19.6 Atoms with More Than Two Electrons 813
The addition is simplified by the fact that contributions to bothMLandMSfrom
filled subshells vanish. The possible values ofLandSand the Russell–Saunders term
symbols can be found as in Chapter 18 from the fact thatMLranges from−Lto+L,
thatMSranges from−Sto+Sand thatJranges fromS+Lto|S−L|. However, the
ground-level term can be determined from the ground configuration by using Hund’s
rules without identifying all of the terms.EXAMPLE19.6
Using Hund’s rules, find the ground-level term symbol for the nitrogen atom.
Solution
The ground-level configuration is (1s)^2 (2s)^2 (2p)^3. The filled 1sand 2ssubshells make no
net contribution toLorS. The three electrons in the 2psubshell can have their spins parallel
if they occupy different space orbitals, so that the largest value ofMSis+ 3 /2 and the largest
value ofSis 3/2. The ground level corresponds toS 3 /2.
To investigate values ofL, we use the complex orbitals that are eigenfunctions of̂Lz.
We have assigned one electron to each of theψ 2 p 1 ,ψ 2 p 0 , andψ 2 p,− 1 space orbitals. The
only possibility isML 1 + 0 − 1 0. The only value ofLcompatible with the maximum
value ofSis zero. The only possible value ofJis equal toS, so the ground-level term symbol
is^4 S 3 / 2 (“quartetSthree-halves”).Exercise 19.5
Find the ground-level term symbols for (a) Be, (b) B, (c) C, (d) O, and (e) F.One possible explanation of Hund’s first rule is that the higher values ofScorrespond
to more electrons occupying different space orbitals with parallel spins. Occupying
different space orbitals lowers the probability that the electrons will be found close
together, thus lowering the potential energy. Statistical correlation can also have an
effect. For two electrons, singlet wave functions have symmetric space factors and
antisymmetric spin factors. There is no statistical correlation. In the triplet state wave
functions the spin factor is symmetric. The space factor is antisymmetric, corresponding
to statistical correlation. The electrons have only a small probability of being close
together, giving the triplet state a lower electron repulsion energy than the singlet
state. However, it is found that the antisymmetric space factor corresponds to lower
probability that the electrons will be far apart so that this analysis is oversimplified.
There is also a difference in the probability that the electrons will be found close to
the nucleus, and this may be an important factor.^28 It is best to regard Hund’s rules as
empirical rules without theoretical justification.Dmitri Mendeleev,1834–1907,was a
Russianchemist who correlated
valence with atomic mass. Julius Lothar
Meyer,1830–1895,was a German
chemist who correlatedatomic volume
with atomic mass.
The Periodic Table of the Elements
The periodic table was invented independently by Mendeleev and Meyer. Both noticed
that if the elements were listed in the order of increasing atomic mass, there was a repe-
tition (periodicity) of chemical and physical properties. For example, lithium, sodium,
potassium, rubidium, and cesium all form oxides with the formula M 2 O and chlorides(^28) I. N. Levine,op. cit., p. 328ff (note 2).