IGNOU PHE 13 2026 - Is the following statement true for vibrations of a chain of two diffe

Question

Is the following statement true for vibrations of a chain of two different types of atoms: “At the centre of the Brillouin zone, the frequency of the optical branch is less than the frequency of the acoustic branch”? Explain.

29 Jan 2026

Answer :

Word Count : 244

For a one-dimensional chain consisting of two different types of atoms of masses (m_1) and (m_2) connected by identical force constants, the statement is false. At the centre of the Brillouin zone, i.e. at wave vector (k = 0), the acoustic and optical branches show distinctly different physical behavior. In the acoustic mode at (k =

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