Assume that an electron moving in a circular orbit of radius r around a hydrogen nucleus behaves as a matter wave of wavelength λ.
(i) Derive the condition that the circumference of the orbit must contain an integral number of wavelengths.
(ii) Show that the condition obtained in part (i) leads to the quantisation of angular momentum mvr=nℏ.
(iii) Explain why the wave picture introduced above suggests the existence of additional stationary states beyond perfect circles and how this insight removes two specific limitations of the original Bohr model (identify the two limitations).