2.2.6

# Wave-Particle Duality

Test yourself

## Wave-Particle Duality - Light

Interference and diffraction show that light is a wave. The photoelectric effect shows that light must be a particle. Quantum physics means light can be both a wave and a particle at the same time.

### Light as a wave

• Experiments such as shining light through a diffraction grating show us that light must be a wave.
• Light must diffract through the grating and then interfere constructively and destructively to produce bands of light and dark.
• Only a wave would be able to do this.
• A classical particle (e.g. a tennis ball) cannot interfere with another tennis ball to produce one larger one!

### Light as a particle

• The photoelectric effect displays that light must be a particle.
• The experiment shows that light particles (photons) have a one-on-one interaction with an electron on the metal surface.

## Particle Duality

In 1924, physicist Louis de Broglie suggested that particles might exhibit wave properties, such as diffraction. At the time, scientists dismissed his theory. But electron diffraction and other experiments showed de Broglie was right.

### De Broglie wavelength

• De Broglie suggested that any particle with a momentum, mv, must have an associated wavelength, λ, given by:
• $\lambda = \frac{h}{mv}$

### Electron diffraction experiments

• After de Broglie came up with this theory, other scientists set up experiments trying to prove (or disprove) his equation.
• These experiments showed that electrons did diffract like waves through a grating, and had a wavelength equal to what de Broglie had suggested.
• Given this experimental evidence, scientists changed their minds and accepted de Broglie's theory.

## Effects of Wave-Particle Duality

Diffraction experiments have shown de Broglie's equation to be true. The equation applies to all particles.

### Wavelength dependence

• The wavelength of an object is inversely proportional to its momentum (mass × velocity).
• A proton travelling at the same speed as an electron will have a smaller wavelength.
• This is because its mass is larger than the electron's.
• A faster moving electron will have a shorter wavelength than a slow moving one.

### Conditions for observing diffraction

• Diffraction patterns are only visible if the wavelength of the particle is roughly equal to the width of the diffraction grating.
• Electrons are tiny. So it is possible to reduce their de Broglie wavelength to the distances between atoms in a crystal (a few hundred nanometres).
• This means we can observe diffraction effects in electrons.

### Conditions for observing diffraction 2

• You are a particle with a mass of a few tens of kilograms.
• According to the de Broglie equation, if you travel at 1m/s you have a wavelength of around 10-35m.
• That is 1025 times smaller than the size of an atom.
• Fortunately for us, there is nothing that small for us to diffract through!