Physical Chemistry Third Edition

810 19 The Electronic States of Atoms. III. Higher-Order Approximations

elements from titanium through zinc (element 30) have two 4selectrons in the ground

configuration except for chromium (element 24) and copper (element 29), which have

a single 4selectron. A similar behavior occurs with the 4dand 5sorbital energies.

Assuming the energies in the figure to be essentially correct, it appears that other factors

besides orbital energy are important in determining the ground-level configuration.^23

Two possible factors are the omission of the correlation energy and the fact that the

total electronic energy is not equal to the sum of the orbital energies because the sum

of the orbital energies includes the potential energy for each pair of electrons twice.

The ground-level configuration for most elements can be obtained from the scheme

of Figure 19.5, which shows the “diagonal mnemonic device” or the “diagonal rule.”

To determine the order of orbitals for a given element, one follows each diagonal path

from upper right to lower left and then moving from the lower end of one diagonal to

the upper end of the next lower diagonal. The number of spin orbitals in each subshell

is listed at the top of the figure, so that one can tell when enough subshells have been

chosen for the electrons of a given atom. The diagonal mnemonic device is equivalent

to the “n+ 1 rule,” which states that subshells of a given value ofn+1 are occupied

before those of the next higher value ofn+1, and that within a given value ofn+1,

the subshells are occupied in the order of increasingn. This rule predicts that the 4s

subshell is always occupied before the 3dsubshell is occupied.

EXAMPLE19.5

Give the ground-level configuration of (a) Al, (b) Mn.

Solution

a.Al (13 electrons): (1s)^2 (2s)^2 (2p)^6 (3s)^2 (3p)

b.Mn (25 electrons): (1s)^2 (2s)^2 (2p)^6 (3s)^2 (3p)^6 (3d)^5 (4s)^2

Configurations are often abbreviated by including an inert gas configuration as part of the con-

figuration. The Mn ground configuration is abbreviated as [Ar](3d)^5 (4s)^2 and the Cu ground

configuration is abbreviated as [Ar](3d)^10 (4s) where [Ar] stands for the ground configuration

of argon.

Number of spin orbitals in subshell

2 6 10 14 18 22

1 s

2 s

3 s

4 s

5 s

6 s^6 p^6 d^6 f^6 g^6 h

7 s^7 p^7 d^7 f^7 g^7 h^7 i

3 p^3 d

4 p^4 d^4 f

5 p 5 d 5 f^5 g

2 p

Figure 19.5 The Diagonal Mnemonic Device for Applying the Aufbau Principle to

Neutral Atoms.Exceptions to the rules of this device are given in Table 19.1.

(^23) M. P. Melrose and E. R. Scerri,J. Chem. Educ., 73 , 498 (1996).