Chapter 2 Quantum Theory

2.7

ELECTRON CONFIGURATIONS

AB C

D

Figure 2.13 The Pauli exclusion principle A and B are acceptable, but C and D are not because they violate the Pauli Exclusion Principle.

Neither the orbital quantum number (

m

) nor the spin quantum number (ml

) can be s

determined unambiguously for a particular elec

tron in an atom. However, the sublevel in

which the electron resides can be determined because the energy of an electron can be determined. For example, we can determine that

an electron is a p electron, but we cannot

distinguish between p

, px

and py

. Consequently, the electronic structure of an atom is z

normally given as a list of its occupied sublevels and the number of electrons in each of those sublevels. This list is called the atom’s

electron configuration

. The notation used

for a sublevel is

nl

#, where n is the n

quantum number,

l is the letter of the sublevel (s, p,

d, ...), and

is the number of electrons in the sublevel. For example, 1s

2 2s

2 2p

1 implies

that there are two electrons in the 1s (n =1;

l = 0) sublevel, two electrons in the 2s (n = 2,

l^

= 0) sublevel, and one electron in the 2p

(n

= 2;

l = 1) sublevel.

The orbitals of an atom are filled in such

a way as to satisfy the following three rules:

1.

The electrons in atoms and molecules strive toward the lowest energy electron configuration known as the

ground state

. Electron configurations

that do not yield

the lowest energy represent

excited states

. Atoms and molecules have many

excited states but onl

y one ground state.

2. The Pauli Exclusion Principle

states that no two elec

trons in an atom can have

the same set of four quantum numbers

. Two electrons in the same orbital have the

same values of n,

l and m

, so they must have opposite spins (Figure 2.13)l

. Thus,

an orbital can accommodate no more than two electrons

, one with

ms

= +

1 /^2

and

one with

ms

= -

1 /^2

. An orbital with two electrons is filled while one with a single

electron is a half-filled orbital

. When two electrons occupy the same orbital, they

are said to be

paired

; that is, their spins are opposed and their magnetic fields

cancel.

3. Hund’s rule

states that the electrons in a subl

evel that is less than half-filled must

occupy different orbitals within the sublevel and have the

same spin

(Figure 2.14)

.

This is because electrons with the same spin tend to stay away from one another, which minimizes the electrostatic repulsion between them

.Paired electrons, on the

other hand, spend more time close to one another, which increases their electro-static interaction

.Consequently, the energy of two electrons in a sublevel is lower

if the electrons have the same spin.

The atomic orbitals, in order of increasing energy (n +

l), are shown in Figure 2.15.

The electron configuration of the ground state of an atom is obtained by placing its electrons into the lowest energy orbitals in

a manner consistent with the Pauli exclusion

principle and Hund’s rule.

The two electrons of He are in the 1s sublevel, so He has a 1s

2 configuration. Neon’s

4p 3d 4s 3p 3s 2p 2s 1s

Ga, Ge, As, Se, Br, KrSc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, ZnK, Ca Al, Si, P, S, Cl, ArNa, Mg B, C, N, O, F, NeLi, Be H, He

Fourth Period Third Period Second PeriodFirst Period

Figure 2.15 Atomic orbitals in order of increasing energy The atoms to the right of eac

h sublevel are the atoms

whose highest energy electrons reside in that sublevel. Atoms between dotted lines are in the same period.

AB

C

Figure 2.14 Hund’s rule A is the lowest energy configuration because it obeys Hund’s rule. The energies of B and C are greater than that of A because the three spins are not the same in B and C.

© by

North

Carolina

State

University