How does the Heisenberg Uncertainty Principle relate to the wave-like behavior of electrons in atomic orbitals and their interference patterns?

The Heisenberg Uncertainty Principle says that we cannot know both an electron’s exact position and its exact momentum at the same time; the more precisely we pin down one, the fuzzier the other becomes. In an atom, electrons behave like waves, so their position is spread out over an orbital while their momentum is fixed by the wavelength of that wave. This spread in position is exactly the “wave‑like” distribution of probability that shows up as interference patterns when electrons pass through slits or are measured in orbitals. For example, if we try to locate an electron very precisely in an orbital, the uncertainty in its momentum grows, causing the orbital’s shape to broaden and the interference fringes to become less sharp. Thus, the uncertainty principle explains why electrons in orbitals show both particle‑like and wave‑like behavior, producing the characteristic interference patterns that reveal their wave nature.