Electrons spiralling into the nucleus is a pre-Bohr-ian idea. They thought that as the electron accelerated around the nucleus it would radiate off energy, thus losing energy and spiralling into the nucleus. Bohr fixed this with the energy-level picture of the atom. Unfortunately I don't think Bohr said that electrons would spiral into the nucleus, rather that the electrons wouldn't occupy those energy levels in the first place.
But they important part of your answer is "the wave will cease to exist". After all, your statement "the electron will spiral into the orbit" is a hypothetical. There is no way of knowing what would happen if the electron occupied that energy level simply because it can't. So I think you've got the main points dow and they'll give you the mark for that.