# how electrons in discrete orbits in an atom do not radiate energy?

SAGAR SINGH - IIT DELHI
879 Points
12 years ago

Dear student,

1. The electrons can only travel in special orbits: at a certain discrete set of distances from the nucleus with specific energies.
2. The electrons of an atom revolve around the nucleus in orbits. These orbits are associated with definite energies and are also called energy shells or energy levels. Thus, the electrons do not continuously lose energy as they travel in a particular orbit. They 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:

$\Delta{E} = E_2-E_1=h\nu \ ,$

3. The frequency of the radiation emitted at an orbit of period T is as it would be in classical mechanics; it is the reciprocal of the classical orbit period:

$\nu = {1\over T}$

The significance of the Bohr model is that the laws of classical mechanics apply to the motion of the electron about the nucleus only when restricted by a quantum rule. Although rule 3 is not completely well defined for small orbits, because the emission process involves two orbits with two different periods, Bohr could determine the energy spacing between levels using rule 3 and come to an exactly correct quantum rule: the angular momentum L is restricted to be an integer multiple of a fixed unit:

$L = n{h \over 2\pi} = n\hbar$

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All the best.

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