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Classical theory of atomic structure
Subhrajyoti Maji
The simplest atomic structure is that it contains negatively charged electrons and
a nucleus at the centre with positively charged protons and neutral neutrons. The
electrons move around the nucleus in circular orbits. In this structure classical
theory fails to explain the stability of atomic structure as accelerated electron
radiates energy in the form of electromagnetic waves and consequently it will loose
energy gradually and at last fall into the nucleus due to gravitational and
coulombic attractions. Secondly classical theory fails to predict that electrons can
move only in certain discrete orbits whose radii are fixed. In this paper I will
explain you these two facts of electron classically.
At first try to understand when an electron radiates electromagnetic waves. The
characteristic of electromagnetic waves is that both electric and magnetic field varies
sinusoidally in phase with space and time. You know that the magnetic field produced
by an electron moving in a circular orbit is uniform and perpendicular to the plane of the
orbit. Therefore an accelerated electron in a circular orbit cannot radiate electromagnetic
waves.
According to classical theory the velocity v of an electron moving in an orbit of
radius r is given by, v = e/√(4
0mr)
where e is electronic charge,
0
is the permittivity
of free space and m is the mass of the electron. Simplifying this you will gate the radius
of the electronic orbit will be such that, mv2r = 3×10-29. This explains the discreteness of
the radius of the electron orbits. In this way you can explain all the atomic and nuclear
phenomena classically if you wish.