atomic physics - How does quantum mechanics explain stability of electron orbitals?

According to classical physics, an electron orbiting the nucleus would emit electromagnetic radiation. Losing energy in that way, it would spiral into the nucleus and the atom would collapse. Quantum mechanics explains that the electron cannot be treated as a classical particle having a definite position and velocity. The best we can do is specify the probability of it manifesting itself at any point in space and then something about Heisenberg uncertainty principle. How does quantum mechanics explain why the orbiting electron doesn't emit EM radiation and the atom doesn't collapse?