Classically, an electron will emit energy every time it's vector changes. For an electron orbiting a nucleus, that's a lot of vector changes. Thus, classically, an electron should radiate all of it's energy and spiral into the nucleus within fractions of a second. However, the energy emitted by electrons can only come in discrete packets, called photons. Photons are quantized packets of energy. An electron can only emit a photon as it makes the transition from one state to another, and even then with limits on the transitions.
That's what is taught in freshman chemistry, not to mention, it's also taught in modern physics, so you 'should' have seen it twice.