As discussed in Exercise 7.1.2, we can model a metal as an ensemble of classical oscillators with ω₀ = 0. Calculate the absolute reflectivity r for an infrared electromagnetic wave, with wavelength 10 μm, incident normal to the surface of a metal with electron density n = 10²¹ c^m−3, electron scattering time τ = 1 ps, and electron mass equal to the vacuum electron mass.

Data from Exercise 7.1.2

Using the result of the previous exercise, calculate the skin depthλ = 1/k_I for the penetration of an electromagnetic wave into a metal surface, as a function of frequency and the material parameters n (the electron density), m (the electron mass) and τ (the average electron scattering time). For realistic parameters for a metal, that is, n = N/V = 10²¹ cm⁻³ and τ = 1 ps, what is the skin depth of a 10 MHz electromagnetic wave?