(a) A 2D hexagonal lattice of lattice spacing a = 3 Å has isotropic speed of sound v = 10³m/s. Starting from the basic assumptions of the Debye model, show that the Debyefrequency OD is 1.27 x 10¹3s-¹, and find the magnitude of the Debye wave vector KD(hint: think about how you will accommodate the correct number of phonon modes).(b) Na (sodium) has a body-centered cubic structure with lattice constant a = 4.225 Å

Given, Lattice spacing, a=3A˙a=3×10-10m Speed of sound, v=103m/s The debye frequency, ωD=4πNAvs2…

Answered: (a) A 2D hexagonal lattice of lattice…

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