Paper 4 Wave-Particle Duality Drills

Q1 Electron Diffraction Data Analysis

A student records the diameter $D$ of one diffraction ring for electrons accelerated through different p.d.s $V$. A derived column $x=V^{-1/2}$ is included to test the prediction $D\propto V^{-1/2}$.

| $V$/V | 1000 | 1500 | 2000 | 2500 | 3000 | 3500 | |---:|---:|---:|---:|---:|---:|---:|---:| | $x$/$10^{-2}{\mathrm{V}}^{-1/2}$ | 3.162 | 2.582 | 2.236 | 2.000 | 1.826 | 1.690 | | $D$/mm | 37.9 | 31.0 | 26.8 | 24.1 | 21.8 | 20.4 |

1. Plot a graph of $D$ against $x$ and draw a best-fit straight line. [5]
2. Determine the gradient, including its unit. [2]
3. State whether the data support $D\propto V^{-1/2}$ and justify your conclusion. [2]
4. Explain the predicted relationship using $eV=p^2/(2m_e)$ and $\lambda =h/p$. [3]
5. State one measurement difficulty and a matched improvement. [2]

Q2 Model Choice

A student writes: “Light is a wave in diffraction, but a particle in the photoelectric effect. Therefore it switches identity depending on the experiment.”

1. Identify what is useful in the statement. [1]
2. Explain what is misleading about it. [2]
3. Rewrite the idea more carefully. [2]