De Broglie's wave-particle duality implies that a particle has an associated wave. A particle's position is spread over the extent of its wave packet. To localize a particle precisely in position (small \(\Delta x\)), many wavelengths must be superposed, which spreads the momentum (\(\Delta p\)). This wave nature directly leads to Heisenberg's uncertainty principle: \(\Delta x \cdot \Delta p \geq \frac{\hbar}{2}\).