Quick questions on Wave-particle duality explained: H2 Physics Modern Physics

Light shows wave behaviour in interference and diffraction (the double slit, the grating) and particle behaviour in the photoelectric effect (photons of energy $hf$). Neither model alone is complete: light is described as a wave when it propagates and as particles when it exchanges energy with matter. This is wave-particle duality.

In 1924 de Broglie proposed that if light can behave as particles, then matter can behave as waves. Any particle of momentum $p$ has an associated wavelength:

The decisive evidence is electron diffraction. When a beam of electrons passes through a thin crystal or graphite film, it produces a diffraction pattern of rings, exactly as X-rays do. Diffraction is a wave phenomenon, so this proves electrons have a wave nature. The ring spacing matches the de Broglie wavelength calculated from the electrons' momentum, confirming the relation quantitatively.

State the de Broglie relation and explain what it tells us about matter. [2 marks]

Find the de Broglie wavelength of a proton (mass $1.67 \times 10^{-27}\ \text{kg}$) moving at $2.0 \times 10^4\ \text{m s}^{-1}$ ($h = 6.63 \times 10^{-34}\ \text{J s}$). [2 marks]

Explain why a moving car does not show observable wave behaviour. [2 marks]