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4.
Diatomic chain. Consider the normal modes of a linear chain in which the force
constants between the nearest-neighbor atoms are C and 10C. Let the masses be equal
and let the nearest-neighbor separation be a/2. Find w(K) at K = 0 and K = π/a.
Sketch in the dispersion relation by eye. The problem simulates a crystal of diatomic
molecules such as H₂.

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