Number of Subshells Number of Maximum Number
Shell per Shell Atomic Orbitals of Electrons
nn n^22 n^21 1 1 (1s)2
2 2 4 (2s, 2px, 2py, 2pz)8
3 3 9 (3s, three 3p’s, five 3d’s) 18
4 4 16 32
5 5 25 50ELECTRON CONFIGURATIONS
The wave function for an atom simultaneously depends on (describes) all of the electrons
in the atom. The Schrödinger equation is much more complicated for atoms with more
than one electron than for a one-electron species such as a hydrogen atom, and an explicit
solution to this equation is not possible even for helium, let alone for more complicated
atoms. We must therefore rely on approximations to solutions of the many-electron
Schrödinger equation. We shall use one of the most common and useful, called the orbital
approximation.In this approximation, the electron cloud of an atom is assumed to be
the superposition of charge clouds, or orbitals, arising from the individual electrons; these
orbitals resemble the atomic orbitals of hydrogen (for which exact solutions are known),
which we described in some detail in the previous section. Each electron is described by
the same allowed combinations of quantum numbers (n, , m, and ms) that we used for
the hydrogen atom; however, the order of energies of the orbitals is often different from
that in hydrogen.
Let us now examine the electronic structures of atoms of different elements. The elec-
tronic arrangement that we will describe for each atom is called the ground state electron
configuration.This corresponds to the isolated atom in its lowest energy, or unexcited,
state. Electron configurations for the elements, as determined by experiment, are given
in Appendix B. We will consider the elements in order of increasing atomic number, using
as our guide the periodic table on the inside front cover of this text.
In describing ground state electron configuration, the guiding idea is that the total
energyof the atom is as low as possible. To determine these configurations, we use the
Aufbau Principleas a guide:5-17
Figure 5-27 Electron spin. Electrons act as though they
spin about an axis through their centers. Because electrons
may spin in two directions, the spin quantum number has
two possible values, ^12 and ^12 . Each electron spin
produces a magnetic field. When two electrons have
opposite spins, the attraction due to their opposite
magnetic fields (gray arrows) helps to overcome the
repulsion of their like charges. This permits two electrons
to occupy the same region (orbital).214 CHAPTER 5: The Structure of Atoms
One electron has ms = + –;
the other has ms = – –.^121
2The great power of modern computers
has allowed scientists to make
numerical approximations to this
solution to very high accuracy for
simple atoms such as helium. As the
number of electrons increases,
however, even such numerical
approaches become quite difficult to
apply and interpret. For multielectron
atoms, more quantitative
approximations are used.
The German verb aufbauenmeans “to
build up.”
See the Saunders Interactive
General Chemistry CD-ROM,
Screen 8.2, Spinning Electrons.