Motion in a straight line (non-relativistic) is F = ma, the force changes the velocity and therefore increases the energy E = 1/2mv2.
For motion in a circle, the centrifugal (centripetal if you are a purist) is F = mv2/r . Energy is = 1/2 m times tip speed squared.
i.e. energy is a function of change in force (delta force) not the centrifugal.
So an electron in free space when acted on by a force (to accelerate it) changes energy, but one circulating a nucleus in a molecule has a force but no change in energy.
Yes, of course accelerated electrons emit EM radiation.
Considering Maxwell's equations:
d_t B + rot E = 0
d_t E + rot B = alpha * j
where E is electric field, B is magnetic field, alpha a proportionality constant and j the current density, it holds:
d_t^2 E + rot (d_t B) = d_t^2 E - Laplace E = alpha * d_t j.
The right hand side of this electromagnetic wave equation is the source term; it is proportional to the change of current density (= charge density * velocity) with time and if charge density is set constant, this source term is proportional to acceleration (acceleration = d_t velocity).
Since centrifugal forces are only forces that keep some things in circular motion, these forces are constraining forces. Constraining forces doing no work; therefore energy is the same in a circular motion of constant velocity.
All non-constraining forces acting on a particle are changing the energy. The first law of thermodynamics states that total energy is also the same (in absence of quantum fluctuations) in a closed system.
Patrick,
a useful answer thank you.
Bohr modified his orbit model of the molecule because he said that electrons are accelerating around the nucleus, therefore would radiate and the molecule would decay.
Here is a common and current (2016) quote.
"A rotating charge, such as the electron classically orbiting around the nucleus, would constantly lose energy in form of electromagnetic radiation (via various mechanisms: dipole radiation, Bremsstrahlung,...). But such radiation is not observed."
(from a source we all use but don't like to admit it:-) )https://en.wikipedia.org/wiki/Bohr_model
I agree with Patrik Linker and others that the accelerated electrons emit EM radiation.
Remi said exhaustively.
Such questions were timely 100 (!) years ago. Today it looks too strange. Is it just a reduction for some educational applications?
The radiation of accelerated particles is very good described in a well-known old good book: J.D. Jackson "Classical Electrodynamics", 1962. In my opinion, this book is the best in this area.
In schools we learn that when electron jumps from higher energy level to lower one, it emits energy (in electromagnetic form) equivalent to the difference between the orbits(energy bands/levels).
However, for an electron free from electric and magnetic field, changes in the mechanical form of energies is observed and there is no electromagnetic emissions. May be internal energy is unchanged and only external energy undergo a change.
In an atom even if the orbit is non-circular still the external energy changes but the internal energy remain invariant.
What is important here, is that many of the old understandings are still being taught. One then ends up with myths being propagated and outsiders just see the community arguing with itself. We need researchers that hone their understanding skills, deepen their knowledge and can question teaching without fear of ridicule or attacks on the person rather than the argument.
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