Paper 4 Wave-Particle Duality Answers

Q1 Electron Diffraction Data Analysis

1. Axes correctly oriented and labelled [1]; sensible scales [1]; six points accurately plotted [2]; best-fit straight line [1].
2. Gradient $\approx 12.0\mathrm{mm}$ per $10^{-2}{\mathrm{V}}^{-1/2}$, equivalently $1.20\times 10^3\mathrm{mm}{\mathrm{V}}^{1/2}$. Accept graph-consistent values. [2]
3. Yes: the points lie close to a straight line whose intercept is consistent with zero within the scatter. [2]
4. $p=\sqrt{2m_{e}eV}$, so $\lambda =h/\sqrt{2m_{e}eV}\propto V^{-1/2}$. For fixed apparatus geometry and crystal spacing, diffraction ring diameter is proportional to diffraction angle and hence to $\lambda$ for small angles. [3]
5. Example: the ring edge is broad, producing uncertainty in diameter [1]; measure diameters in several directions and average, or measure across opposite edges and use the midpoint/fit the ring [1]. Accept equivalent matched pairs.

Q2 Model Choice

1. It correctly links different evidence to wave-like and particle-like behaviour. [1]
2. It suggests a classical object changes identity, whereas quantum theory uses one framework with different observed behaviours. [2]
3. Light and matter have quantum behaviour; experiments reveal wave-like interference/diffraction or particle-like localized energy transfer depending on what is measured. [2]