nucleus, further increasing ionization energies across the period.

The decrease at aluminum: The value for aluminum might be expected to be greater than that of magnesium due to the  extra proton. However, this effect is offset by the fact that the outer electron of aluminum occupies a 3p orbital rather than a 3s orbital. The 3p electron is slightly farther from the nucleus than the 3s electron, and partially screened by the 3s electrons as well as the inner electrons. Both of these factors offset the effect of the extra proton.

The decrease at sulfur: In this case  something other than the transition from a 3s orbital to a 3p orbital must offset the effect of an extra proton. The screening (from the inner electrons and, to some extent, from the 3s electrons) is identical in phosphorus and sulfur , and the electron is removed from an identical orbital. The difference is that in the case of sulfur, the electron being removed is one of the 3p_x² pair. The repulsion between the two electrons in the same orbital creates a higher-energy environment, making the electron easier to remove than predicted.