Geology Reference
In-Depth Information
y
y
y
x
x
x
2p x
3p x
3d xy
Figure 5.4 Cross-sections of electron density distributions in 2p, 3p and 3d orbitals. Electron density is represented by the
density of dots. The 2p x orbital has ( n − 1) = one nodal surface in the y-z plane passing vertically through the origin/nucleus.
The 3p x orbital has two: one as for 2p x and a spherical surface separating inner and outer lobes. The 3d xy orbital also has two
nodal surfaces in the x-z and y-z planes, both passing through the origin/nucleus.
The Schrödinger equation indicates that there are three
equivalent, but independent, forms of p-orbital, desig-
nated p x , p y and p z , in which these balloons are aligned
along the x , y and z axes respectively (Figure 5.5). These
variants share the same values of n and l, but are distin-
guished by having different values of the magnetic quan-
tum number, m (Table  5.3), which serves to define the
different orientation of each of these orbitals.
For reasons we need not discuss, the Schrödinger
equation prohibits values of l greater than n − 1
(Table  5.3). Accordingly there is no p-orbital when
n = 1, and the simplest p-orbitals (2p x , 2p y and 2p z ) are
encountered when n = 2. (Consistent with this value of
n, we observe the existence of a nodal plane separating
the two balloons, which - although different in shape -
has a similar significance to the nodal surface in the
2 s orbital.) As with s-orbitals, the maximum electron
density in each balloon is found close to the nucleus
(Figure 5.4). Three such p-orbitals exist for each value
of n greater than 1, and these families are designated
2p, 3p, 4p, and so on, according to the value n . (For
most purposes, the subscripts x, y and z may be omit-
ted.) As Figure 5.4 illustrates, the size of the orbital and
the number of nodal surfaces increases as the value of
n increases.
out from the nucleus at right angles to each other
(Figure 5.4). As stated in Table 5.3, m can now have the
values −2, −1, 0, +1 and +2, and we therefore find five
equivalent d-orbitals for each value of n (greater than
2). Their orientation in space is shown schematically in
Figure 5.5. Three orbitals, d xy , d yz and d zx , have balloons
extending diagonally between the coordinate axes,
whereas the other two have their electron density
directed broadly along the axes. Our experience of
wave theory so far suggests that, because n = 3, we
should encounter two nodal surfaces in each of the 3d
orbitals, and the nodal planes or surfaces evident in
Figure 5.4 confirm this expectation. A separate family
of five d-orbitals exists for every value of n greater than
2 (=3d, 4d, and so on).
As we shall see in Chapter 9, d-orbitals arc respons-
ible for the distinctive chemistry of transition metals
such as iron, copper and gold, and play an important
role in the aqueous-complex formation upon which
their hydrothermal transport and deposition in ore
bodies depend.
f-orbitals
The final class of solutions to Schrödinger's equation
are those for which l = 3. Their geometry is too complex
to consider here, but we should note that they first
occur when n = 4, and that seven equivalent orbitals
having various orientations will exist for each value of
n above 3. The f-orbitals only become important chem-
ically in the context of heavy elements such as cerium
and uranium.
d-orbitals
Setting l equal to 2 generates a third class of orbital
called a d-orbital, which is first encountered when
n = 3. Except for one special case, d-orbitals consist of
four elongated balloons of electron density, extending
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