Electron Echoes from a Crystal Surface

A materials scientist at a Wellington laboratory studies the surface of a new alloy using low-energy electron diffraction. Electrons are accelerated from rest through a potential difference $V$ and strike the crystal surface at normal incidence. The surface atoms are arranged in parallel rows a distance $d$ apart, and they act like a reflection grating: back-scattered electrons produce strong maxima at angles $\theta$ from the normal given by $d\sin\theta = n\lambda$, where $n$ is the order. The electron speeds are non-relativistic. The scientist measures the angle $\theta_1$ of the first-order maximum at several accelerating voltages: $V\ (\text{V})$: 50.0, 80.0, 120, 180, 250 $\theta_1\ (^\circ)$: 44.3, 33.1, 26.6, 21.7, 17.9