Page 67 - Theory and Problems of BEGINNING CHEMISTRY

56 ELECTRONIC CONFIGURATION OF THE ATOM [CHAP. 4

(Table 4-3) are in the first shell and in the same subshell. The third and fourth electrons are in the same shell and
subshell with each other. They are also in the same shell with the next six electrons (all have n = 2) but a different
subshell (l = 0 rather than 1). With the letter designations of Sec. 4.3, the first two electrons of aluminum are in
the 1s subshell, the next two electrons are in the 2s subshell, and the next six electrons are in the 2p subshell.
The following two electrons occupy the 3s subshell, and the last electron is in the 3p subshell.
Since the possible numerical values of l depend on the value of n, the number of subshells within a given
shell is determined by the value of n. The number of subshells within a given shell is merely the value of n, the
shell number. Thus, the first shell has one subshell, the second shell has two subshells, and so forth. These facts
are summarized in Table 4-4. Even the atoms with the most electrons do not have enough electrons to completely
fill the highest shells shown. The subshells that hold electrons in the ground states of the biggest atoms are in
boldface.
Table 4-4 Arrangement of Subshells in Electron Shells

Energy level n Type of Subshell Number of Subshells

1 s 1
2 s, p 2
3 s, p, d 3
4 s, p, d, f 4
5 s, p, d, f , g 5
6 s, p, d, f, g, h 6
7 s, p, d, f, g, h, i 7

EXAMPLE 4.8. What are the values of n and l in each of the following subshells? (a)2p,(b)3s,(c)5d, and (d)4 f .
Ans. (a) n = 2,l = 1(b) n = 3,l = 0(c) n = 5,l = 2(d) n = 4,l = 3

EXAMPLE 4.9. Show that there can be only two electrons in any s subshell.
Ans. For any given value of n, there can be a value of l = 0, corresponding to an s subshell. For l = 0 there can be only
one possible m l value: m l = 0. Hence, n,l, and m l are all specified for a given s subshell. Electrons can then have
1
1
spin values of m s =+ or m s =− . Thus, every possible set of four quantum numbers is used, and there are no
2 2
other possibilities in that subshell. Each of the two electrons has the first three quantum numbers in common and has
a different value of m s . The two electrons are said to be paired.
Depending on the permitted values of the magnetic quantum number m l , each subshell is further broken
down into units called orbitals. The number of orbitals per subshell depends on the type of subshell but not on
the value of n. Each consists of a maximum of two electrons; hence, the maximum number of electrons that can
occupy a given subshell is determined by the number of orbitals available. These relationships are presented in
Table 4-5. The maximum number of electrons in any given energy level is thus determined by the subshells it
contains. The first shell can contain 2 electrons; the second, 8 electrons; the third, 18 electrons; the fourth, 32
electrons; and so on.

Table 4-5 Occupancy of Subshells

Allowed Values Number of Maximum Number
Type of Subshell of m l Orbitals of Electrons

s 0 1 2
p −1, 0, 1 3 6
d −2, −1, 0, 1, 2 5 10
f −3, −2, −1, 0, 1, 2, 3 7 14