Bohr's atoms model Why might Bohr have been especially curious about the possible values of the angular momenta of electrons in quantum mechanics? What looks special about them?
 A: 
What looks special about them?

Not so much the momentum specifically, that was the outcome not the problem.
The problem was that the light that comes out of heated atoms has a very distinct spectrum. Why? If the light is simply energy being released by the electrons on the atom, why isn't it continuous, any allowable energy? Why is it always 1 or 2, not 1.5?
Bohr noticed that the difference in those energy levels corresponded to the difference in energy of the electrons if they always had integer angular momentums. So if the electron could only have momentum 1 or 2, moving from the one state to the other would give off a certain amount of energy, and that corresponded to the spectrums that were being seen (mostly).
This also solved another mystery. If there was no limiting feature of the energy being given off by the electrons, why didn't they just give off a whole lot of low-energy light constantly, and the electron eventually run out of energy and fall into the nucleus? Well if the minimum allowed state is 1, then that problem disappears.
It leaves you having to explain why this happens, but I think everyone agreed that it was happening.
