How does ionization of the elements relate with the periodic table?

Answer 1

To have a stable atom, ion or molecule, the outer shell of all atoms must be even empty or full. When you look at he filling of the shells, you see that for all atoms except H and He, the outer shells have 8 electrons, for the two exceptions the outer Shell has only two electrons. So ,the consequence is the following : atoms which have more than 4 electrons on the outer shell tends to grasp some electrons to fill this shell to8. Conversely, those with few electrons tend to give their electrons to empty the shell.
All the chemistry is based on this principle.

Answer 2

As the nuclear charge increases, the attraction between the nucleus and the electrons increases and it requires more energy to remove the outermost electron and that means there is a higher ionization energy. As you go across the periodic table, nuclear charge is the most important consideration. So, going across the periodic table, there should be an increase in ionization energy because of the increasing nuclear charge.
Going down the table, the effect of increased nuclear charge is balanced by the effect of increased shielding, and the number of energy levels becomes the predominant factor. With more energy levels, the outermost electrons (the valence electrons) are further from the nucleus and are not so strongly attracted to the nucleus. Thus the ionization energy of the elements decreases as you go down the periodic table because it is easier to remove the electrons. Another way of looking at that is that if you are trying to take something from the first energy level, you have to take it past the second, the third, the fourth and so on, on the way out. But if something is already in the third or fourth energy level, it doesn't have to be taken as far to get away from the nucleus. It is already part way removed from the nucleus.