Biomedical Engineering Reference
In-Depth Information
They are often presented as plots of ψ versus ρ or of 4π
r
2
ψ
2
versus ρ. The latter is
known as the radial distribution function and it gives the probability of finding the electron
between two shells of radii
r
and
r
+
d
r
surrounding the nucleus. Representative plots for
hydrogen are shown in Figures 13.2 and 13.3. The dimension of ψ is (length)
−
3/2
and so
the quantities plotted are respectively
a
3/
0
ψ and
a
0
(4π
r
2
ψ
2
) against
r
/
a
0
.
0.5
0.4
0.3
0.2
0.1
0
2
4
6
8
10
-0.1
Distance/a0
Figure 13.2
Hydrogen 1s, 2s and 3s orbital plots
0.6
0.5
0.4
0.3
0.2
0.1
0
2
4
Distance/a0
6
8
10
Figure 13.3
Radial distribution curves for the hydrogen 1s, 2s and 3s orbitals
All the curves are asymptotic to the horizontal axis at infinity. The 2s curve crosses the
axis once (it has a
single radial node
), the 3s curve crosses the axis twice and so on. There is
