You have an unlabeled container in the laboratory that contains the solid lithium fluoride (LiF) and an identical unlabeled container that contains the solid sodium chloride \((\mathrm{NaCl})\). You know that both materials crystallize in a cubic structure, with alternating \(\mathrm{Na}\) and \(\mathrm{Cl}\) ions in the \(\mathrm{NaCl}\) lattice and alternating \(\mathrm{Li}\) and \(\mathrm{F}\) ions in the LiF lattice. The only testing instrument available is a diffraction apparatus that uses monochromatic \(0.154-\mathrm{nm} x\) rays. After reading in the literature that the lattice spacing is \(0.202 \mathrm{~nm}\) for LiF and \(0.283 \mathrm{~nm}\) for \(\mathrm{NaCl}\), you test one of the samples in the apparatus and observe the first intensity peak at a Bragg angle of \(22.4^{\circ}\).