- 1 6 00 5 00 400 3 00 Refractive Index 200 2 100 0 00 0 00 100 2 00 10 00 12 00 400 6 00 8 00 Frequency 10 Hz This Fi 1 (158.6 KiB) Viewed 30 times
1. 6.00 5.00 400 3.00 Refractive Index 200 2 100 0.00 0.00 -100 2.00 10.00 12.00 400 6.00 8.00 Frequency (10 Hz) This figure shows the refractive index of KCl in the infrared region of the spectrum. (a) Explain the features of the curve in the figure above from your knowledge of the interaction of light with oscillators in solids. [4 marks] (b) Write down and explain the dispersion of the dielectric constant for this case. No derivations are required. Explain how the resonance occurs as shown in the Figure above. [3 marks) (c) The data in the Figure above can be explained by assuming the resonance is due to vibrations of the K*Clions in the solid. The atomic weights of K and Cl are 39.0 and 35.5 respectively. Use the data in the Figure above to estimate: 0) The static dielectric constant of KCI. Estimate from data in graph [2 marks) () The natural vibrational frequency of the vibrations. Estimate from data in graph. [2 marks] () The restoring force for a 1 nm displacement of the oscillator. Hint- Hookes Law and use data from (ii) above. [4 marks] (iv) The density of KCl molecules per unit volume. Hint-Write down an expression for Gat-En. Assume charge on ions = 1.6 x 10°C. [4 marks) () The damping time of the vibrations. Since the line is asymmetric, take reading of peak to trough [3 marks) (vi) How would the resonant frequency change for the case of NaCl if the restoring constant in unchanged from KCI? [3 marks)