178 The Poetry of Physics and The Physics of Poetry
frequencies emitted by an atom, then the same atom is very likely to emit
the frequency f 3 = f 1 + f 2. This rule known as “Ritz’s Combination
Principle" follows trivially for hydrogen from Balmer’s formulae. The
novelty of his discovery, however, is that his principle applies to atoms
other than hydrogen.
The work of Balmer and Ritz played an important role in Bohr’s
formulation of his atomic model by helping him make certain guesses he
might not have made otherwise. The quantization of energy proposed by
Planck and Einstein played an equally important role in Bohr’s thinking.
He was the first to apply the quantum concept to the atom. He assumed
that the electron orbits the nucleus only along certain fixed elliptical
orbits, each of which represents a different quantum state. He also
assumed, in direct contradiction with electromagnetic theory that the
electron would not radiate while moving along any of the allowed orbits.
The electron is more or less stable in one of the allowed orbits or
quantum states. Bohr did postulate, however, that the electron could
jump to a lower energy orbit closer to the nucleus by radiating a quantum
of energy. The electron would continue jumping to lower energy orbits
emitting photons until it landed in the lowest energy orbit or ground state
in which it could remain without ever emitting any more photons.
The energy and hence the frequency of the photon emitted by the
electron as it jumps from an orbit with energy E 2 to an orbit with energy
E 1 is related to the energy difference of the two orbits, E 2 – E 1. The
relation between the frequency, f, of the emitted photon, the energy
difference, E 2 – E 1 and Planck’s constant, h, known as Bohr’s frequency
condition, is similar to Planck’s original quantum condition, namely
hf = E 2 – E 1.
According to Bohr’s hypothesis, an electron not only may jump from
an outer orbit to an inner orbit by emitting a quantum of energy, but it
may also pass back from an inner orbit to a more energetic outer orbit by
absorbing a quantum of energy. In order to make this transition it must
absorb a quantum of energy exactly equal to the energy difference of the
two orbits, E 2 – E 1.
Bohr’s model of the atom violates the laws of classical mechanics
and electromagnetism in a number of ways. First of all, the electron in
the ground state is constantly undergoing acceleration without ever
radiating light in direct contradiction with Maxwell’s laws. Secondly, the
frequency of radiation emitted by an electron as it jumps from one orbit
to another is not equal to the frequency with which it orbits the nucleus.
In classical electromagnetic theory, on the other hand, the frequency of