The Einstein frequency is often expressed in terms of an equivalent temperature θE, where θE = hv/k. Confirm that θE has the dimensions of temperature, and express the criterion for the validity of the high-temperature form of the Einstein equation in terms of it. Evaluate θE for

(a) diamond, for which ν =46.5 THz and

(b) for copper, for which ν = 7.15 THz.

What fraction of the Dulong and Petit value of the heat capacity does each substance reach at 25°C?