513.001 Molecular and Solid State Physics

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Physical
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Wavevectors in a one-dimensional chain

Consider vibrational waves travelling in a one-dimensional monatomic crystal in which equilibrium sites are a = 0.5 nm apart.

a) If the chain contains 6×108 atoms, find the allowed values of the wavevectors.

b) Suppose the length of the chain is doubled by adding atoms with the same equilibrium spacing. What then are the allowed values of the wave vector?

from J. R. Christman, example 6.2