Exercise 2

conjectured that the infrared characteristic frequencies of a solid might be determined by the same forces between atoms as determine the solid’s ordinary elastic behavior. The relevant quantities are these.

Show that there is one dimensionless product. Conclude that, in any complete relationship among quantities with these dimensional formulas, $k$ is a constant times $\nu^{-2}N^{-1/3}m^{-1}$. This conclusion played an important role in the early study of quantum phenomena.