allowed orbit

Why, for instance, should the allowed orbits depend on the angular momentum?

Moreover, the idea of a limited set of allowed orbits seemed very arbitrary.

The laws of classical mechanics do not apply when electrons make the jump from one allowed orbit to another.

The Bohr radius is the radius of the smallest allowed orbit.

Such paths correspond to Bohr's allowed orbits.

The waves for these paths will not cancel out Such paths correspond to Bohr's allowed orbits.

Starting from the angular momentum quantum rule, Bohr was able to calculate the energies of the allowed orbits of the hydrogen atom and other hydrogen-like atoms and ions.

These are like the allowed orbits of the Bohr model of the atom; the system can only be in one of these states and not in any states in between.

For these orbits the wave crest would be in the same position each time round, so the waves would add up: these orbits would correspond to Bohr's allowed orbits.

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: where h is Planck's constant.

With these ideas, in concrete mathematical form, it was relatively straightforward to calculate the allowed orbits in more complicated atoms and even in molecules, which are made up of a number of atoms held together by electrons in orbits that go round more than one nucleus.

However, when an electron changes from one allowed orbit to another one nearer to the nucleus, energy is released and a real photon is emitted - which can be observed as visible light by the human eye, if it has the right wavelength, or by a photon detector such as photographic film.