I'm not asking why the electron doesn't fall into the nucleus. I know this is explained by quantum mechanics.
But in class the other day, my professor said that treating the electron as a classical particle would lead to it crashing into the nucleus. This didn't really make sense to me. An electron experiences a coulombic force from the nucleus, much like a planet experiences a gravitational force from a star. With a classical view of the electron, wouldn't the electrons just adopt an elliptical orbit like a planet on a much smaller scale, or is there some other distinction between a planet and an electron where the electron would act differently and "fall" into the nucleus?
I know the classical view is wrong, I just didn't know if this reasoning really applied.