Bohr’s Atom 183
de Broglie, the theoretician, whose work will be discussed in the
following chapter). M. de Broglie bombarded the atom with x-rays of a
known energy. He then observed the kinetic energy of those electrons
ejected from atom as a result of absorbing the x-rays. From the
difference of the photon’s energy and the electron’s kinetic energy M. de
Broglie was able to determine the energy levels of the atom, which were
also in agreement with those obtained from Bohr’s theory.
In 1913, Moseley, in England, investigated the production of x-rays.
His work revealed that the charge of the nucleus increased from one
element to another by one unit of charge +e. The relation of the energy of
the x-rays emitted by an atom and the charge of its nucleus was found to
be exactly that predicted by Bohr’s theory of the atom.
The experiments of Moseley, M. de Broglie, Franck and Hertz
established, beyond a shadow of a doubt, the validity of the basic
concepts of Bohr’s model of the atom such as the existence of energy
levels and the Bohr frequency condition. As more and more experimental
information was gathered, however, it became evident that Bohr’s theory
was not sophisticated enough to explain all the data. When the
spectroscopists looked closely at the spectral lines of Balmer, they
discovered that each line was actually split into a number of finer lines.
This fine structure of the spectral lines was explained by Sommerfeld
making use of Einstein’s relativity theory. The existence of the fine
structure of the spectral lines revealed that, for each of the atomic orbits
of a given radius postulated by Bohr, there are actually several orbits
each with the same radius and almost the same energy but different
ellipsities or different values of angular momentum. The slight energy
differences of these orbits arise from relativistic effects and accounts for
the fine structure of each line.
For a given value of n, which determines the radius of the orbit or half
the distance of the major axis of the ellipse, the possible values of the
angular momentum in units of h/2π are l = 1, 2, 3 ... n – 1. Studies of the
splitting of spectral lines of atoms in magnetic fields revealed that the
component of the angular momentum or the plane of the electron’s orbit
can take on 2l + 1 different orientations with respect to some external
magnetic field. These studies also revealed that the electron has in
addition to its angular momentum an intrinsic spin of 1/2 of h/2π, which
can be oriented either up or down with respect to the external magnetic
field. An electron in an atom can therefore be defined by four quantum
numbers, namely, n that determines the radius of its orbit, l that