Paper 3 Wave-Particle Duality Answers

Q1 Comparing Light and Electrons

1. Energy is delivered in photons with $E=hf$; emission requires a threshold frequency and occurs without measurable delay above threshold. [3]
2. Electrons produce maxima/minima after scattering by crystal planes/slits, consistent with wavelength $\lambda =h/p$. [3]
3. Frequency sets photon energy and maximum photoelectron kinetic energy, while intensity at fixed frequency sets photon arrival rate and photocurrent. [3]

Q2 Electron Diffraction

1. $K=eV=3.52\times 10^{-17}\mathrm{J}$, $p=\sqrt{2m_{e}K}=8.01\times 10^{-24}\mathrm{kg}\mathrm{m}{\mathrm{s}}^{-1}$, and

   $$\lambda =\frac{h}{p}=8.28\times 10^{-11}\mathrm{m}.$$

   [4]

2. $\sin \theta =\lambda /d=0.414$, so $\theta =24.4^{\circ }$. [2]

3. Increasing $V$ increases $K=eV$ and momentum; therefore $\lambda =h/p$ decreases and the diffraction angle decreases. [3]

4. The ordered maxima/minima require diffraction and hence a wave model [1], while energy and charge are delivered in individual localised detector events [1]. Both observations arise in the same experiment and demonstrate complementary wave-like and particle-like behaviour [1].