Chemistry Reference
In-Depth Information
that found in C and Si. Hence, the outermost
valence
states have similar
character for the three elements.
3 We have already noted that because of the angular-momentum-related
repulsive barrier in eq. (B.11) the valence s states will always lie below
the valence p states.
4 When we again compare C, Si and Ge, we note that in each case the
outermost valence statesmust be orthogonal to the core states. Because
there are more core electrons as we go further down the Periodic Table,
the outermost electrons tend to have a larger spatial extent in Ge than
in Si than in C, so that the atom size increases going down a row of the
Periodic Table. Likewise, the valence electrons have a larger binding
energy in C than in Si than in Ge.
5
If we now look at a set of elements in the same rowof the Periodic Table,
such as aluminium
(
Al,
Z
=
13
)
, silicon
(
Si,
Z
=
14
)
and phosphorus
(
, we note that in each case there are 10 'core' electrons
screening the nuclear attraction, thereby leaving a net attraction of
order three, four and five protons for Al, Si, and P, respectively. There
is also, of course, a repulsive interaction between the increasing num-
ber of valence electrons in each atom, but the increasing net nuclear
attraction dominates, so that the valence state binding energy tends to
increase with increasing atomic number, giving what is referred to as
increasing electronegativity across a row of the Periodic Table.
P,
Z
=
15
)
6
The ordering of some of the higher lying subshells does not always
follow the main shell order. Thus all subshells up to the 3p subshell
are filled for argon
(
Ar,
Z
=
18
)
. However, the 4s subshell lies below
the 3d subshell for potassium
, so that the 4s subshell first
starts to fill with increasing
Z
, followed by the 3d subshell and then
the 4p subshell.
(
K,
Z
=
19
)
7
Finally, we do not discuss here the order in which different states are
filled within a partly filled subshell of an atom. This is discussed in
Chapter 6, where we introduce Hund's rules. They were originally
derived empirically (later justified by careful quantum mecahnical
analysis) and describe the order in which states with different val-
ues of
m
and
s
z
are occupied. This is generally not of relevance when
considering bonding in solids, as in Chapters 2-5, but becomes of key
significance when considering the magnetic properties of atoms and
solids in Chapters 6 and 7.
References
Davies, P. C.W. andD. S. Betts (1994)
QuantumMechanics
, 2nd edn, Nelson Thornes,
Cheltenham.
McMurry, S. M.
Quantum Mechanics
, Addison-Wesley.
Schiff, L. I. (1968)
Quantum Mechanics
, 3rd edn, McGraw-Hill, Tokyo.
