Wave-particle dualityAQA A-Level Physics: Revision notes

Two experiments show that the wave and particle models both have a role.

• The photoelectric effect suggests electromagnetic waves have a particulate nature: radiation arrives as photons of energy $E = hf$, with a threshold frequency and immediate emission
• Electron diffraction suggests particles have wave properties: a beam of electrons passing through a thin graphite film or crystal produces a pattern of rings

Light and matter both show wave–particle duality. You do not need to know the details of particular diffraction methods.

A particle of momentum $p = mv$ has a de Broglie wavelength

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

where $h = 6.63 \times 10^{-34}$ J s. The wavelength is smaller for a greater momentum. Everyday objects have a very large momentum, so their wavelength is too small to notice.

For an electron accelerated from rest through a potential difference $V$: $\tfrac{1}{2}mv^2 = eV$, so $v = \sqrt{2eV/m}$.

Diffraction is significant when the wavelength is comparable to the gap (for electrons, the spacing between atoms, about $10^{-10}$ m).

If the accelerating potential difference is increased:

• the electrons gain more kinetic energy, so their speed and momentum increase
• the wavelength $\lambda = h/mv$ decreases
• there is less diffraction, so the rings in a graphite experiment get smaller

A particle with a greater mass moving at the same speed has a greater momentum and a smaller wavelength.

An electron is accelerated through 250 V.

• $v = \sqrt{2eV/m} = \sqrt{(2 \times 1.60 \times 10^{-19} \times 250) / (9.11 \times 10^{-31})} = 9.4 \times 10^6$ m s⁻¹
• $\lambda = h/mv = 6.63 \times 10^{-34} / (9.11 \times 10^{-31} \times 9.4 \times 10^6) = 7.7 \times 10^{-11}$ m

This is similar to the spacing between atoms in a crystal, so strong diffraction is seen.

Ideas about the nature of matter and light change over time. De Broglie's idea made a testable prediction, and electron diffraction experiments supported it.

New results are published so that other scientists can check them. Peer review is the process in which independent experts examine the methods, data and conclusions. Results that other groups can replicate are more reliable. The scientific community validates a new idea in this way, and the idea can still be revised if new evidence appears.