The Foundations of Chemistry

The sizes of orbitals increase with increasing nand the true shapes of porbitals are

“diffuse,” as shown in Figure 5-26. The directions of p, d, and forbitals, however, are

easier to visualize in drawings such as those in Figures 5-23, 5-24, and 5-25; therefore,

these “slender” representations are usually used.

In this section, we haven’t yet discussed the fourth quantum number, the spin quantum

number, ms. Because mshas two possible values, ^12 and 
^12 , each atomic orbital, defined

Figure 5-23 (a) The relative directional character of a set of porbitals. (b) A model of

three porbitals (px, py, and pz) of a single set of orbitals. The nucleus is at the center. (The

lobes are actually more diffuse (“fatter”) than depicted. See Figure 5-26.)

212 CHAPTER 5: The Structure of Atoms

Figure 5-24 Spatial orientation of dorbitals. Note that the lobes of the dx (^2)
y 2 and dz 2
orbitals lie along the axes, whereas the lobes of the others lie along diagonals between the
axes.
x
y
z
py
(a)
y
x
z
px
x
y
z
pz
(b)
x
y
z
dx^2 – y^2
z
y
x
dz^2
dx y dxz dyz