Neutron scattering, like electron scattering, is used to determine the structures of solid atomic and molecular samples. As we know, to observe diffraction, the wavelength of the neutron must be of the same order of magnitude of the lattice constant $($spacings$)$ within the sample.Let's say we have access to a particle accelerator that has the capacity to produce a beam of thermal neutrons via a process called nuclear spallation, wherein the velocity of a neutron, v$,$ in the beam is determined by the average thermal kinetic energy, E$=\frac{3}{2}{k}_B$T$.$ At what beam temperature will we observe a diffraction pattern when this beam of neutrons falls on a crystalline material with an interatomic spacing of $1\mathrm{.}4?$