0.5 Electron orbitals and electron configurations in atoms  (Page 9/10)

Third is a very exciting conclusion based on the first two. Notice that when n = 2, there are four different orbitals to which we can assign a total of eight electrons. After those eight electrons have been assigned, no more electrons can be assigned to orbitals with n = 2. But we’ve seen this before! The number eight corresponds to our shell model of the atom in which only eight electrons could be in the second or third shell of each atom. Now we have an explanation of why the electron shells “fill up.” Each shell corresponds to a particular n value, and there are a limited number of electrons which can fit into the orbitals in each shell. Once those orbitals have all been assigned two electrons, the shell is “full,” and any additional electrons must be assigned to a new shell at a higher energy.

Looking at the pattern of the data in [link] reveals to us the ordering of the orbitals in terms of increasing energy, at least for this set of atoms. The data show that the orbitals, in order of increasing energy, are:

1s<2s<2p<3s<3p<4s<3d<4p<5s etc.

Observation 4: the importance of electron-electron repulsion

There is a single detail missing from our description, which is of some importance to our discussion. Why is the 2s orbital lower in energy than the 2p orbital? This is something of a surprise. If we go back to look at the energy levels for an electron in a hydrogen atom, we will recall that the energy depends only on the n quantum number. This is the same for an electron in the 2s and 2p orbitals in a hydrogen atom. But in all of the atoms from lithium to neon, it is clear that the 2s orbital is lower in energy than the 2p orbital. Hydrogen is unique because it has only a single electron. As a result, there is no electron-electron repulsion to affect the energy. Apparently, when there is electron-electron repulsion, an electron in the 2s orbital has a lower energy than an electron in the 2p orbital. Therefore, the movement of the electron in the 2s orbital must produce a smaller amount of electron-electron repulsion than that produced by the movement of the electron in the 2p orbital. Electrons do repel each other. If they move in such a way as to maintain distance from one another, the amount of this repulsion is smaller. The 2s orbital must do a better job of this than the 2p orbital.

It is very difficult to calculate the energy from electron-electron repulsion because we do not know, on average, how far apart the electrons typically are so we can’t use Coulomb’s law in any simple way. We need a simple model instead. One way to do this is to think of the shell structure of the atom. An n = 2 electron is farther from the nucleus than an n = 1 electron. In lithium, for example, the lone 2s electron is on the outside of both the nucleus and the two 1s electrons. These two 1s electrons form a negatively charged “core” which surrounds the nucleus. In lithium, the nuclear charge is +3 and the charge on the core electrons is -2, so the 2s electron feels an attraction to a +3 charge and a repulsion from a -2 charge. A simple way to look at this is as though the 2s electron “feels” a net charge from the core of +1. This is sometimes called the “effective nuclear charge” because it takes into account both the attraction to the charge on the nucleus and the repulsion from the negative charge from the core electrons. In one way of viewing this, the nuclear charge is partially “shielded” by the negative charge of the core electrons, reducing the attraction of the 2s electron to the nucleus.