Page 69 - Theory and Problems of BEGINNING CHEMISTRY

58 ELECTRONIC CONFIGURATION OF THE ATOM [CHAP. 4

4.6. SHAPES OF ORBITALS
The Heisenberg uncertainty principle states that, since the energy of the electron is known precisely, its
exact position cannot be known. It is possible to learn only the probable location of the electron in the vicinity of
the atomic nucleus. The mathematical details of expressing the probability are quite complex, but it is possible to
give an approximate description in terms of values of the quantum numbers n,l, and m l . The shapes of the more
important orbitals are shown in Fig. 4-4 for the case of the hydrogen atom. This figure shows that, in general,
an electron in the 1s orbital is equally likely to be found in any direction about the nucleus. (The maximum
probability is at a distance corresponding to the experimentally determined radius of the hydrogen atom). In
contrast, in the case of an electron in a 2p orbital, there are three possible values of the quantum number m l .
There are three possible regions in which the electron is most likely to be found. It is customary to depict these
orbitals as being located along the cartesian (x, y, and z) axes of a three-dimensional graph. Hence, the three
probability distributions are labeled p x , p y , and p z , respectively.

z z z z
y y y y
x x x x
1s 2p z 2p x 2p y

z z z z z
y y y y y
x x x x x
2
d z 2 d xy d x −y 2
d yz d xz
Only these nine orbital shapes need be memorized.
Fig. 4-4. Shapes of various orbitals

4.7. BUILDUP PRINCIPLE
With each successive increase in atomic number, a given atom has one more electron than the previous atom.
Thus, it is possible to start with hydrogen and, adding one electron at a time, build up the electronic configuration
of each of the other elements. In the buildup of electronic structures of the atoms of the elements, the last electron
is added to the lowest-energy subshell possible. The relative order of the energies of all the important subshells
in an atom is shown in Fig. 4-5. The energies of the various subshells are plotted along the vertical axis. The
subshells are displaced left to right merely to avoid overcrowding. The order of increasing energy is as follows:
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d.

EXAMPLE 4.11. Draw the electronic configuration of Ne and Mg on a figure like Fig. 4-5. Use an arrow pointing up to
represent an electron with a given spin, and an arrow pointing down to represent an electron with the opposite spin.
Ans. The drawings are shown in Fig. 4-6.

6f
7p 6d
7s 6p 5d 5f
6s 5p 4f
5s 4d
4p
4s 3d
3p
Energy 2s 2p
3s
1s
Fig. 4-5. Energy level diagram for atoms containing more than one electron (not drawn to scale)