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5.5 ATOMS HAVING MORE THAN ONE ELECTRON
Now that we have some familiarity with the properties of single electrons, we can move on to a discussion of atoms containing more than one electron. In order to do this, we will use the diagrams printed in full color in Plates 4 and 5 in which each electron is indicated in a different color.
Helium
The first element in the periodic table with more than one electron is helium, which has two electrons. Dot-density diagrams for both these electrons are shown in Plate 4. One electron is color coded in blue, and the other in green. Note that both electrons occupy the same orbital, namely, a 1s orbital. It turns out that 2 is the maximum number of electrons any orbital can hold. This restriction is connected with a property of the electrons not yet discussed, namely, their spin. Electrons can not only move about from place to place, but they can also rotate or spin about themselves. Two orientations (clockwise and counterclockwise) are possible for this spin. According to the Pauli exclusion principle, if two electrons occupy the same orbital, they must have opposite spins. Two such electrons are said to be spin paired and are often represented by arrows pointing in different directions, i.e., by the symbol 
. Two electrons spinning in the same direction are said to have their spins parallel and are indicated by 
. The Pauli principle implies that if two electrons have parallel spins, they must occupy different orbitals.
An obvious feature of the helium atom shown in Plate 4 is that it is somewhat smaller than the hydrogen atom drawn to the same scale on the same page. This contraction is caused by the increase in the charge on the nucleus from +1 in the hydrogen atom to +2 in the helium atom. This pulls both the green and the blue electron clouds in more tightly. This effect is offset, but to a lesser extent, by the mutual repulsion of the two electron clouds.
Lithium
In Plate 4 the three electrons of the lithium atom are color-coded blue, green, and red. As in the previous atom, two electrons (blue and green) occupy the 1s orbital. The Pauli principle prevents more than two electrons from occupying this orbital, and so the third (red) electron must occupy the next higher orbital in energy, namely, the 2s orbital. A convenient shorthand form for indicating this electron configuration is
1s22s1
The superscripts 2 and 1 indicate that there are two electrons in the 1s orbital and one electron in the 2s orbital.
As in the case of helium, the increase in nuclear charge to +3 produces a corresponding reduction in the size of the lithium 1s orbital. In sharp contrast to this compact inner orbital is the very large and very diffuse cloud of the outer 2s electron. There are two reasons why this 2s cloud is so large. The first reason is that the principal quantum number n has increased from 1 to 2. As shown in Fig. 5.7, the 2s electron cloud is bigger than 1s even in the hydrogen atom with a nuclear charge of only +1. A second reason is that the two 1s electrons are usually closer to the nucleus than the 2s electron. These two 1s electrons have the effect of screening or shielding the outer electron from the full attractive force of the +3 charge on the nucleus. When the 2s electron is some distance from the nucleus, it “sees” not only the +3 charge on the nucleus but also the two negative charges close by. The overall effect is almost as though two of the three positive charges on the nucleus are canceled, leaving a net charge of + 1 to hold the outer electron to the atom. This situation can also be described by saying that the effective nuclear charge is close to +1.
It should be clear from Plate 4 that when a lithium atom interacts with another atom, the 2s electron is far more likely to be involved than either of the two 1s electrons. In Lewis’ terminology, it is a valence electron and occupies a valence shell. The pair of 1s electrons are a complete shell and form the kernel of the lithium atom. There is thus a close correspondence between the wave-mechanical picture and Lewis’ earlier, less mathematical ideas. It is also worth noting that the wave model of lithium gives a spherical atom―a great advance over the elongated orbits which were needed to describe the alkali-metal atoms in the Bohr theory (see Fig. 5.2).
Beryllium
As shown in Plate 5, there are two 1s electrons and two 2s electrons in the Be atom. Its electron configuration is thus
1s22s2 or [He]2s2
The symbol [He] denotes the inner shell of two 1s electrons which have the same configuration as the noble gas He.
The beryllium atom is noticeably smaller than the lithium atom. This is because of the increase in nuclear charge from +3 to +4. Since the two outer 2s electrons (red and orange) do not often come between each other and the nucleus, they do not screen each other from the nucleus very well. Only the two inner electrons are effective in this respect. The effective nuclear charge holding a 2s electron to the nucleus is thus nearly +2, about twice the value for lithium, and the 2s electron clouds are drawn closer to the center of the atom.
Boron
The next element after beryllium is boron. Since the 2s orbital is completely filled, a new type of orbital must be used for the fifth electron. There are three 2p orbitals available, and any of them might be used. Plate 5 shows the fifth electron (color-coded purple) occupying the 2px orbital. Note carefully the differences between the 2px and 2s electron density distributions in the boron atom. Although on the average both electron clouds extend about the same distance from the nucleus, the 2px electron wave has a node passing through the center of the atom. Thus the 2px electron cloud has a much smaller probability density very close to the nucleus than does a 2s cloud. This means that the 2px electron cloud is more effectively screened by the 1s electrons from the nuclear charge. The atom exerts a slightly smaller overall pull on the 2p electron than it does on the 2s electron. The presence of the inner electrons thus has the effect of making the 2p orbital somewhat higher in energy than the 2s orbital.
This difference in energy between 2s and 2p electrons in the boron atom is an example of a more general behavior. In any atom with sufficient electrons we always find that a p orbital is somewhat higher in energy than an s orbital with the same value of n. In the lithium atom, for example, the third electron occupies a 2s rather than a 2p orbital because this gives it a somewhat lower energy. Further on in the periodic table we will find a similar difference between 3s and 3p orbitals and between 4s and 4p orbitals.
Carbon
We shall examine the electron configuration of one more atom, carbon, with the aid of the color-coded diagrams. In this case six electrons must be distributed among the orbitals—four will be paired in the 1s and 2s orbitals, leaving two p-type electron clouds. These are shown color-coded purple and cyan in Plate 5 as 2px and 2py, although the choice of x, y, or z directions is arbitrary. The choice of two different p orbitals is not arbitrary, however. It can be shown experimentally that both p electrons in the carbon atom have the same spin. Hence they cannot occupy the same orbital.
This illustrates another general rule regarding electron configurations. When several orbitals of the came type but different orientation are available, electrons occupy them one at a time, keeping spins parallel, until forced to pair by lack of additional empty orbitals. This is known as Hund's rule. Thus the electron configuration of carbon is
[He]2s22p1x2p1y
This might also be written (using arrows to indicate the orientations of electron spins):
The notation
[He]2s22p2
may also be found. In such a case it is assumed that the reader knows that the two 2p electrons are not spin paired.
It is worth noting that the arrangement of electrons in different 2p orbitals, necessitated by Hund’s rule, produces a configuration of lower energy. If both 2p electrons could occupy the same orbital, say the 2px orbital, they would often be close to each other, and their mutual repulsion would correspond to a higher potential energy. If each is forced to occupy an orbital of different orientation, though, the electrons keep out of each other’s way much more effectively. Their mutual repulsion and hence their potential energy is less.
In talking about polyelectronic atoms, the terms shell and subshell are often used. When the two electrons have the same principal quantum number, they are said to belong to the same shell. In the carbon atom, for example, the two 2s electrons and the 2px and the 2py electrons all belong to the second shell, while the two 1s electrons belong to the first shell. Shells defined in this manner can be further divided into subshells according to whether the electrons being discussed occupy s, p, d, or f orbitals. We can thus divide the second shell into 2s and 2p subshells. The third shell can similarly be divided into 3s, 3p, and 3d subshells, and so on.
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