I think electrons are not actually 'revolving' around the nucleus, that was the old description we had in classical mechanics, which has been replaced by a wave function in QM. The wavefuction as you know gives the probability of finding an electron here (A) or there (B) but how it gets from A to B, I believe, we don't know, but they are certainly not travelling or orbiting in the classical sense.

Quantum Mechanics has the electron in a bound state as a probability density function so there is no 'circular orbit'.

In Classical mechanics, the orbit is around a positive charge which is revolving in the opposite direction around the center of mass. Perhaps you would prefer to think of this as canceling the relative motion of the electron? (anti-photon?) In any case, a emission of a photon would entail energy being lost from the system. Since the electron is in a 'stable orbit' this has to be prohibited or the orbit would decay with each emission until the radius goes to 0.

The electrons revolving in certain fixed orbit act as wave with wavelength given by de-broglie's equation, and they form stationary wave.. Since energy is not transferred, rather it is confined in a stationary wave, electrons (which act as stationary wave) don't release energy in fixed orbits.

The formulae of classical electrodynamics which you have in mind refer to a moving point charge. It is not appropriate to view the psi function of an electron as being the description of an underlying classical electron moving around. In quantum mechanics, if you go through the same steps which you went through in the classical case, you would find that radiation processes involve a change in the quantum state of the electron accompanied by the emission of a photon. It is not possible to have this if the atom is initially in the ground state.

Electrons radiate via interaction with an electromagnetic field which is always present. Now when an atom ( for simplicity , think of H-atom) is in an excited state, the electron DOES radiate to go to a lower excitation. This happens because there are always perturbations in nature, and these perturbations cause the electrons to transit from one state to another. Since this is a bound state problem, the energy levels of the electrons are quantized and so the transitions are discrete causing those beautiful atomic spectra. Here is the important point : since the electron is localized, the position uncertainty is finite (not infinity) and therefore, from uncertainty principle, one can obtain a minimum value of momentum uncertainty and consequently we get a MINIMUM energy for the electron which we call the ground state energy. For H atom it is -13.6 eV. So an electron's energy cannot be less than this. When the electron is in the ground state, it WISHES it could radiate further but it cannot because it cannot find a quantum state with less energy.

But if we consider a FREE electron, allowed to roam freely to infinity, the energy will not be quantized and can take continuous values from 0 to infinity. If this electron suffers acceleration, I suppose, it will radiate and radiate continuously.

Because Bohr said so. LOL

The short answer is that nobody knows why the laws of classical mechanics don't apply. It is a postulate of quantum mechanics that there exists a lowest energy state called the ground state. Since energy is apparently conserved, radiation cannot be emitted from the ground state.

That doesn't answer your question though, it simply restates the question as one of the laws of quantum mechanics.

It's a good thing that lowest energy states exist, otherwise we couldn't make atoms. A similar thing happens with the weak interaction. A free neutron will decay to a proton, an electron, and a neutrino. But a neutron bound in a nucleus may not decay if energy cannot be conserved (i.e. if the neutron is in its lowest energy configuration).

Yes, Bohr said so, and that is it. You can try to go further, but without a useful profit... Stationary orbit means the electron stays there. If it were radiating, that would mean losing the energy and that means electron jumping to lower state => orbit was not stationary. Now, if you consider the lowest = ground state orbit, Schroedinger equation says there is no lower state = no way to go even lower with the energy --> electron cannot radiate.

Concept of constantly orbiting electrons hardly represents the reality. Electrons sure move around a nucleus due to interactions inside atom (e.g. electron-electron) and those originated from outside, but if an atom is isolated from the rest of the universe then its electrons won't orbit around its nucleus constantly.

Accelerated charged particle does not radiate energy while moving, but when it interacts with other charged particle, generally, in inelastics interactions, by bremsstrahlung. Remember that wich is stationary is the orbit (energy level - distance by the nucleus) but not the electron. This one has a resonance movement with the atom's nucleus which has a positive charge so this resonance agree a "energy change (harmony)" between this moments that won´t be released but conserved until a external or nucleus pertubation. If this happens with superior energy them the associated energy of the resonance (bonding energy), the electron is released with corresponding kinetic energy and if it interacts with another charged particle, probably his kinetic energy will be converted in electromagnetic wave. Sorry by my poor english.

I think electrons are not actually 'revolving' around the nucleus, that was the old description we had in classical mechanics, which has been replaced by a wave function in QM. The wavefuction as you know gives the probability of finding an electron here (A) or there (B) but how it gets from A to B, I believe, we don't know, but they are certainly not travelling or orbiting in the classical sense.

According to classical laws of physics electrons should emit radiation and should collapse into the nucleous but that's not happening.

Because being very small at plank scale electrons obeys quantum laws not classical laws.

According to quantum mechanics only certain energy level is assigned to the electron orbit and it has to follow that orbit..i.e if an electron jumps from n=2 to n= 1 state, it simply dissappear from n=2 and again appers at n=1 without crossing the area of pi* (r2 - r1)*(r2 -r1) so as to not emit the radiation and fall into nucleous..

