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Maybe there's an easy answer, but I don't know if it's what you were looking for.Do electrons in higher energy orbitals move faster than ones in lower energy orbitals?

The answer is written in the Uncertainty Principle: if you "confine" the "motion" of a particle, then its "momentum" will increase. Now, higher energy of the orbital means that is more bounded to the nucleus, and the probability of finding the electron is a function that drops to zero rapidly: The "Box" that contains the electron is small so its momentum will be high.