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Firstly, we should define the first ionisation energy
The first Ionisation Energy is the energy required to remove one mole of electrons from one mole of gaseous atoms to form a mole of gaseous ions, each with an 1+ charge.
The expected trend as we go across the period is that ionisation energy will increase as the nuclear charge increases and the number of shielding shells of electrons does not change. So the extra amount of protons means the nucleus holds the outer electrons more strongly so it requires more energy to remove an electron.
Aluminium has a lower ionisation energy than Magnesium. This is unexpected as Al has more protons. This can be explained by electron configurations.
Magnesium's electron config: 1s2 2s2 2p6 3s2
Aluminium's electron config: 1s2 2s2 2p6 3s2 3p1
Aluminium's outer electron is in a p orbital. This p sub-level is of higher energy than the s sub-level and so less energy is required to remove this electron.
Sulfur has a lower ionisation energy than phosphorous. This again is explained by their electron configurations
Phosphorous: 1s2 2s2 2p6 3s2 3p3
Sulphur: 1s2 2s2 2p6 3s2 3p4
A p sub-level has 3 sub-shells which can hold 2 electrons in each sub-shell. In phosphorous, the electrons are unpaired with one electron in each sub-shell with parallel spins. However, sulphur has 4 electrons so one of them must pair in a sub shell. As electrons are both negative particles, the paired electrons repel each other and so it is easier to remove the unpaired electron in phosphorous- so less energy is required.see more