1. The visible light of wavelength 5000˚A undergoes scattering from a crystal of refractive index 1.5. Calculate the maximum frequency of the phonon generated and the fractional change in the frequency of the incident radiation, given the velocity of sound in the crystal as 5000 m/s. 2. The Young’s modulus of NaCl in [100] direction is 5 × 1010N/m2 . Assuming that the extension in the [100] direction produces negligible contraction in the perpendicular directions, calculate the wavelength at which the electromanetic radiation is strongly reflected by the NaCl crystal. Atomic masses of Na and Cl are 23 and 35.5 a.m.u respectively.3. Gold has the structure as copper. The velocity of sound in gold is 2100 m/s and that in copper is 3800 m/s. If the Debye temperature of copper is 348 K, determine the Debye temperature of gold. The densities of gold and copper are 1.93 × 104kg/m3 and 8960kg/m3 and their atomic weights are 197.0 and 63.54 a.m.u respectively. 4. The Debye temperature of diamond is 2000 K. Calculate the mean velocity of sound in diamond, given the density and atomic mass of diamond as 3500 kg/m3 and 12 a.m.u respectively. If the inter-atomic spacing is 1.54 ˚A, estimate the frequency of the dominant mode of lattice vibration. 5. Derive an expression for the lattice heat capacity of a solid following Einstein model. Discuss the assumptions and predictions of this model and compare it with experimental observations.
1. The visible light of wavelength 5000˚A undergoes scattering from a crystal of refractive index 1.5. Calculate the maximum frequency of the phonon generated and the fractional change in the frequency of the incident
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