|MadSci Network: Physics|
Wavelength=Planck's constant / momentum. This, de Broglie's formula, is a fundamental law of nature, without which the world would be completely different and life as we know it could not exist - for example, it is quantum theory that is responsible for the periodic table, and therefore all of chemistry. Thus, the answer to your question is the anthropic principle - if this were not the case, you wouldn't exist to notice that it was not the case. You can only ask why it is or is not true because it is true. Perhaps recent, as yet incomplete, 'theories of everything' such as superstring or twistor theory will show something more fundamental (such as the vibration of a string in 10 dimensions) to lie behind wave-particle duality, but the question "why is this so?" will always remain. In the two slit experiment, light (or electons, or - more recently - neutrons) can show interference effects, a property of waves. The photo- electric effect shows light to be made up of particles, photons. Both are true to an extent. QED (Quantum Electro-Dynamics), the most successful and accurate theory in the history of the human race uses this wave-particle duality. Feynman diagrams eg: \ / /~~~\ can be drawn to show an interaction, but the particles can take any route and do anything. The particles, however, have a wave-like property called phase, which can make two routes cancel (interfere) so that when all possible routes are summed, it appears that they move in a straight line. For more information, I suggest you read a book on Quantum theory or on QED.
Try the links in the MadSci Library for more information on Physics.