Question 2: Suppose that the electron in Hydrogen atom obeyed classical mechanics rather than quantum mechanics. Why would such a hypothetical atom emit a continuous spectrum rather than a line spectrum?
Classical electromagnetic theory assumes that an accelerated charge continuously emits energy in the form of electromagnetic radiations. Therefore, it should produce a continuous spectrum.
Now an electron is moving in circular orbit in the atom. As the motion is in a circular path, it is an accelerated motion. The direction of motion of the electron changes every moment and the particle undergoes an accelerated motion. Mathematically, this acceleration is given by (a = v2/r), where v is the linear acceleration of the particle and r is the radius of the orbit.
So according to classical electromagnetic theory, this electron would emit energy continuously giving rise to a continuous spectrum.
This is, however, contrary to the experimentally observed facts because Hydrogen atom gives line spectrum and can be explained on the basis of applying theory of quantum mechanics.