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3. The Bohr model of the atom

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Rutherford's planetary model of the atom was understood
in terms of classical electrodynamics. This model could in principle
explain the occurrence of radiation, since in Maxwell's theory,
light is emitted by accelerated charges, hence by the electrons in orbit.
(Note that acceleration is required in a circular orbit)
At the same time this causes a contradiction in the theory,
since the decelerated electrons, while emitting light, would continuously
loose energy, collaps with the nucleus and make the atoms unstable.
So the quest was for a theory explaining the stability of the atom
and the existence of stationary states.

Bohr made a break with classical physics by adopting notions from quantum
theory and by simply postulating the existence of stationary states.

The assumptions of Bohr, stated in his
original paper
were simply:

the electron is in a stationary state of which there exist a discrete set

a quantisation condition is given by: L = nh_{bar},
where L is the angular momentum of the eletron,
n is a positive integer and h is
Planck's constant.

transitions between these states are possible with frequency v, v given by:

hv = E_{m} - E_{n}

N. Bohr
Nobel Prize laureate 1922

Within this model Bohr could give a
Mathematical derivation of the Rydberg formula.

A few comments on Bohr's model:

the quantisation condition is introduced in an ad hoc way without a justification

an explanation is given for the frequencies of the observed optical transitions (spectra)

but a theory of radiative transitions is still lacking

an explanation for the intensities of the spectral lines is not yet given

the Bohr model does give us a theory for the size of the atom

the model works only for the hydrogen atom;
spectra of other atoms are not yet explained

Extension of the Bohr-model

Bohr, in his semiclassical analysis, had only allowed for circular orbits in his model.
Later the model was extended by
Sommerfeld also allowing for elliptical orbits.
This version, based on the same ad hoc quantization condition for the
angular momentum is referred to as the
Bohr-Sommerfeld model.
Sommerfeld already postulated the azimuthal quantum number,
in addition to the principle quantum number n defined by Bohr.

Explanation of characteristic X-rays in the Bohr-model

Based on the Bohr model also the observed characteristic X-rays of more than 40
elements could be explained. Moseley performed a
comprehensive study of the X-rays
and their characteric wavelengths.
The
characteristic X-rays with a typical resonance structure,
should be distinguished from background X-rays, known as "Bremsstrahlung".
An interesting aspect of this work is that the characteristic frequency of some
K or L lines can be
plotted as a function of the element with the
atomic number Z on one axis.

A
derivation shows the Z vs root-frequency law for characteristic
X-rays.

The K and L indices refer to the shell to where the atoms decay to the
X-ray transition.
This method hence allows for an identification of
the atomic number Z by experimental means. So the periodic system could finally
be given in terms of Z instead of the mass number, and even some questionable
assignements of elements could be resolved.

Last change: 18 February 2001