The velocity of an orbiting electron in an atom cannot be defined as a single value due to the principles of quantum mechanics. Instead, the electron's state is described by a wave function, which indicates that both position and velocity are probabilistic rather than definite. Measurements of the electron's position yield varying results, and similarly, its velocity is represented by a wave function in velocity space. While certain special states, like plane waves, can yield specific velocity measurements, these do not apply to stationary states of the electron in an atom. Thus, the concept of a fixed velocity for an electron is not applicable in quantum mechanics.