If the electron were punctual around the nucleous, then it would radiate as Classical Mechanics predicts. But it is not, it is a spherical cloud of probabilities around the nucleous. An spherical distribution of charge does not radiate even in CM. Therefore, if one would be able to modify this distribution where in one side more charge is concentrated as in the another, it will surely radiate and a decay in a further base state observed.

Unfortunately most of our contributors above have not heard of Randell

Mills (see https://en.wikipedia.org/wiki/Brilliant_Light_Power) and his

"hydrino" energy state hypothesis for the hydrogen atom—which is BELOW the vaunted ground state — and which blithely tosses aside QM, of course.

LOL . . .

The key in this context is the word "stationary": a stationary state is characterized by a time evolution governed by a phase factor exp(-iEn*t), where E_n is the nth-energy level.

Now, suppose the electron is "moving" (if this concept has some sense in quantum mechanics) in the nth-state: the probabilistic density charge and current distributions (via the wave function) do not depend on time. Now, by applying the Maxwell equations, you will find that there is no radiation from a stationary current source.

The situation is very different from a current density probability between two states: the phase factor is exp[i(En-Em)t], which is an oscillating function and radiate by following the Maxwell electrodynamics.

The above was a purely mathematical description. But, what about the physics behind this? First, note that the description that you have in mind is incomplete: Borh, as well as the Schrödinger formulation for the atom, does not take into account the electromagnetic field (real or virtual), and therefore, talking about radiation has no sense in this context.

On the other hand, the quantum nature of the electron in atom neglect the existence of an energy continuum to be radiated, and given that there exists a ground state E0, there is no possibility of going down of states with energy less than E0.

The Standard model claims that an electron is a relatively stationary 10^-18 cm diameter particle. Its relatively huge magnetic moment, its mass, and its angular momentum are “characteristics”, which is to say they are due to “magic”.

In reality, the electron’s 10^-18 cm particle revolves at the speed of light in a Compton wavelength orbit as if it were a trapped photon. This provides the electron’s magnetic momentum (the Bohr magneton) in three easy equation, the angular momentum ( ђ/2 ), in three easy equations, and the mass-energy (E = mc^2) in two easy, trivial equations.

This revolving charge model produces an outwardly spiraling impulse so that the electric field around the electron is a spiraling wave field having a Compton wavelength. This produces a periodic interaction with a nearby moving electron, the spatial interval being a de Broglie wavelength. This is derived, again, as a periodic interaction in three easy algebraic equations. There are no waves here except for the Compton wavelets. Hence, interactions between particles occur as de Broglie wavelengths or de Broglie intervals.

However, the electron does not have internal waves and is not required to have a wave equation to describe its internals.

The only sensible units of measurement for describing electron phenomena are electron units, or EUs. The unit of length is a Compton, or 2.4263102367E-10 cm. The frequency of its rotation is fe = 1.23558996E+20 Hz. This provides a rotation time of te = 8.09329979E-21 seconds. This is the time unit for EUs, i.e., a Rotation, or a Rote, for short. Velocity is given as Comptons per Rote. The unit of mass is the rest mass of the electron itself.

The first Bohr radius is a0 = 5.2917721092E−9 cm, or a0 = 21.809956634 Comptons. If we multiply this by 2π, we have the circumference of the first Bohr radius, i.e. 2π a0 = 137.03599907 Comptons, which is the fine structure constant. This result should speak for itself. Any other hidden meaning is not clear at this time.

When an electron accelerates, the wavelets in front of it become more and more compressed and the wavelets behind it become more and more decompressed, resulting in an increasing electric field across the extent of the electron. As a result of this changing field, the electron radiates.

In the Bohr atom (Yes, the “obsolete” Bohr atom.), this compression / decompression happens as the electron accelerates towards the nucleus. Meanwhile, the compressed Compton wavelets from the front of the electron reflect off the nucleus until they are intense enough to add wavelets to the backside of the electron and add to the decompressed wavelets, thus increasing its field. This effect suppresses the radiation. This is described in Section 6 of this author’s web page, RevolvingChargePhysics.com.

In this whole process, the Bohr atom is flooded with the electron’s Compton wavelets, or if more than one electron, it is flooded with Compton wavelets from all of those electrons, and they interact via the de Broglie interval of the wavelets, thus giving rise to the remarkable Schroedinger equation and the Dirac equation. How to reconcile these equations with the de Broglie interval is totally new ground.

As to why the electron’s revolving charge does not radiate: When the electron’s internal 10^-18 charge revolves, it does not produce wavelets because it does not spin around its own center. Hence, it does not radiate. As to what keeps it in its Compton wavelength orbit, that is more complicated and is described in this author’s web page, above.

Using the above description, anyone with a little bit of physics in their background can derive the above results. Or, they can see this author’s web page, above, where it is already done for you.