1. de Broglie Hypothesis and the de Broglie Equation★★☆☆☆⏱ 5 min
In 1924, Louis de Broglie proposed that wave-particle duality is not unique to electromagnetic radiation: all moving particles exhibit both particle and wave properties. These wave-like properties are described as *matter waves*.
\lambda = \frac{h}{p} = \frac{h}{mv}
Exam tip: You may be asked to state de Broglie's hypothesis in 2-3 marks: always mention that *all moving matter* has a wavelength related to its momentum.
2. de Broglie Wavelength for Accelerated Charged Particles★★★☆☆⏱ 7 min
The most common exam question asks you to calculate the de Broglie wavelength of an electron accelerated through a known potential difference. We can derive a simplified formula for this case using conservation of energy.
3. Experimental Confirmation: Electron Diffraction★★★☆☆⏱ 6 min
de Broglie's hypothesis was confirmed in 1927 by Davisson and Germer, who observed that electrons scattered off a crystalline nickel target produced a clear diffraction pattern. Diffraction is an exclusively wave property, so this proved that electrons exhibit wave-like behaviour.
Maximum diffraction occurs when the de Broglie wavelength of the incident particles is approximately equal to the size of the diffracting gap. For crystals, the gap is the inter-atomic spacing (~0.1 nm), which matches the wavelength of electrons accelerated through ~100 V, as we saw in the previous example.
Exam tip: When asked to explain why electron diffraction supports de Broglie's hypothesis, explicitly state that diffraction is a wave property, proving particles have wave behaviour.
Common Pitfalls
Why: $c = f\lambda$ only applies to electromagnetic radiation, not matter waves
Why: All SI unit calculations require potential difference in volts, leading to a wavelength 1000 times smaller than the correct value
Why: All moving matter has a de Broglie wavelength, regardless of size
Why: At speeds close to $c$, relativistic effects make the non-relativistic kinetic energy approximation invalid