182 The Poetry of Physics and The Physics of Poetry
The transfer of energy from the electron can take place either by
exciting the atom through an inelastic collision or by elastic scattering in
which the atom remains in its ground state. In an elastic collision the
total kinetic energy is conserved and in an inelastic collision it is not. Let
us first consider the elastic case in which the atom is not excited. The
atom will not gain very much velocity as a result of the elastic collision
because its mass is so much greater than that of the electron. As a result,
only an exceedingly small amount of kinetic energy is transferred from
the electron to the atom and hence, the electron’s energy loss is
practically negligible.
The energy loss the electron suffers in the inelastic collision, on the
other hand, is considerable. In this case, the atom is excited from its
ground state to one of its excited levels. Because the energy levels of the
atom are discreet, that is discontinuous, there is a minimum amount of
energy, which must be transferred to the atom before it can be raised to
one of its excited levels. This minimum amount of energy is exactly
equal to the energy difference between the atom’s ground state and its
first excited state, E 2 – E 1. If the kinetic energy of the incoming electron
is less than this amount, then there is no possibility of an inelastic
collision since the electron does not have enough energy to raise the
atom to one of its excited states. This is exactly what Franck and Hertz
observed. As long as the kinetic energy of the electron was less than the
threshold for inelastic collision, E 2 – E 1 , they only observed elastic
collision in accordance with the predictions of Bohr’s theory. As soon as
this threshold was exceeded, inelastic collisions were observed in which
the electron’s energy loss was equal exactly to E 2 – E 1. These collisions
obviously corresponded to the excitation of the atom from its ground
state to its first excited state.
As the kinetic energy of the electron is increased even further beyond
the threshold, E 2 – E 1 , other inelastic collisions are observed in which
the atom is excited to even higher excited states. From the observed
energy losses of the electrons, Franck and Hertz were able to determine
the energy differences of the various atomic levels. These values were
compared with the values obtained from spectroscopic data. The two sets
of values for the energy levels were in complete agreement with each
other. Franck and Hertz had verified Bohr’s theory of the atom
mechanically.
Another experiment, which demonstrated the existence of Bohr’s
energy levels, was devised by Maurice de Broglie (brother of Louis