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GATE 2024 PH – Question 16

Solid State Physics · free electron theory · 1 mark · Multiple choice

Crystal structures of two metals A and B are two-dimensional square lattices with same lattice constant a. Electrons in metals behave as free electrons. The Fermi surfaces corresponding to A and B are shown by solid circles in figures. The electron concentrations in A and B are nA and nB, respectively. The value of ( nB nA ) is

Circular Fermi surfaces inscribed in and circumscribed about the first square Brillouin zone.
  1. 3
  2. 2
  3. 3√3
  4. √2

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Show answer and explanation

Correct answer: (B) 2

Explanation

In two dimensions density scales as Fermi-circle area. The circumscribed radius in B is $\sqrt2$ times the inscribed radius in A, so the density ratio is 2.