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GATE 2020 PH – Question 47

Solid State Physics · Lattice vibrations and thermal properties of solids · 2 marks · Multiple choice

A two-dimensional crystal has three atoms in its basis. Find the numbers n of optical and m of acoustic branches of lattice vibrations.

  1. (n,m) = (2,4)
  2. (n,m) = (3,3)
  3. (n,m) = (4,2)
  4. (n,m) = (1,5)

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Correct answer: (C) (n,m) = (4,2)

Explanation

With motion restricted to two dimensions, each of the three basis atoms has two displacement components, yielding six vibrational branches. Two correspond to uniform translations in the two independent directions and are acoustic. The remaining $6-2=4$ are optical. Thus $(n,m)=(4,2)$, C.

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