Physics (9630) | Wave particle duality

Physics 9630: Wave Particle Duality (Section 3.5.11)

Welcome to one of the most mind-bending yet fascinating concepts in Physics: Wave-Particle Duality! Up until now, you've learned that light is a wave (showing interference and diffraction) and electrons are particles (they have mass and momentum). But what if everything—light, electrons, and even you—can be both a wave and a particle?

This short but powerful chapter is where classical physics breaks down and modern quantum mechanics begins. Understanding duality is essential for appreciating the true nature of matter and energy.

1. The Core Idea: What is Duality?

Wave-particle duality states that every quantum entity—like a photon or an electron—exhibits properties of both waves and particles, depending on how you observe it.

• When we look for wave properties (like diffraction), we see them acting like waves.
• When we look for particle properties (like momentum or energy packets), we see them acting like particles.

1.1 Evidence for Duality: Two Sides of the Same Coin

To accept duality, physicists needed evidence that defied the classical definitions of waves and particles. The syllabus highlights two crucial experiments:

A. Waves (Electromagnetic Radiation) Behaving Like Particles: The Photoelectric Effect

The Photoelectric Effect (covered in 3.5.10, but vital here) demonstrated that electromagnetic radiation (like light), which everyone believed was purely a wave, must instead be made up of discrete packets of energy called photons.

• If light were purely a wave, increasing its intensity should eventually cause electrons to be emitted from a metal surface.
• However, experiments showed that emission only depends on the frequency of the light, regardless of intensity, suggesting the energy is delivered in "bundles."

Key Takeaway: Light (a wave) has a particulate nature (photons).

B. Particles (Electrons) Behaving Like Waves: Electron Diffraction

Diffraction is a characteristic property of waves—it’s the spreading out of waves as they pass through an opening or past an obstacle. When you shine electrons (which are definite particles) through a crystalline structure (like thin graphite film), a startling pattern emerges:

1. The electrons scatter and produce a pattern of rings.
2. This pattern is identical to the diffraction pattern produced by X-rays (known waves) passing through the same material.

Because the electrons produced a diffraction pattern, they must possess a wavelength and exhibit wave characteristics.

Key Takeaway: Electrons (particles) have a wave nature.

2. The de Broglie Wavelength: Quantifying the Wave Nature

In 1924, Louis de Broglie proposed that if light waves could behave like particles, then particles of matter should also exhibit wave properties. He derived an equation that links the particle property (momentum) to the wave property (wavelength).

2.1 The de Broglie Equation

The wavelength (\(\lambda\)) associated with any moving particle is given by:

$$\lambda = \frac{h}{mv}$$

Let's break down the variables:

• \(\lambda\): The de Broglie wavelength (in metres, m).
• \(h\): Planck's constant (a fundamental constant, \(6.63 \times 10^{-34}\) J s).
• \(m\): Mass of the particle (in kilograms, kg).
• \(v\): Velocity of the particle (in metres per second, m/s).
• \(mv\): The momentum (\(p\)) of the particle (in kg m/s).

Since \(mv\) is the momentum (\(p\)), the equation is often written simply as:

$$\lambda = \frac{h}{p}$$

Memory Aid: De Broglie links the quantum world (\(h\)) to the particle world (\(p\)) and the wave world (\(\lambda\)).

2.2 Why We Don't Notice Our Own Wavelength

Don't worry, you are not constantly diffracting through doorways! This is because the de Broglie wavelength is usually incredibly small for macroscopic objects (large masses).

• Imagine a tennis ball (mass approx. 0.05 kg) moving at 30 m/s. Its momentum (\(p\)) is 1.5 kg m/s.
• $$\lambda = \frac{6.63 \times 10^{-34} \text{ J s}}{1.5 \text{ kg m/s}} \approx 4.4 \times 10^{-34} \text{ m}$$

This wavelength is far, far too small to ever measure or observe, so the wave nature of large objects is irrelevant. However, for tiny particles like electrons, whose mass is around \(9 \times 10^{-31}\) kg, the wavelength is comparable to the spacing between atoms in crystals, making diffraction observable!

3. The Relationship Between Momentum, Wavelength, and Diffraction

A key skill required by the syllabus is explaining how and why the amount of diffraction changes when the particle’s momentum changes.

Remember the inverse relationship from the de Broglie equation:

$$\lambda \propto \frac{1}{\text{Momentum}}$$

In wave physics, the amount of diffraction (how much the wave spreads out) is proportional to its wavelength. Longer wavelengths diffract more noticeably.

Step-by-Step Explanation: Changing Momentum

Scenario 1: Increasing Momentum (e.g., speeding up the electron)

1. Increase the speed (\(v\)) of the electron.
2. Momentum (\(mv\)) increases.
3. According to \(\lambda = \frac{h}{mv}\), the de Broglie wavelength (\(\lambda\)) decreases.
4. Since the wavelength is smaller, the wave nature is less prominent, and the amount of diffraction decreases (the rings in the diffraction pattern move closer together).

Scenario 2: Decreasing Momentum (e.g., slowing down the electron)

1. Decrease the speed (\(v\)) of the electron.
2. Momentum (\(mv\)) decreases.
3. According to \(\lambda = \frac{h}{mv}\), the de Broglie wavelength (\(\lambda\)) increases.
4. Since the wavelength is larger, the wave nature is more prominent, and the amount of diffraction increases (the rings in the diffraction pattern spread further apart).

Analogy: Think of trying to get around a corner. A massive truck (high momentum, tiny wavelength) follows a nearly straight path (little diffraction). A short sound wave (low frequency, long wavelength) easily bends around the corner (large diffraction).

4. Historical Context: A Changing View of Nature

The study of wave-particle duality is a perfect example of how scientific knowledge evolves over time.

The Classical View (Before 1900):

• Matter: Strictly composed of particles (e.g., electrons, atoms). Governed by Newton's laws.
• Light/Energy: Strictly composed of waves (e.g., Maxwell's equations).

The Quantum Revolution (Early 20th Century):

The discovery of the photoelectric effect (by Einstein, building on Planck) and electron diffraction forced scientists to abandon the rigid classical definitions. We learned that the universe is far stranger than we thought.

• This shift showed that the distinction between waves and particles is not fundamental; they are simply two different manifestations of the same underlying reality.
• Our current understanding is that quantum entities are neither purely waves nor purely particles, but possess an intrinsic duality that reveals itself depending on the experimental setup.

Did you know?

De Broglie proposed his hypothesis as part of his PhD thesis. His supervisors were so stunned by the radical nature of the idea that they sent it to Albert Einstein for review. Einstein immediately saw the genius in the concept, which secured de Broglie his degree and eventually earned him the Nobel Prize!