Problem 6.185

Assuming the propagation velocities of longitudinal and transverse vibrations to be the same and equal to \(v,\) find the Debye temperature (a) for a unidimensional crystal, i.e. a chain of identical atoms, incorporating \(n_{0}\) atoms per unit length; (b) for a two-dimensional crystal, i.e. a plane square grid consisting of identical atoms, containing \(n_{0}\) atoms per unit area; (c) for a simple cubic lattice consisting of identical atoms, containing \(n_{0}\) atoms per unit volume.