Page 68 - Theory and Problems of BEGINNING CHEMISTRY

CHAP. 4] ELECTRONIC CONFIGURATION OF THE ATOM 57

Suppose we want to write the electronic configuration of titanium (atomic number 22). We can rewrite the
first 13 electrons that we wrote above for aluminum and then just keep going. As we added electrons, we filled
the first shell of electrons first, then the second shell. When we are filling the third shell, we have to ask if the
electrons with n = 3 and l = 2 will enter before the n = 4 and l = 0 electrons. Since n + l for the former is 5
and that for the latter is 4, we must add the two electrons with n = 4 and l = 0 before the last 10 electrons with
n = 3 and l = 2. In this discussion, the values of m l and m s tell us how many electrons can have the same set of
n and l values, but do not matter as to which come first.

14 15 16 17 18 19 20 21 22
n 3 3 3 3 3 4 4 3 3
l 1 1 1 1 1 0 0 2 2
0 +1 −1 0 +1 0 0 −2 −1
m l
1 1 1 1 1 1 1 1 1
m s − − + + + − + − −
2 2 2 2 2 2 2 2 2
n + l 4 4 4 4 4 4 4 5 5

Thus, an important development has occurred because of the n +l rule. The fourth shell has started filling before
the third shell has been completed. This is the origin of the transition series elements. Thus, titanium, atomic
number 22, has two electrons in its 1s subshell, two electrons in its 2s subshell, six electrons in its 2p subshell,
two electrons in its 3s subshell, six electrons in its 3p subshell, two electrons in its 4s subshell, and its last two
electrons in the 3d subshell.
We note in the electronic configuration for electrons 13 through 20 for titanium that when the (n + l) sum
was 4 we added the 3p electrons before the 4s electrons. Since each of these groups has an (n + l) sum of 4
[the (n + l) values are the same] we add electrons having the lower n value first.
We conventionally use a more condensed notation for electronic configurations, with the subshell notation
and a superscript to denote the number of electrons in that subshell. To write the detailed electronic configuration
of any atom, showing how many electrons occupy each of the various subshells, one needs to know only the
order of increasing energy of the subshells, given above, and the maximum number of electrons that will fit into
each, given in Table 4-5. A convenient way to designate such a configuration is to write the shell and subshell
designation, and add a superscript to denote the number of electrons occupying that subshell. For example, the
electronic configuration of the titanium atom is written as follows:

Number of electrons occupying each subshell

Ti 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 2

Shell
numbers Subshell designations

The shell number is represented by 1, 2, 3, ... , and the letters designate the subshells. The superscript numbers
tell how many electrons occupy each subshell. Thus, in this example, there are two electrons in the 1s subshell,
two in the 2s subshell, six in the 2p subshell, two in the 3s subshell, six in the 3p subshell, two in the 4s subshell,
and two in the 3d subshell. (The 3d subshell can hold a maximum of 10 electrons, but in this atom this sub-
shell is not filled.) The total number of electrons in the atom can easily be determined by adding the numbers in
all the subshells, that is, by adding all the superscripts. For titanium, this sum is 22, equal to its atomic number.

EXAMPLE 4.10. Write the electronic configuration of aluminum.
2
2
1
6
2
Ans. 1s 2s 2p 3s 3p .