Why is there a tedency for electrons to settle around a nuclei in up to eight layers?

Quantized energy levels result from the relation between a particle’s energy and its wavelength. For a confined particle such as an electron in an atom, the wave function has the form of standing waves. Only states with energies corresponding to integral numbers of wavelengths can exist; for other states the waves interfere destructively, resulting in zero probability density. ie the lowest possible electron orbit has a distance equal to the electron’s wavelength. The next possible orbit has a distance twice the electron’s wavelength. There can be nothing in between.