The Foundations of Chemistry

Electrons are indistinguishable. We

have numbered them 1, 2, 3, and so on

as an aid to counting them.

5-17 Electron Configurations 221

Let us now write the quantum numbers to describe each electron in an atom of nitrogen.
Keep in mind the fact that Hund’s Rule must be obeyed. Thus, there is only one (unpaired)
electron in each 2porbital in a nitrogen atom.

EXAMPLE 5-8 Electron Configurations and Quantum Numbers

Write an acceptable set of four quantum numbers for each electron in a nitrogen atom.

Plan

Nitrogen has seven electrons, which occupy the lowest energy orbitals available. Two electrons
can occupy the first shell, n1, in which there is only one sorbital; when n1, then
must
be zero, and therefore m
0. The two electrons differ only in spin quantum number, ms. The
next five electrons can all fit into the second shell, for which n2 and
may be either 0 or

1. The
   0 (s) subshell fills first, and the
   1 (p) subshell is occupied next.

Solution

not be viewed as hard-and-fast rules; the total energyof the atom is as low as possible.

Some of the reasons for exceptions are

1.The Aufbau order of orbital energies is based on calculations for the hydrogen atom,

which contains only one electron. The orbital energies also depend on additional

factors such as the nuclear charge and interactions of electrons in different occupied

orbitals.

2.The energy scale varies with the atomic number.

3.Some orbitals are very close together, so their order can change, depending on the

occupancies of other orbitals.

Some types of exceptions to the Aufbau order are general enough to remember easily,

for example, those based on the special stability of filled or half-filled sets of orbitals.

Other exceptions are quite unpredictable. Your instructor may expect you to remember

some of the exceptions.

EXAMPLE 5-9 Electron Configurations and Quantum Numbers

Write an acceptable set of four quantum numbers for each electron in a chlorine atom.

Plan

Chlorine is element number 17. Its first seven electrons have the same quantum numbers as
those of nitrogen in Example 5-8. Electrons 8, 9, and 10 complete the filling of the 2psubshell

Electron n 
 m
 ms e
Configuration

1,2

10 0^12 

1 s^2

10 0
^12 

3,4

20 0^12 

2 s^2

20 0
^12 

21 
 1 ^12 or 
^12  2 px^1

5, 6, 7 2 1 0 ^12 or 
^12  2 py^1 or 2p^3

21  1 ^12 or 
^12  2 pz^1











          

         

 In the lowest energy configurations,

the three 2pelectrons either have ms

 2 ^1 or all have ms
^12 .