Successive ionization energies can be plotted on a graph, and when done so they demonstrate consistency and periodicity.

The first ionization energy of successive elements across a period (excluding the transition metals, which rather behave in their own way electronically speaking) form a shape like this:

```|
|
|                      x
|
|                   x
|             x
|                x
|          x
|    x
|       x
| x
|____________________________
```
(In this case the xs represent the first ionization energies of elements across one period, e.g. the period lithium to neon.)

There is an overall increase because, as the above writeup states, the nucleus has a stronger positive charge in each element. The successive nuclei each contain one more proton, so they attract the orbiting electrons more strongly, meaning it takes more energy to remove the outer electron.

However there are also two decreases, which would occur at the same point in each period. The first, between the second and third elements, is due to electronic sub-shells. Elements one and two contain two outer electrons, both in the s sub-shell. This sub-shell is now filled, so element three places its outermost electron in the p sub-shell. This has a higher energy than s, so the electron requires less energy to be removed, despite the increased attraction from the nucleus.

The second decrease, between elements five and six, occurs because of the pairing of electrons. The p sub-shell holds the electrons from 3 to 8, meaning that if an element has between 3 and 8 electrons in its outer shell, its outer electron will be in p. These up-to-six electrons are held in three pairs. In the elements with one, two and three p electrons in the outer shell, each electron will occupy a different pair-space, so as to be as far as possible from the other electron(s). As soon as there are four electrons in p, there is no choice but for two to pair up. Electrons repel each other, and this pairing up significantly increases the amount of electronic repulsion, meaning that the outer electron is easier to remove than it would have been if there was no pairing.

If the first ionization energies of two successive periods are plotted, the graph looks this:

```|
|                      x
|
|                   x
|             x
|                x                           x
|          x
|    x                                    x
|       x                           x
| x                                    x
|                                x
|                          x
|                             x
|                       x
|
|__________________________________________________
```
The second period has the same shape but is lower than the first because the outer electrons of these elements are further out from the nucleus, and because they have one more electron shell between them and the nucleus, which provides extra shielding as mentioned in the above writeup.

When the successive ionization energies of one particular element are plotted, the shape is determined by the group that element is in. The electrons in the outer shell will be significantly easier to remove than those in the next shell inwards, which in turn will be easier to remove than those in the next shell, and so on. The ionization energies are therefore arranged (almost) in rows, each row corresponding to an electron shell.

For a Group 1 element, the graph will look like this:

```
|
|          xx
|        xx
|      xx
|    xx
|
|
|
|
|
| x
|________________```
The first ionization energy is much lower than the next eight, because the outer electron is in a higher shell than the others. If it was a Group 2 element, there would be two electrons in the outer shell, so the first two ionization energies would be relatively close, and the third much larger than the second, and so on.

(Note that in the above diagram, ionization energies are placed next to each other in pairs, but in a real graph each would be slightly higher than the last. The point is that the difference between 1 and 2 is much greater than between 2 and 3, or 3 and 4 etc.)

With much thanks to Cletus the Foetus.