Question

10.11 Using the data for KCl given in Exercise 5.4 estimate a frequency at which the dielectric constant of KCl will relax to a lower value. [Hint: Around the equilibrium value the force is proportional to displacement (to a first approximation), whence a characteristic frequency can be derived.]

(From Ecercise 5.4: Take m = 1,n = 9,B = (1.75 e²) / (4π$\epsilon_{0}$). The bulk modulus of elasticity is 1.88×10¹⁰ Nm^–2.)

Answer given as: 2.68 × 10^12 Hz.

Please show how to get the answer for 10.11, thank you.

10.11. Using the data for KCl given in Exercise 5.4 estimate a frequency at which the dielectric constant of KCl will relax to a lower value. [Hint: Around the equilibrium value the force is propor- tional to displacement (to a first approximation), whence a characteristic frequency can be derived.] .68 x 1012 H:z 10.11 Answer: 5.4. For the KCl crystal the variation of energy may also be described by eqn (5.8), but now r means the interatomic dis- tance in the cubic crystal, and the energy is for an ion pair. Take m1, 9,B1.75e2/4TE0. The bulk modulus of elasticity is 1.88 x 1010 Nm 2. Calculate the separation of the K -CI ions in the ionic solid (5.8) 5.4 Answer: 3.12×10-10m

Answer 1

rN Cy 1919 -26 5.8 N/ -26 1.5 x 10 Lo 2