Avogadro's number \(N_{A}\) is a universal constant equal to the number of particles (such as atoms, molecules) in one mole of a substance. One mole of aluminum has a mass of \(26.98 \mathrm{~g}\). The density of aluminum is \(2.70 \mathrm{~g} \cdot \mathrm{cm}^{-3}\). In XRD experiments with aluminum powder, where he determined the lattice structure to be fcc, Hull observed strong interference at Bragg angle \(\theta=14.63^{\circ}\) using a molybdenum X-ray tube \((\lambda=0.0714 \mathrm{~nm})\). He assigned Miller index 110 . From these data, what is the predicted value of \(N_{A}\) ?