Bohr’s Atom 181
Bohr also noticed that as n increases, the frequency of the photon
associated with the transition from the level En to En-1 approaches the
frequency of the periodic motion of the level En, as expected in the
classical theory. Bohr concluded, therefore, that in the limit of n
approaching infinity classical physics is also able to provide a proper
description of the atom. He concluded, consequently, that for large n, the
quantum theory passes over into the classical theory. This statement
forms the basis of Bohr’s correspondence principle. He argued that if the
classical theory correctly describes the frequency of the radiation for
large n then the predictions of the classical theory regarding relative
intensity of spectral lines, polarization and the existence of forbidden
transitions would also be valid for small n.
Bohr carried the correspondence principle even further, however. He
proposed that the predictions of the classical theory regarding intensity,
polarization and forbidden transitions are valid for all energies. There is
no theoretical justification for this extrapolation since we know that the
extrapolation of the classical theory to lower energies of the radiated
frequencies is incorrect. Nevertheless, Bohr’s conjecture is somewhat
justified on empirical grounds. It provides a fairly accurate description of
polarizations. Some of its predictions regarding the relative intensities of
spectral lines have also been correct but its success in this area is
definitely limited.
Bohr’s theory of the atom was a hodge-podge of ideas. It incorporated
the concept of the quantization of energy and violated a number of the
basic rules of classical theory. Through the correspondence principle,
however, it still included the classical theory upon which it depended for
its theory of polarization, the relative intensity of spectral lines and
forbidden transitions. Despite its hodge podge nature, the Bohr model of
the atom explained a surprisingly large number of the features of the
spectroscopic data. Perhaps the most important prediction of the theory
was the existence of discreet atomic energy levels. This aspect of the
theory was dramatically confirmed one year after its formulation by
Franck and Hertz.
Franck and Hertz studied the collisions of free electrons with the
atoms of a gas, initially in an unexcited state. A beam of electrons with a
fixed kinetic energy was directed at the gas atoms. The kinetic energy of
the electrons after the collision was measured. As a result of the collision
the free electrons transferred energy to the atom.