Page 79 - Electrical Properties of Materials

62 The hydrogen atom and the periodic table

shell in magnesium. Then come aluminium, silicon, phosphorus, sulphur, and
chlorine with one, two, three, four, and five 3p electrons, respectively. Chlorine
is again short of one electron to fill the 3p shell, and so behaves like fluorine.
The 3p shell is completed in argon, which is again inert.
So far everything has gone regularly, and by the rules of the game the next
electron should go into the 3d shell. It does not. Why? Well, why should it? The
electrons in potassium are under no obligation to follow the energy hierarchy
of the hydrogen atom like sheep. They arrange themselves in such a way as to
have the lowest energy. If there were no interaction between the electrons, the
2
energy levels of the element would differ only by the factor Z , conforming
otherwise to that of the hydrogen atom. If the interaction between the electrons
mattered a lot, we should completely abandon the classification based on the
energy levels of the hydrogen atom. As it happens, the electron interactions
∗
∗ In the hydrogen-type solutions the en- are responsible for small quantitative changes that cause qualitative change
ergy depends only on n, whereas tak- in potassium—and in the next few elements, called the transition elements.
ing account of electron interactions the First the 4s shell is filled, and only after that are the 3d states occupied. The
energy increases with increasing val-
ues of l. It just happens that in po- balance between the two shells remains, however, delicate. After vanadium
tassium the energy of the 3d level (n =3, (with three 3d and two 4s electrons) one electron is withdrawn from the 4s
l = 2) is higher than that of the 4s level shell; hence chromium has five 3d electrons but only one 4s electron. The same
(n =4, l =0).
thing happens later with copper, but apart from that everything goes smoothly
up to krypton, where the 4p shell is finally completed.
The regularity is somewhat marred after krypton. There are numerous
deviations from the hydrogen-like structure but nothing very dramatic. It might
be worthwhile mentioning the rare earth elements in which the 4f shell is being
filled while eleven electrons occupy levels in the outer shells. Since chemical
properties are mainly determined by the outer shells, all these elements are
hardly distinguishable chemically.
A list of all these elements with their electron configurations is given in
Table 4.1. The periodic table (in one of its more modern forms) is given in
Fig. 4.5. You may now look at the periodic table with more knowing eyes. If you
were asked, for example, why the alkali elements lithium, sodium, potassium,
rubidium, caesium, and francium have a valency of one, you could answer in
the following way.
The properties of electrons are determined by Schrödinger’s equation. The
solution of this equation for one electron and one proton tells us that the elec-
tron may be in one of a set of discrete states, each having a definite energy
level. When there are many electrons and many protons, the order in which
these states follow each other remains roughly unchanged. We may then derive
the various elements by filling up the available states one by one with elec-
trons. We cannot put more than one electron in a state because the exclusion
principle forbids this.
The energy of the states varies in steps. Within a ‘shell’ there is a slow
Whenever a new shell is initiated, variation in energy but a larger energy difference between shells.
there is one electron with consid- All the alkali elements start new shells. Therefore each of them may
erably higher energy than the rest. lose an electron; each of them may contribute one unit to a new chemical
Since all electrons strive for lower configuration; and each of them has a valency of one.
energy, this electron can easily be We may pause here for a moment. You have had the first taste of the
lost to another element. power of Schrödinger’s equation. You can see now that the solution of all the
basic problems that have haunted the chemists for centuries is provided by