Physical Chemistry Third Edition

19.6 Atoms with More Than Two Electrons 809

0.1 6 s

1.0

10

100

1.0 10 100

5 s

3 d

3 p

4 p

2 s

1 s

2 p

3 s

7 p

4 s 7 d 6 d 6 f 6 g- 6 h

7 s 6 g

5 f 6 f

7 p 6 d

6 s

5 p 5 f

4 f

6 s

5 d

3 d

4 d

6 p

7 s

ÖE

/E

H

Z

Figure 19.4 Approximate Orbital Energies in Neutral Atoms.Note that the axes in this

diagram are logarithmic. From R. Latter,Phys.Rev., 99 , 510 (1955).

discuss the method, but it gives orbital energies that generally agree with those from

the Hartree–Fock method. The orbitals in different subshells of the same shell have

different energies, with higher values oflgenerally corresponding to higher energies.

These energy differences can be ascribed to shielding. Just as an electron in ansorbital

is less effectively shielded than an electron in aporbital, an electron in aporbital is

less effectively shielded than an electron in adorbital, and so on. The energies depend

strongly on the nuclear charge, with some pairs of curves crossing and recrossing as a

function of the nuclear charge.

The Aufbau Principle and Electron Configurations

According to theAufbau principlethe ground configuration of an atom is obtained

by choosing the lowest-energy set of orbitals compatible with the Pauli exclusion

principle. For the first 18 elements, the subshell energies lie in the increasing order

1 s,2s,2p,3s,3p, so that for example the ground configuration of phosphorus is

(1s)^2 (2s)^2 (2p)^6 (3s)^2 (3p)^3. For atomic numbers 19 through 21, the 3dorbital energy

is higher than that of the 4s. Elements 19 (potassium) and 20 (calcium) in their ground

states therefore have the 4sorbitals occupied in preference to the 3dorbitals and ele-

ment 21 (scandium) has a single 3delectron. Beyond atomic number 21, the figure

shows the 4senergy above the 3denergy so that the elements beginning with titanium

(element 22) should have no 4selectrons. However, it is found experimentally that the