CHAPTER 32 : BOHR'S THEORY OF HYDROGEN ATOM AND ITS SPECTRUM
The development of Spectroscopy and gas discharge tubes enabled physicists in the second half of
the 19th Century to analyze the spectrum of various gases, particularly that of Hydrogen gas. The analysis
culminated in an empirical formula developed by Balmer (1885) to describe the visible line spectrum of
the hydrogen atom.
where R is empirical constant called Rydberg's Constant (1.097
´ 10^{ 7}m^{ 1}).
The classical wave theory of light was again found to be completely
inadequate while accounting for Balmer's formula. On the contrary
the theory predicted continuous spectrum. Rutherford's nuclear atom
model is also flawed on account of the classical theory because
an electron in circular orbit would radiate away its mechanical
energy due to its centripetal acceleration and would spiral into
the nucleus destroying the stability of atom.
In 1913, Niels Bohr developed a remarkable theory based on extension of concepts of quantizations
of Planck and Einstein. His theory is based on the following three postulates :
(i) Rutherford's nuclear atom model is essentially correct.
(ii) Only those circular orbits of electrons are permissible in which the angular momentum of an electron is
the integral multiple of .
These permissible orbits are 'steady' or 'stationary'.
(iii) Electrons in 'stationary' orbits do not radiate their energy ; only when electrons jump from a higher
energy stationary orbit to a lower energy stationary orbit, the difference of energy
(DE) is radiated
off in the form of a photon of light of frequency (
n ) given by Einstein's relation.
Is it not strange that an electron obeys Newton's law of motion Equation (2)? Yet the consequence of
this motion namely the radiation of energy of motion is prohibited; not only that, but the mechanism of
radiation emitted is totally different from classical mechanism. To some extent the concept of photon seems
to provide some justification; but that is about all. The only logic, that apparently justifies these
assumptions is that they work.
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