Past exam of the condensed matter physics course of the University of Oxford / 2021 / 1 / b / Solution

The neutron is nonrelativistic at this kinetic energy. Its de Broglie wavelength isIn elastic scattering, Bragg's law gives $2d\sin \theta =\lambda$. The measured total deflection is $2\theta$, so it must be halved before taking the sine. The reflection order is absorbed into the Miller indices of the diffracting lattice planes. In the order of the four measured rings, the interplanar spacings areThe last digits give the numerical calculation, rather than accuracy beyond the supplied angular precision.