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.