ELECTRONS IN ATOMS - Chemical Fundamentals of Geology and Environmental Geoscience - page 95

At this point the fourth quantum number s , represent-
ing 'spin' of the electron, enters the discussion.
According to the Exclusion Principle, two electrons in
the same atom may possess the same values of n, l and
m (that is, they may 'occupy the same orbital') only if
they have different values of s . Wave mechanics allows
s only two possible values, −½ and + ½ ('½' is the con-
tribution that electron spin makes to the atom's angu-
lar momentum, but such details need not concern us.)
The important property of the spin is that it can have
one of two directions, a positive or negative 'sense'.
Although 'spin' in this quantized, wave-mechanical
form is rather an abstract concept, it leads to an impor-
tant practical outcome: each of the orbitals we have
been considering can accept two electrons, subject only
to the proviso that their spins are opposed.
We can now predict the arrangement of electrons in
any atom. Each electron entering an atom will of course
occupy the orbital that offers accommodation at the
lowest available energy level. In the atom of helium,
the two electrons present can share the 1 s orbital.
However in the lithium atom, with three electrons, the
third electron cannot - according to the Exclusion
Principle - enter the 1 s orbital, and must make do with
2 s instead, in spite of the much higher energy that
entails. One could in principle continue feeding elec-
trons into Figure 5.6, filling orbitals in order of ascend-
ing energy, to build an electronic model of any species
of atom, but before we can do so accurately we must
recognize two features of multi-electron atoms which
have been neglected in Figure 5.6.
In the first place, Figure 5.6 has to be modified a lit-
tle to allow for electrostatic repulsion between elec-
trons, an effect we did not have to consider in the
hydrogen atom. Mutual repulsion in multi-electron
atoms, when incorporated into the Schrödinger equa-
tion, leads to solutions with a slightly modified energy
structure, as shown in Figure 5.7. Orbitals that are not
spatially equivalent no longer share the same energy
level, but have energies which depend on l as well as
n. Thus although all of the 3d orbitals still have a com-
mon energy level (at least in an isolated atom), their
energy now exceeds that of the three 3p orbitals, which
in turn is greater than the 3 s energy. Figure 5.7 pro-
vides a more general framework for comparing the
electronic structure of different elements. However,
note that the energy axis in Figure 5.7 is non-linear
(see caption).

The second point to be remembered in discussing
multi-electron atoms is the increased nuclear charge
(owing to the greater number of protons, Z , in the
nucleus), which causes each electron to experience a
stronger electrostatic attraction towards the nucleus.
This changes the orbital picture quantitatively but not
qualitatively. The shapes of the various orbitals stay
the same, but with increasing nuclear charge they all
diminish in size as electron density is confined ever
more closely to the immediate vicinity of the nucleus.
The overall form of Figure 5.7 changes little from elem-
ent to element, but the negative energy associated with
a particular orbital becomes progressively greater (the
level becomes 'deeper' in energy space) with increas-
ing nuclear charge, as the energy scales on the left of
Figure 5.7 illustrate. In energy terms the two 1 s elec-
trons of the uranium atom are held 2000 times more
tightly (~ − 10 5 eV) than is the 1 s electron of a lithium
atom (−55 eV).

Electronic configurations

The electronic configuration of an atom is a symbolic
code describing the location of its electrons in the vari-
ous orbitals, something one can readily work out from
Figure 5.7. The element boron, for instance, has an
atomic number ( Z ) of 5, so that its nucleus contains five
protons and has five positive units of charge (5+).
Accordingly the boron atom has to accommodate five
electrons, and their distribution can be written:

221

boron:1s 2s 2p

The requirement to minimize total electron energy is
satisfied by putting two electrons into the 1 s orbital
(this is what the code '1 s 2 ' means), a further two into the
2 s orbital (hence '2 s 2 '), and the one remaining electron
into one of the three 2p orbitals ('2p 1 '). We do not need
to specify - indeed we have no way of knowing - which
of the three 2p orbitals receives this single electron.
Another example is the element sodium ( Z = 11). Its
electronic configuration is

2261

sodium :1s2s2p3s

In the sodium atom, the three 2p orbitals have accepted
their joint quota of six electrons, but one more electron
still remains to be accommodated. This goes in the