Biomedical Engineering Reference
In-Depth Information
13
One-Electron Atoms
The hydrogen atom occupies an important place in the history of molecular modelling and
quantum theory. It is the simplest possible atom, with superficially simple properties, yet
it was a thorn in the side of late nineteenth and early twentieth century science. Rutherford
had discovered the nucleus by 1911, and had a rough idea of its size from his scattering
studies and so people pictured the hydrogen atom as a negative charge (the electron) making
a circular orbit with constant angular velocity round the nucleus (a positive charge). This
is shown in Figure 13.1.
Nucleus
r
Electron
Figure 13.1
A one-electron atom
I should mention a small technical point: if we want to eliminate the overall translational
motion of the atom from our discussion, the atomic system, nucleus plus electron, actually
rotates round the centre of gravity. This rotational motion of the electron (mass
m
e
) and the
nucleus (mass
M
) is equivalent to rotation of a single particle with reduced mass μ about
the origin. Here
1
μ
=
1
M
+
1
m
e
