There exist some contradictory conclusions between the old Quantum Theory and Quantum Mechanics in explaining the atomic structure. Such as how to explain the difference of eigenvalue expression, the possibilities for the existence of a zero angle between the angular momentum and a specific axis and zero minimum angular momentum, as well as how to interpret the fact that the zero angular momentum corresponds to a linear periodic motion in the old Quantum Theory but to a spherical prbability distribution in the Quantum Mechanics. In this paper, we explain these conclusions from the point of wave-particle duality theory and show the connection and difference between the two theories.