In chemistry courses students blithely accept the notion of negative ions such as Cl^- and O^2- without realizing what surprising, even puzzling, entities they are. In the O^2- ion there is an electron, with a negative charge, clinging to an entity O^- which has a net negative charge. An entity with a net negative charge would be thought to repel an electron.

My recollection is that these multiply negative ions were justified by the power involved in completing a shell of eight. Somehow the supposed energy advantage of a filled shell overcame the energy disadvantage of bringing in a repulsive particle.

The Correct Explanation of Negative Ions

The correct explanation of negative ions is entirely different from the matter of completing a shell of eight. First it is necessary to consider some aspects of electrostatic charge. When a charge is distributed uniformaly on a spherical shell it has the effect on another charge outside of the sphere equal to what that same charge would have concentrated at the center of the sphere. On the other hand, the effect on a charge within the sphere is zero. What is left out is the effect of a charge distributed on a spherical shell on a charge located on particles located at the middle of that distributed charge. That effect is equal to what half the charge would have located at the center of the sphere. Thus if the number of electrons in a shell is denoted as ε₁ and there are ε₀ electrons located interior to the shell then the effective charge Z acting on one electron in the shell is

Z = p − ε₀ − ½(ε₁-1)

where p is the number of protons in the nucleus.

Thus the energy required to remove an electron from a shell should decrease with the number of electrons in that shell. This is due to the shielding of some of the positive charge of the nucleus by electrons in the same-shell.

Negatively charged ions are created when an atom acquires enough electrons to complete a shell. For example, the fluorine atom has nine protons and nine electrons. There are two electrons in the first shell and seven in the second shell. The capacity of the second shell is eight. The fluorine ion F- has a net negative charge yet the electrons are some how clinging to it. The notion of shielding of electrons in the same-shell provides a different sort of justification for the F-. The two electrons in the inner shell fully shield two protons. For any electron in the second shell there are seven other electrons in the same shell, each shielding a half unit of positive charge each. That make the charge experienced by the eighth electron in the second shell equal to (9-2-½(7))=3.5 positive charges. That is sufficient to hold that eighth electron in the second shell.

An oxygen nucleus has 8 protons and 8 neutrons. There are two electrons in the first shell. In the oxygen atom there are six electrons in the second shell. The net positive charge experienced by a seventh electron in the second shell is (8−2−½6)=3. Thus it would be held as tightly as the third electron in a lithium atom; i.e., not strongly but definitely held. The eighth electron in the second shell of oxygen would experience a net positive charge of (8−2−½7)=2.5. Again definitely there is a positive attraction holding the eighth electron in the O^2- ion.

The reality is more complicated but this computation explains how the extra electrons in negatively charged ion could be clinging to a system with no net positive charge. Outside of the last shell the ion has a net negative charge but within the last shell there is a net positive charge because of the fractional same-shell shielding.

The greater chemical activity of fluorine compared to oxygen is sometime thought to be because fluorine is only one short of completing a shell of eight while oxygen is two short. That is not the case. Fluorine has a more powerful attraction for an eighth electron in the second shell than does oxygen because fluorine has nine protons in its nucleus and oxygen has only eight. Thus the net positive charge experienced by the eighth electron for fluorine is 3.5 whereas for oxygen it is only 2.5. Thus fluorine more readily forms ions than oxygen and fluorine is more active chemically than oxygen.

For sodium the next electron is in the third shell. All of the electrons in the second shell then full shield eight units of charge in the nucleus. Thus the net positive charge experienced by the first electron in the third shell is (11−2−8)=1. A sodium atom thus very easily relinquishes that electron in the third shell. The net charge experienced by the second electron in the third shell for a magnesium atom is (12−2−8−½1)=1.5. Thus that last electron is more tightly held by a magnesium atom and positive magnesium ions are less readily formed than sodium ions. Hence magnesium is less chemically active than sodium.