In class, we were first introduced to classical mechanics, and how Bohr used the hydrogen electron to explain the atomic emission spectrum of that element. And it made sense. But then classical mechanics fails to explain other things, so we jump to quantum mechanics. And we learn about Newton's ideas of particles of light, and how Einstein said that light quanta are called photons, and how Louis de Broglie suggested that particles of matter can also behave like waves.
But I'm frustrated because, while the book does explain the history of quantum mechanics and the Heisenberg uncertainty principle, it doesn't explain how quantum mechanics has anything to do with atomic emission spectra. So my question is, how does quantum mechanics explain the atomic emission spectrum of elements better than classical mechanics does?
And how much of classical mechanics fails to account for what quantum mechanics does? So is the idea that an electron moving from one high energy level to a lower energy level in an atom releases energy/light is only true for hydrogen, and false for all the other elements? How can this be true?