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GATE 2025 PH – Question 11

Solid State Physics · Elements of crystallography · 1 mark · Multiple choice

For a two-dimensional hexagonal lattice with lattice constant $a$, the atomic density is

  1. $1/(\sqrt3a^2)$
  2. $1/(\sqrt6a^2)$
  3. $4/(3\sqrt3a^2)$
  4. $1/(3\sqrt3a^2)$

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Show answer and explanation

Correct answer: (C) $4/(3\sqrt3a^2)$

Explanation

A honeycomb cell of area $3\sqrt3a^2/2$ contains two atoms, giving density $4/(3\sqrt3a^2)$.

Official GATE 2025 answer key: https://gate2026.iitg.ac.in/doc/download/2025_Key/PH_Keys.pdf