Page 78 - Electrical Properties of Materials

The periodic table 61

elements. We shall see how Mendeleev’s periodic table can be built up with the There are two important points to
aid of the quantum-mechanical solution of the hydrogen atom. realize:
We shall start by taking the lowest energy level, count the number of states,
1. We have our set of quantum
fill them up one by one with electrons, and then proceed to the next energy
numbers n, l, m l , and s, each
level; and so on.
one specifying a state with a
According to eqn (4.31) the lowest energy level is obtained with n = 1. Then
1
l =0, m l = 0, and there are two possible states of spin s = ± . Thus, the lowest definite energy. The energy de-
2 pends on n only, but several
energy level may be occupied by two electrons. Putting in one electron we get
states exist for every value of n.
hydrogen, putting in two electrons we get helium, putting in three electrons ...
2. Pauli’s exclusion principle
No, we cannot do that; if we want an element with three electrons, then the
must be obeyed. Each state can
third electron must go into a higher energy level.
be occupied by one electron
With helium the n = 1 ‘shell’ is closed, and this fact determines the chemical
properties of helium. If the helium atom happens to meet other electrons (in only.
events officially termed collisions), it can offer only high-energy states. Since
all electrons look for low-energy states, they generally decline the invitation.
They manifest no desire to become attached to a helium atom.
If the probability of attracting an electron is small, can the helium atom give
away one of its electrons? This is not very likely either. It can offer to its own
electrons comfortable low-energy states. The electrons are quite satisfied and
stay. Thus, the helium atom neither takes up nor gives away electrons. Helium
is chemically inert.
We now have to start the next energy shell with n = 2. The first element
there is lithium, containing two electrons with n =1, l = 0 and one electron
with n =2, l = 0. Adopting the usual notations, we may say that lithium has
two 1s electrons and one 2s electron. Since the 2s electron has higher energy,
it can easily be tempted away. Lithium is chemically active.
The next element is beryllium with two 1s and two 2s electrons; then comes
boron with two 1s, two 2s, and one 2p electrons, which, incidentally, can be de-
2
2
1
noted in an even more condensed manner as 1s ,2s ,2p . Employing this new
2
2
2
notation, the six electrons of carbon appear as 1s ,2s ,2p , the seven electrons
2
2
3
2
4
2
of nitrogen as 1s ,2s ,2p , the eight electrons of oxygen as 1s ,2s ,2p , and
2
5
2
the nine electrons of fluorine as 1s ,2s ,2p .
Let us pause here for a moment. Recall that a 2p state means n = 2 and l =1,
which according to eqn (4.28) can have three states (m l = 0 and m l = ±1) or,
taking account of spin as well, six states altogether. In the case of fluorine
five of them are occupied, leaving one empty low-energy state to be offered
to outside electrons. The offer is often taken up, and so fluorine is chemically
active.
Lithium and fluorine are at the opposite ends, the former having one extra
electron, the latter needing one more electron to complete the shell. So it seems
quite reasonable that when they are together, the extra electron of lithium will
occupy the empty state of the fluorine atom, making up the compound LiF.
A chemical bond is born, a chemist would say.
We shall discuss bonds later in more detail. Let us return meanwhile to the
rather protracted list of the elements. After fluorine comes neon. The n =2
shell is completed: no propensity to take up or give away electrons. Neon is
chemically inert like helium.
The n = 3 shell starts with sodium, which has just one 3s electron and
should therefore behave chemically like lithium. A second electron fills the 3s