Electron's speed at any radius
The electrons can only orbit stably, without radiating, in certain orbits at a certain discrete set of distances from the nucleus. These orbits are associated with definite energies and are also called energy shells or energy levels. In these orbits, the electron’s acceleration does not result in radiation and energy loss as required by classical electromagnetics.
The Bohr model of an atom was based upon Planck’s quantum theory of radiation.
Electrons can only gain and lose energy by jumping from one allowed orbit to another, absorbing or emitting electromagnetic radiation with a frequency ν determined by the energy difference of the levels according to the Planck relation.
Electron’s speed at any radius is related to electron’s mass, the charge of the electron, and the atom’s atomic number.
|v||Electron's speed (m/s)|
|Z||Atomic number (dimensionless)|
|e||atomic unit of charge|
|r||Orbit radius (m)|