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GATE 2024 PH – Question 54

Solid State Physics · lattice vibrations and thermal properties of solids · 2 marks · Multiple select

Apart from the acoustic modes, 9 optical modes are identified from the measurements of phonon dispersions of a solid with chemical formula AnBm, where A and B denote the atomic species, and n and m are integers. Which of the following combination of n and m is/are possible?

  1. n= 1, m= 1
  2. n= 2, m= 2
  3. n= 3, m= 1
  4. n= 4, m= 4

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Show answer and explanation

Correct answer: (B) n= 2, m= 2; (C) n= 3, m= 1

Explanation

Nine optical modes imply $3r-3=9$, hence four atoms in the primitive cell. The key interprets $n+m$ as that cell count, so $n+m=4$ gives B (2,2) and C (3,1). Allowing two AB formula units in a cell is a broader interpretation, but A is not accepted in this paper.

Official GATE 2024 answer key: https://gate2026.iitg.ac.in/doc/download/2024/PHFinalAnswerKey.pdf