electron beams at a crystal of nickel and observing the reflected beams via a detector. This study soon developed into the study of neutron scattering to study magnetism in solids. If either massive particle had a purely particulate nature, the detector should only observe single particles. However, the observation of distinct interference patterns provided evidence of the wave-like nature of electrons and neutrons as predicted by de Broglie. In Nickel Oxide (NiO), a famous antiferromagnet, shown in FIG 3, you can measure the distance between magnetic moments by scattering neutrons off of the magnetic layers. The blue(red) spheres in FIG 3 show Ni atoms that are spin up(down). Figure 2b shows a simplified diagram of the experimental setup. Consider two layers of a NiO crystal (in blue) separated by distance d. Neutron beams (in red) incident on the crystal are reflected back by different layers of the crystal, and hence, develop a path difference leading to constructive or destructive interference on the receiver screen. 1. What is the path difference between the two beams shown in the diagram? Hint: Assume that the beams are parallel. Notice that AOA is longer than BO B by the lengths CO + OC . [2] 2. Write down the condition for constructive interference by equating the path difference to integer multiples of wavelength n. This is called Bragg s law of diffraction. [1] 3. NiO crystals have a separation between the magnetic layers of d = 0.32nm. The experiment found that construc- tive interference occurs when 0 = 35. What is the wavelength of the incident neutron beam when n = = 1? [2] 4. Calculate the momentum and kinetic energy of the incident neutrons. Take the mass of the neutron to be m = 1.67 10-27kg. [3]