The Foundations of Chemistry

4.The spin quantum number,ms, refers to the spin of an electron and the orienta-

tion of the magnetic field produced by this spin. For every set of n, 
, and m
values,

mscan take the value ^12 or 
^12 :

ms^12 

The values of n,
, and m
describe a particular atomic orbital. Each atomic orbital can
accommodate no more than two electrons, one with ms^12 and another with ms
^12 .
Table 5-4 summarizes some permissible values for the four quantum numbers. Spec-
troscopic evidence confirms the quantum mechanical predictions about the number of
atomic orbitals in each shell.

ATOMIC ORBITALS

Let us now describe the distributions of electrons in atoms. For each neutral atom, we
must account for a number of electrons equal to the number of protons in the nucleus,
that is, the atomic number of the atom. Each electron is said to occupy an atomic orbital
defined by a set of quantum numbers n,
, and m
. In any atom, each orbital can hold a
maximum of two electrons. Within each atom, these atomic orbitals, taken together, can
be represented as a diffuse cloud of electrons (Figure 5-19).
The main shell of each atomic orbital in an atom is indicated by the principal quantum
number n(from the Schrödinger equation). As we have seen, the principal quantum
number takes integral values: n1, 2, 3, 4,.... The value n1 describes the first, or
innermost, shell. These shells have been referred to as electron energy levels. Successive
shells are at increasingly greater distances from the nucleus. For example, the n2 shell
is farther from the nucleus than the n1 shell. The electron capacity of each shell is
indicated in the right-hand column of Table 5-4. For a given n, the capacity is 2n^2.
By the rules of Section 5-15, each shell has an ssubshell (defined by
0) consisting
of one satomic orbital (defined by m
0). We distinguish among orbitals in different

5-16

As you study the next two sections,

keep in mind that the wave function,

, for an orbital characterizes two

features of an electron in that orbital:

(1) where(the region in space) the

probability of finding the electron is

high and (2) how stablethat electron is

(its energy).

5-16 Atomic Orbitals 209

TABLE 5-4 Permissible Values of the Quantum Numbers Through n
 4

Electron Capacity of Electron Capacity of
n
m
ms Subshell
4
 2 Shell
2 n^2

10 (1s)0 ^12 ,
^12  22

20 (2s)0 ^12 ,
^12  28

1 (2p) 
1, 0,  1 ^12 for each value of m
 6

30 (3s)0 ^12 ,
^12  218

1 (3p) 
1, 0,  1 ^12 for each value of m
 6

2 (3d) 
2, 
1, 0, 1,  2 ^12 for each value of m
 10

40 (4s)0 ^12 ,
^12  232
1 (4p)
1, 0,  1 ^12 for each value of m
6
2 (4d)
2,
1, 0, 1,  2 ^12 for each value of m
10
3 (4f)
3,
2,
1, 0, 1, 2,  3 ^12 for each value of m
14

See the Saunders Interactive

General Chemistry CD-ROM,

Screen 7.12, Quantum Numbers and

Orbitals.