Electrons in Bohr's atomic model [duplicate]








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[Stability of Bohr Orbits](/questions/54914/stability-of-bohr-orbits)

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Why electrons don't fall into the nucleus in bohr's atomic model?
Is there a reason or explanation or is just a consideration?




As far as I know, it's a consideration that the electrons must describe circular orbits around the nucleus of the atom without radiating energy.


So this is because is a "postulate", since according to classical electrodynamics a charge with an accelerated movement must emit energy in the form of radiation.


To maintain the circular orbit, the force experienced by the electron (the Coulombian force due to the presence of the nucleus) must be equal to the centripetal force. So here it is:


Taken from [Chemistry Libretexts - 6.2 The Bohr Model](https://chem.libretexts.org/Bookshelves/General_Chemistry/Chemistry_(OpenSTAX)/06%3A_Electronic_Structure_and_Periodic_Properties_of_Elements/6.2%3A_The_Bohr_Model)



> 
> $$k\frac{Ze^2}{r^2} = \frac{m\_ev^2}{r}$$
> 
> 
> 


Note that this model is only valid for hydrogen-like systems (only with 1 electron).


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