Question

Estimate the Debye temperature of gold if its atomic weight is 197, the density is 1.9 x 104 kg/m3 and the velocity of sound in it is 2100 m/s.

Answer 1

The Debye temperature is

$$T_D=\frac{hv}{\lambda},$$

where

$$\lambda=\sqrt[3]{\frac{m_a}{\rho}}=\sqrt[3]{\frac{197·1.66·10^{-27}}{19000}}=2.58·10^{-10}\text{ m},$$

$$T_D=\frac{6.63·10^{-34}·2100}{2.58·10^{-10}}=5.39·10^{-21}\text{ K}.$$