Biomedical Engineering Reference
In-Depth Information
nothing else particularly remarkable about such plots of decreasing exponential functions.
The radial distribution curves are a little more interesting.
The radial distribution curve shows a maximum at the first Bohr radius for the 1s orbital.
Bohr's theory states that the electron would be in a fixed circular orbit round the centre
of mass with exactly this radius! As the principal quantum number increases, so does the
average value of the radial distribution function. Elementary chemistry texts attach much
importance to diagrams of these kinds.
There are other ways to visualize the atomic orbitals. Figures 13.4 and 13.5 show contour
diagrams for the 1s and 2s hydrogen atomic orbitals. The particular software package I used
marks the axes with somewhat arbitrary units depending on the range of points chosen,
although the contour values themselves are correct and the nucleus is at the centre of the
plane.
80
60
0.086
0.429
0.171
0.086
0.343
0.257
40
20
0
0
20
40
60
80
Figure 13.4
Hydrogen 1s contour diagram (nucleus at centre)
13.7.2 The p-orbitals
For angular momentum quantum number
l
=
1, there are three possible values of
m
l
,
namely
−
1, 0 and
+
1. The angular factors for m
l
=±
1 are complex (they involve the
