ELECTRONS IN ATOMS - Chemical Fundamentals of Geology and Environmental Geoscience - page 94

Free electron ( E = 0)

0

4s 4p 4d 4f

n = 4

N-shell
M-shell

n = 3

3s 3p 3d

L-shell

n = 2

2s 2p

-5

Ionization energy
of hydrogen

Figure 5.6 A scale diagram of the energy-level
structure of orbitals in the hydrogen atom (with
only one electron), the electron energy being
expressed in electron-volts (eV). Note that in
hydrogen the 2 s and 2p orbitals have the same
energy (together they constitute a 'shell', in this
case the 'L-shell'), as do the 3 s, 3p and 3d
orbitals ('M-shell'). Note also that the zero on
the electron energy scale is equivalent to the
energy of a free electron at rest. A negative
electron energy therefore signifies that the
electron is trapped in the atom by the nuclear
field. The more negative the energy, the more
tightly bound the electron has become, and the
harder it is to remove from the atom. Positive
energy values signify free electrons having
appreciable kinetic energy.

-10

1s

K-she l l

n = 1

-15

l = 0 l = 1 l = 2 l = 3

Multi-electron atoms

therefore, they are energetically equivalent, at least in
the hydrogen atom. The same is true of the one 3 s
orbital, the three 3p orbitals and the five 3d orbitals,
all of which share a still higher energy level. Note
that there is a direct relationship between an orbital's
relative size and its energy level. Evidently an elec-
tron must possess quite a high energy before it can
overcome the nuclear attraction sufficiently to spread
itself into these more far-flung provinces of the
atom's territory. In the hydrogen atom these orbitals
are normally unoccupied, except temporarily
(Chapter 6).
As n increases further, the energy levels get progres-
sively closer together, and so the highest levels have
been omitted from Figure 5.6 for clarity.

In order to describe the chemistry of elements other
than hydrogen, the Schrödinger model needs to be
extended to explain how more than one electron can be
accommodated together in a single atom. Can separate
electrons adopt identical waveforms in the same atom,
or does wave mechanics organize them into different
spatial domains around the nucleus?
The answer to this vital question was provided by
another Austrian, Wolfgang Pauli, who in 1925 (act-
ually a year before Schrödinger's paper) formulated
the Exclusion Principle . Stated in wave-mechanical
terms, it says: 'No two electrons in the same atom may
possess identical values of all four quantum numbers'.