Astronomy Principles and Practice Fourth Edition.pdf

Spectral lines 221
Figure 15.6. The Bohr model of the hydrogen atom.
his now famous α-particle scattering experiment, indicated that the positive charge in an atom is
concentrated at its centre, the nucleus occupying only a small space in relation to the distances between
atoms. In order to keep the atom electrically neutral, he proposed that the correct number of electrons
should surround the nucleus and revolve around it in orbits in a similar way to the planetary orbits
round the Sun. This explanation caused difficulties as it immediately contradicted the laws of classical
physics. If the electrons are revolving in circular or elliptical orbits round the positive nucleus, they
are subject to a constant acceleration along the line joining the electron and the nucleus. According
to the classical laws of Maxwell and Lorentz, a charge which suffers an acceleration will radiate
electromagnetic waves with energy which is proportional to the square of the acceleration. Classical
laws predict that electrons could not occupy such stable orbits as suggested by Rutherford and these
rapidly lose their orbital energies by radiation and spiral into the nucleus. However, this difficulty was
overcome by Bohr in 1913 who applied a quantum concept based on the principle suggested by Planck.
His theory was first applied to the hydrogen atom because of its apparent simplicity.
15.7.2 The Bohr hydrogen atom
According to Bohr’s theory, the hydrogen atom consists of the heavy, positively charged nucleus around
which the electron performs orbits under a central force provided by the electrostatic force which
normally exists between charged bodies. (As the mass of the proton, M, is very much greater than the
mass of the electron, m e , it can be assumed that the proton is at a fixed centre of the electron’s orbit).
The orbit is illustrated in figure 15.6. For simplicity, we shall consider the simplest case of an electron
orbit which is circular.
Suppose that the electron is at a distance r from the proton, that its velocity is v and that its energy
is E. Now the electron’s energy is made up of two parts: it has kinetic energy (KE) and potential
energy (PE), i.e.
E = PE + KE. (15.14)
According to classical dynamics, the kinetic energy of the electron is m e v 2 /2. Coulomb’s law,
relating the force which exists between charged bodies, shows that the electrostatic force, F, between
the proton and electron is given by
e2
F =
4πε 0 r 2
where ε 0 is the permittivity of free space and that for the orbit to be stable this must be balanced by the