Youhei Tsubono
Top page (correct Bohr model including the two-electron atoms)
What is "Photon" ? Particle or Wave?
The usual textbooks often say that the Bohr model is wrong because the electron is moving on the circular orbit and radiating energy by the "accelerated" charge.
But the textbooks don't say why the electron of the standard quantum mechanics doesn't radiate energy.
This explanation about the Bohr model is not correct.
In the Bohr model, when the orbital length is an integer times the de Broglie's wavelength, it doesn't radiate energy.
The Bohr-Sommerfeld theory includes not only the Maxwell's law(equations) but also the de Broglie's theory.
And recently the two-electron atom can be expressed correctly by the Bohr model using the computational methods. (see the top page!)
If we use only the Maxwell's law, all the "accelerated" electrons surely radiate energy.
But adding the de Broglie's theory
to this, the result becomes completely different.
To begin with, there are no atomic models which use only the Maxwell's law since 1913.
Using only the Maxwell's theory, we can not explain about the two-slit behavior of the electron.
And using only the Maxwell's theory, we can NOT explain why the energy levels of Bohr (or Schrodinger ) model are discrete.
Actually, the Maxwell's theory already existed before Bohr-Sommerfeld model was born.
And of course, the physicists at that time understood the Maxwell's theory well, but tried to explain the three-body helium atom by Bohr model.
This means that the above reason of "accelerated" charge about Bohr model was made later "intentionally" to justify the quantum mechanics.
By the way, in the quantum mechanics (QM), why doesn't the electron radiate energy?
To tell the truth, this reason is not clearly written in the QM textbooks.
"Unclearly" they say that the QM electrons are static as electron clouds obeying the probability density, so they are not accelerated.
But is it really so ?
If the QM electrons are static and aren't actually moving, how can we explain about the following phenomena?
If we consider the atomic nuclear movement around the center of mass, and use the reduced mass of an electron, the calculation result of the energy levels (for example, of the hydrogen atom) becomes better.
This means the atominc nucleus is "actually" moving around the center of mass. And of course this means the electron is moving around the center of mass, too.
The standard QM textbooks say that the electrons of the two-electron atom have no magnetic moment, because it has spin-up and spin-down electrons and they cancel the magnetic fields out.
But to be precise, the magnetic fields are theoretically produced in almost all areas because the two electrons of the opposite spin magnetic moments are apart from each other by the repulsive Coulomb force.
So if the two electrons are not moving, the magnetic fields can't be canceled out.
It is inconsistent !
How can the relativistic effect be explained ?
( The effect of the relativistic mass change by the high speed electron was actually observed especially in the heavy atoms).
The Schroedinger equation shows the probability density, but can't express the relativistic effect including the spin-orbital interactions.
Again, it is inconsistent to the above "static" state !
( Even if the electrons are static (= not moving), the relativistic mass change can occur ?? )
So, if the electron is static, the various phenomena can't be explained. This means the quantum mechanics contains the self-inconsistency.
How about the bohr model ? As shown in the top page , the Bohr model doesn't contain self-inconsistency at all.
If we consider the emitted electromagnetic waves (or "photon"), we must consider the de Broglie's waves around the electron.
See also point-like electron doesn't radiate energy.
The quantized de Broglie's waves can rule out the "particle nature" of the photon (Only the wave nature is left).
See Photon is particle ?
2010/3/13 updated. Feel free to link to this site.