Wave-Particle Duality
Discover how matter and light exhibit both wave and particle properties, including the de Broglie wavelength, electron diffraction, and the principle of complementarity.
The Dual Nature of Light
By the early 20th century, experiments showed that light sometimes behaves like a wave (diffraction, interference) and sometimes like a particle (photoelectric effect). This is known as wave-particle duality.
Evidence for Both Models
Wave Behaviour
- • Diffraction through slits
- • Interference patterns (Young's double slit)
- • Polarisation
- • Refraction
Particle Behaviour
- • Photoelectric effect
- • Compton scattering
- • Discrete energy emission (line spectra)
- • Photon momentum (p = h/λ)
Key insight: Light is not simply a wave or a particle. It is a quantum object that can exhibit either behaviour depending on the type of experiment performed.
The de Broglie Wavelength
In 1924, Louis de Broglie proposed that if light (a wave) can behave like a particle, then matter (particles) should also exhibit wave behaviour. He proposed that every moving particle has an associated wavelength.
λ = h / mv
λ
de Broglie wavelength (m)
h
Planck's constant
6.63 × 10-34 J s
mv
Momentum (kg m/s)
m = mass, v = velocity
Why Don't We Notice Matter Waves?
For everyday objects, the de Broglie wavelength is incredibly small -- far too small to detect.
Cricket ball (0.16 kg at 40 m/s):
λ = 1.04 × 10-34 m
Far too small to observe
Electron (9.11 × 10-31 kg at 106 m/s):
λ = 7.27 × 10-10 m
Comparable to atomic spacing -- detectable!
Electron Diffraction and Complementarity
In 1927, Davisson and Germer confirmed de Broglie's hypothesis by firing electrons at a nickel crystal and observing diffraction patterns -- something only waves can produce.
Electron Diffraction Experiment
Electron Gun
Accelerated e⁻
Thin Crystal
Acts as a grating
Detector Screen
Ring pattern
Concentric rings on the screen are characteristic of wave diffraction.
The Principle of Complementarity
Niels Bohr proposed the principle of complementarity: the wave and particle descriptions of matter and radiation are complementary -- both are needed for a complete picture, but they are never observed simultaneously in the same experiment.
• In a diffraction experiment, electrons show wave behaviour.
• In the photoelectric effect, light shows particle behaviour.
• The type of behaviour observed depends on the experiment being performed.
Key Vocabulary
de Broglie Wavelength
The wavelength associated with a moving particle: λ = h/mv. Smaller for faster or heavier particles.
Wave-Particle Duality
The concept that all matter and radiation exhibit both wave-like and particle-like properties.
Electron Diffraction
The bending of electron beams around obstacles, producing interference patterns that confirm their wave nature.
Complementarity
Bohr's principle that wave and particle descriptions are both needed but are never observed in the same experiment.
Worked Examples
Calculate the de Broglie wavelength of an electron travelling at 2.0 × 106 m/s. (me = 9.11 × 10-31 kg)
Step 1: Identify: h = 6.63 × 10-34 J s, m = 9.11 × 10-31 kg, v = 2.0 × 106 m/s
Step 2: λ = h / mv = 6.63 × 10-34 / (9.11 × 10-31 × 2.0 × 106)
Step 3: λ = 6.63 × 10-34 / 1.822 × 10-24 = 3.64 × 10-10 m (0.364 nm)
A proton (m = 1.67 × 10-27 kg) has a de Broglie wavelength of 1.0 × 10-12 m. What is its speed?
Step 1: Rearrange: v = h / (mλ)
Step 2: v = 6.63 × 10-34 / (1.67 × 10-27 × 1.0 × 10-12)
Step 3: v = 6.63 × 10-34 / 1.67 × 10-39 = 3.97 × 105 m/s
Explain why the Davisson-Germer experiment supports de Broglie's hypothesis.
Step 1: Davisson and Germer fired a beam of electrons at a nickel crystal.
Step 2: They observed a diffraction pattern -- bright and dark rings on a detector screen. Diffraction is a wave phenomenon.
Step 3: The spacing of the diffraction pattern matched predictions using the de Broglie wavelength λ = h/mv, confirming that electrons have wave properties.
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
According to de Broglie, the wavelength of a particle is inversely proportional to its:
Question 2
The Davisson-Germer experiment provided evidence that electrons exhibit:
Question 3
If an electron is accelerated to a higher speed, its de Broglie wavelength will:
Question 4
The principle of complementarity states that:
Question 5
Why is a cricket ball's de Broglie wavelength undetectable?
Key Concepts Summary
- ●Light and matter exhibit both wave and particle properties (wave-particle duality).
- ●The de Broglie wavelength: λ = h/mv. Larger momentum means shorter wavelength.
- ●Electron diffraction (Davisson-Germer) confirmed that electrons have wave properties.
- ●Macroscopic objects have immeasurably small wavelengths due to their large mass.
- ●The principle of complementarity: wave and particle behaviours are both needed but never observed simultaneously.