Quick questions on De Broglie matter waves: HSC Physics Module 8

Clinton Davisson and Lester Germer at Bell Labs were studying low-energy electron scattering from a nickel target. An accident (a vacuum leak followed by a heat treatment that crystallised the nickel) left the surface as a single crystal. Subsequent scattering of electrons at 54 V from the now-crystalline surface showed a sharp angular peak at 50 degrees, exactly where Bragg-like diffraction predicted for the nickel lattice spacing and the de Broglie wavelength of 54 eV electrons (0.167 nm).

The wave nature of matter is the basis of much of modern science:

Write de Broglie's hypothesis as an equation and state which physical quantities link wave and particle properties. [2 marks]

Calculate the de Broglie wavelength of an electron accelerated through $100 \text{ V}$. [3 marks]

A neutron from the ANSTO OPAL reactor has KE $= 0.025 \text{ eV}$ (thermal). (a) Calculate the neutron's de Broglie wavelength. (b) Compare this with the spacing between atoms in a solid ($\sim 0.2 \text{ nm}$).