In the de Broglie model, electrons orbiting the nucleus are akin to standing waves. In order for constructive interference to occur, and the orbit to be periodic and to close properly, the circumference of these orbits must be a whole number of electron wavelengths. This places a condition on allowed orbital radii, i.e., they are discrete. Since the electron’s energy depends upon the distance of the electron from the nucleus, the electron’s energy values are also discrete.
Work Step by Step
This is according to the de Broglie model, explained on pages 608-609.