**Evans SPH 4U1**

**Physics Grade 12**

**Unit 9: Quantum
Theory**

**Note 5:
Wave-Particle Duality**

Reference: Chapter 12.2

So far,

~ Blackbody Radiation, Compton effect and the Photoelectric Effect show light behaving as a particle.

~ Reflection, Refraction, Diffraction, Interference, and Polarization show light behaving like a wave.

**Taylor's Experiment:**

Demonstrated that the wave model determines the probability that a photon will be at a certain position in space at a given time.

For plain particles the probability of being in a certain place is either 100% or 0%. HOWEVER, it is not so for photons.

For example - If the wave model predicts constructive interference then the probability is high that a photon will be in that position.

**Bohr's Principle of
Complementarity:**

One must use either the wave theory or the photon theory but not both.

As a general rule, when light passes through a medium or space it behaves like a wave. Light behaves as a particle when it reacts with matter.

**Wave Nature of Matter:**

Louis de Broglie suggested that, if light sometimes behaves like a wave and sometimes like a particle, then perhaps particles of matter might also have wave properties. He proposed that the wavelength of a particle would be related to its momentum in the same way as for a photon. This wavelength is called de Broglie's wavelength.

Recall: Then:

He called them matter waves - originally people thought he was 'nuts' and they held back his graduation.

*This does not say that if you hit
a baseball, it will all of a sudden start dancing like a wave.*

**Example Problem:**

Calculate the wavelength of a bullet
which has a mass of 18 g when it is traveling at a speed of 9.5 x 10^{2 }
m/s. (Answer: 3.9 x 10^{-35} m)

*Note how small this is - it is so
negligible that it doesn't come into everyday life*