Why are wavelike properties of electrons useful in determining the velocity and position of a particle?
This question deals with quantum mechanics. This is the theory about the relationship between energy and matter at the atomic scale. This theory deals with the dual wave and particle like nature of all matter. This applies to all matter but is most important at the atomic scale. Particles like electron and protons have both particle like and wave like behavior. This allows us to treat electrons with wave function equations to help determine different features such as position and momentum. But note that the Heisenberg Uncertainty Principle states that both of these quantities cannot be precisely known at the same time for an electron.