177Chapter 19Bohr’s Atom
In 1911 a young man, named Niels Bohr, journeyed from his native
Denmark to England to study physics. The following year he joined
the great Rutherford in Manchester and began to work on the problem of
the atom. Bohr was a keen supporter of the Rutherford solar system
model of the atom despite its problematic nature. Rutherford’s model of
the atom, in which the positive charge is concentrated in a nucleus whose
radius is 10-13 cm around which electrons orbit with radii approximately
10 -8 cm, was in deep conflict with classical electromagnetic theory on
two accounts. According to electromagnetic theory an electron orbiting a
nucleus should emit a constant stream of continuous electromagnetic
radiation and because of the ensuing loss of energy quickly spiral in to
the nucleus. The apparent stability of the atom as well as the presence of
discreet lines in the energy spectrum of atomic radiation had to be
explained within the framework of Rutherford’s model. It was this
problem that Bohr set out to solve in 1912.
In addition to explaining the stability of the atom and the discreteness
of its radiation spectrum, Bohr also had the task of explaining certain
regularities of the spectral lines that had been observed by the
spectroscopists. As early as 1885, Balmer had shown that the observed
frequencies of the hydrogen atom could be represented by the following
simple mathematical formula, f = Ry/h{1/n^2 – 1/p^2 }, where f is the
frequency of the radiation, Ry is Rydberg’s constant equal to 3.27 ×
1015 sec-1, h is Planck’s constant and n and p are integers almost always
less than 10 or so. Balmer’s formula provided a very tidy description of
the spectral lines observed in 1885. As more and more data was collected
it was found that the spectral lines of hydrogen occurred at precisely
those places predicted by Balmer’s formula.
In 1908, Ritz discovered a regularity in the spectrum of light emitted
by atoms, other than just hydrogen. He found that if f 1 and f 2 are the