How Bohr's model explains the stability of atoms? How Bohr's model explains the stability of atoms? From Maxwell's equation, we know that an electron or any other charge will radiate energy on acceleration.
This problem is said to be solved by Bohr without any proper explanation, rather considering stability as an axiom. I don't understand nor did I find anywhere how can this charge not radiate energy while performing any kind of oscillatory motion around a center, which would definitely involve accelerations. It would be helpful even if someone explains how this problem is resolved in modern quantum mechanics.
 A: Its is one of the fundamental postulate of the Bohr Model that no radiation is emitted when the electron occupies an allowed orbit.
As unsatisfactory as it is, it was a makeshift solution in an attempt to explain the experimental evidence of it's time, and it worked! It might have even suggested that classical electrodynamics was completely incorrect back in the day.
Using Bohr's model, which required that angular momentum be quantized, we would have found that $l=0$ was a valid solution. Does that mean that the electron is not orbiting in the Bohr model? There clearly were alot of issues with the Bohr model.
In modern quantum mechanics, we would solve for solutions to time-independent Schrödinger equation $$H | \psi \rangle = E | \psi \rangle$$ of a Hydrogen atom. The result would be a eigenstate, independent of time. The use of wavefunctions and its probabilistic interpretation of today has instead taken away meaning from the Bohr model and a literal electron orbit.
A: Thing you need to understand is Bohr's orbit is a failure not only when it comes to explain how it does not fall into nucleus radiating energy but also due to Heisenberg's Uncertainty Principle.
Bohr's model of atom suggested that electrons are revolving in definite shells so we should be able to calculate the position and momentum of electron but according to heisenberg 's uncertainty principle we can't measure momentum and position the electron simultaneously. If you're able to calculate position there might be uncertainty in momentum and vice-versa.
Edit :- There is nothing like revolving you just calculate the probability density through the Schrodinger Wave Function which leads us to "no probability of electron being in nucleus".
$\psi_{n l m}(r, \theta, \phi)=R_{n}(r) Y_{l m}(\theta, \phi)$. This wavefunction explains it.
You need to drop the "electron is a particle" mindset to understand this. Heisenberg Principle rules that out. This link might be useful.
A: Bohr in order to explain why the spectrum of light from atoms was not continuous, as expected from classical electrodynamics, but had distinct spectra in frequencies that could be fitted with mathematical series, used a planetary model , imposing axiomaticaly angular momentum quantization.


Although the Bohr model of the atom was shown to have many failures, the expression for the hydrogen electron energies is amazingly accurate. The Schrodinger equation for the hydrogen atom actually gave the same energies, so the Bohr model was a helpful step along the way to developing a quantum mechanical model for hydrogen. 

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In the Bohr model, the wavelength associated with the electron is given by the DeBroglie relationship



and the standing wave condition that circumference = whole number of wavelengths. 

This standing wave requirement brings in the quantization of angular momentum.
Quantization was at the time used to explain the black body radiation graphs. The Bohr model's success in getting the mathematical  series that described the spectra showed that this was the way to go.
Have a look at the history of quantum mechanics.
