# Why can't an energy level exist containing 0.9 electron wave wavelengths? Why must it be a whole number? [duplicate]

So, I was reading Atom: Journey Across The Subatomic Cosmos by Isaac Asimov in order to better understand quantum mechanics when I came across this sentence:

The electron couldn't spiral into the proton because it couldn't take up an orbit with a length less than a single wave.

I was wondering why that is? Why can't an electron not have non-whole number wavelengths in atomic energy levels?

Those started the idea of atomic orbits being quantized. It started with Bohr in 1913 simply hypothesizing that angular momentum came in half integer multiples of h. For deBroglie around 1924 it was that n times the wavelength is $2\pi r$, in deBroglie's model that led to the momentum (which equals h/$\lambda$) being quantized. From either one the energy levels are also quantized.