Ionization potential Energy

Ionization potential Energy:

It is the energy needed to remove one or more electrons from a neutral atom to form a positively charged ion.
A multi-electron atom would have many ionization energies

So by definition:

1st ionization potential: it is the energy required to remove the outer most electron from a neutral atom in the gas phase

2nd ionization potential: it is the energy required to remove the next outer electron from the singly charged ion

Each successive removal of an electron requires more energy because as electrons are removed the remaining electrons experience a greater attraction to the nucleus

In horizontal period
Ionization potential increases from left to right due to decreasing of atomic radius. And this is due to:

Gradual increasing in positively nuclear charge that increase the attraction force for valence electrons

In vertical group
Ionization potential decreases from up to down due to increasing of atomic radius. And this is due to:

The effect of extra energy levels being added is more than the effect of extra positively nuclear charge
Increasing of the repulsion forces between valence electrons and inner core electrons

Important Notes:

(1) Ionization potential of noble gases (group zero) is very high due to the stability of electronic configuration since it is difficult to remove electron from a completely filled shell. (Highest peaks are noble gases)
(2) Lowest troughs are alkali metals.
(3) A local maximum occurs for filled subshells and half-filled p subshells.
(4) Second ionization energy is always higher than the first ionization energy (usually a lot higher)
(5) Alkali metals and hydrogen: first ionization energy very low. Second ionization much higher.
(6) Alkaline earth metals: first ionization energy low. Second ionization energy also low.
(7) Although there is a general trend toward an increase in the first ionization energy as we go from left to right across row, there are two minor inversions in this pattern:
The first ionization energy of boron (B) is smaller than beryllium (Be)
The first ionization energy of oxygen (O2) is smaller than nitrogen (N2).
The first ionization energy of aluminum (Al) is smaller than magnesium (Mg).
The first ionization energy of silicon (Si) is smaller than phosphor (P5).
By looking at the electron configurations of these elements:
In case of boron (5B) and beryllium (4Be):

The first ionization energy of beryllium (Be) is higher than boron (B) due to stability of beryllium (Be) than boron (B) where (s) is completely filled
In case of nitrogen (7N) and oxygen (8O):

The first ionization energy of nitrogen (N) is higher than oxygen (O) due to stability of nitrogen (N) than oxygen (O) where (p) is half completely filled
In case of chlorine (17Cl) and sodium (11Na):
Ionization energy of (17Cl) > (11Na) because Ionization potential increases from left to right due to decreasing of atomic radius. And this is due to:
Gradual increasing in positively nuclear charge that increase the attraction force for valence electrons
In case of magnesium (12Mg) and calcium (20Ca):

Ionization energy of (12Mg) > (20Ca) because ionization potential decreases from up to down due to increasing of atomic radius. And this is due to:
The effect of extra energy levels being added is more than the effect of extra positively nuclear charge
Increasing of the repulsion forces between valence electrons and inner core electrons
An atom would become stable if its outer sublevel is completely or half completely filled
3rd ionization energy > 2nd ionization energy > 1st ionization energy due to one of:
Increasing positively nuclear charge and decreasing of ionic radius
Stability where the outer sublevel of the ion may becomes completely or half completely filled
2nd ionization energy > 1st ionization energy due to Increasing positively nuclear charge and decreasing of ionic radius
3rd ionization energy > 2nd ionization energy due to stability where the outer sublevel of the ion becomes half completely filled.
For each of the following sets of atoms, decide which has the highest and lowest ionization energies and why
(1) Mg, Si, and S
Mg, Si, and S: All are in the same period and use the same number of energy levels. Mg has the lowest I.E. because it has the lowest effective nuclear charge. S has the highest I.E. because it has the highest effective nuclear charge.
(2) Mg, Ca, and Ba
Mg, Ca, and Ba: All are in the same group and have the same effective nuclear charge. Mg has the highest I.E. because it uses the smallest number of energy levels. Ba has the lowest I.E. because it uses the largest number of energy levels.
(3) F, Cl, and Br
F, Cl, and Br: All are in the same group and have the same effective nuclear charge. F has the highest I.E. because it uses the smallest number of energy levels. Br has the lowest I.E. because it uses the largest number of energy levels.
(4) Ba, Cu, and Ne
Ba, Cu, and Ne: All are in different groups and periods, so both factors must be considered. Fortunately both factors reinforce one another. Ba has the lowest I.E. because it has the lowest effective nuclear charge and uses the highest number of energy levels. Ne has the highest I.E. because it has the highest effective nuclear charge and uses the lowest number of energy levels
(5) Si, P, and N
Si, P, and N: Si has the lowest I.E. because it has the lowest effective nuclear charge and is tied (with P) for using the most energy levels. N has the highest I.E. because it uses the fewest energy levels and is tied (with P) for having the highest effective nuclear charge