Physical Chemistry , 1st ed.

Orbitals are designated by pairing the value of the principal quantum number

and the letter representing the value of:1s,2s,2p,3s,3p,3d, and so forth. A

numerical subscript can be used to label the mvalues of the individual or-

bitals: 2p 1 ,2p 0 ,2p 1 , and so on. Since the value ofnrestricts the value of,

the first shell has only an ssubshell (because can only be 0). The second shell

has only sand psubshells (because can only be 0 or 1), and so forth. These

restrictions are due to the nature of the mathematical solution of the

Schrödinger equation.

Example 11.23

What are the possible subshells in the n5 shell? How many orbitals are in

each subshell? Do not include mlabels.

Solution

For n5,can be 0, 1, 2, 3, or 4. Each subshell has 21 orbitals. In tab-

ular form:

n, Label No. of Orbitals

5, 0 5s 1

5, 1 5p 3

5, 2 5d 5

5, 3 5f 7

5, 4 5g 9

11.11 The Hydrogen Atom Wavefunctions 359

n  1 E  109,737 cm^1

n  2

n  3

n  4

n  5

E  27,434 cm^1

E  12,193 cm^1

E  6,858 cm^1

E  4,389 cm^1

E  0

Energy

 0

 0

 0  1

 1

 2

 0  1  2  3

Figure 11.17 The energy level diagram for a hydrogen atom, showing the nand quantum

numbers for the levels. The quantized energy levels are labeled. Degenerate wavefunctions are

shown.