Ionization potential

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The ionization potential, or ionization energy, of an atom or molecule is the energy required to strip it of an electron. More generally, the nth ionization energy is the energy required to strip it of an nth electron after the first [n-1] have already been removed. It is centrally significant in physical chemistry as a measure of the "reluctance" of an atom or of a molecule to surrender an electron, or the "strength" by which the electron is bound.

Contents

1 Values and trends
2 Electrostatic explanation
3 Quantum-mechanical explanation
4 See also

Values and trends

Main article: Ionization energies of the elements

Generally speaking, atomic ionization energies decrease down a group of the periodic table, and increase left-to-right across a period. Ionization energy exhibits a strong negative correlation with atomic radius. Successive ionization energies of any given element increase markedly. Particularly dramatic increases occur after any given block of atomic orbitals is exhausted. This is because, after all the electrons are removed from an orbital, the next ionization energy involves removing an electron from a closer orbital to the nucleus. Electrons in the closer orbital experience greater forces of electrostatic attraction, and thus, require more energy to be removed.

Some values for elements of the third period are given in the following table:

Successive ionization energies in kJ/mol
Element First Second Third Fourth Fifth Sixth Seventh
Na 496 4,560
Mg 738 1,450 7,730
Al 577 1,816 2,744 11,600
Si 786 1,577 3,228 4,354 16,100
P 1,060 1,890 2,905 4,950 6,270 21,200
S 999 2,260 3,375 4,565 6,950 8,490 11,000
Cl 1,256 2,295 3,850 5,160 6,560 9,360 11,000
Ar 1,520 2,665 3,945 5,770 7,230 8,780 12,000

*Successive ionization energies in kJ/mol*
Element	First	Second	Third	Fourth	Fifth	Sixth	Seventh
Na	496	4,560
Mg	738	1,450	7,730
Al	577	1,816	2,744	11,600
Si	786	1,577	3,228	4,354	16,100
P	1,060	1,890	2,905	4,950	6,270	21,200
S	999	2,260	3,375	4,565	6,950	8,490	11,000
Cl	1,256	2,295	3,850	5,160	6,560	9,360	11,000
Ar	1,520	2,665	3,945	5,770	7,230	8,780	12,000

In order to determine how many electrons are in the outermost shell of an element, one can use the ionization energy. If, for example, it required 1,500 kJ/mol to remove one electron and required 6,000 kJ/mol to remove another electron and then 5,000 kJ/mol, etc. this means that the element had one electron in its outermost shell. This means that the element is a metal and in order for this element to achieve a stable octet, it looks to lose one electron. Thus, the first electron is easy to remove and consequently the ionization energy is low. Notice, however, that once the stable octet has been formed, it becomes much more difficult to remove the next electron. If that electron can be removed the consequent one can be removed a bit more easily.

Electrostatic explanation

Atomic ionization energy can be predicted by a simple analysis using electrostatic potential and the Bohr model of the atom, as follows.

Consider an electron of charge -e, and an ion with charge +ne, where n is the number of electrons missing from the ion. According to the Bohr model, were the electron to approach and bind with the atom, it would come to rest at a certain radius a. The electrostatic potential at distance a from the ionic nucleus, referenced to a point infinitely far away, is:

[V = \frac \frac \,\!]

Since the electron is negatively charged, it is drawn to this positive potential. (The value of this potential is called the ionization potential). The energy required for it to "climb out" and leave the atom is:

[E = eV = \frac \frac \,\!]

This simple analysis is incomplete, as it leaves the distance a as an unknown. It can be made more rigorous by assigning to each electron of every chemical element a characteristic distance, chosen so that this relation agrees with experimental data.

Quantum-mechanical explanation

According to the more sophisticated theory of quantum mechanics, the location of an electron is best described as a "cloud" of likely locations that ranges near and far from the nucleus. The energy can be calculated by integrating over this cloud. This cloud corresponds to a wavefunction or, more specifically, to a linear combination of Slater determinants, i.e., according to Pauli exclusion principle, antisymmetrized products of atomic or molecular orbitals. This linear combination is called a configuration interaction expansion of the electronic wavefunction.

In general, calculating the nth ionization energy requires subtracting the energy of a [Z-n+1] electron system from the energy of a [Z-n] electron system. Calculating these energies is not simple, but is a well-studied problem and is routinely done in computational chemistry. At the lowest level of approximation, the ionization energy is provided by Koopmans' theorem.

Ionization potential

Values and trends

Electrostatic explanation

Quantum-mechanical explanation

See also