If we consider again the linear term (r) in the result of Problem 29, we have a harmonic...

If we consider again the linear term (r) in the result of Problem 29, we have a harmonic oscillator. (a) Find an

expression for the frequency of oscillation and evaluate using the correct values of α, r₀, and ρ for NaCl. (b) Find the photon wavelength corresponding to the frequency you computed in (a) and compare with the observed absorption wavelength for NaCl of about 61 μm.

Problem 29

Starting with the result of Problem 28, approximate r r₀ + δ r (where δ r << r₀) and show that

Perform a Taylor series expansion about r = r₀, keeping terms up to and including order (δ r)². Show that

where

and

Problem 28

Use Equation (10.19) to evaluate the net force (F =-dV/dr) on an atom in a sodium chloride lattice. Then show that the force can be expressed as