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GATE 2024 MT – Question 40

Materials Science and Non-Metallic Materials · Crystal structures and bonding · 2 marks · Multiple choice

In a cubic lattice, what is the ratio of interplanar spacings of the (100), (110) and (111) planes? (Round off to two decimal places)

  1. 1 ∶ 0.32 ∶0.71
  2. 1 ∶ 0.71 ∶0.58
  3. 1 ∶ 0.58 ∶0.71
  4. 1 ∶ 0.58 ∶0.32

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Correct answer: (B) 1 ∶ 0.71 ∶0.58

Explanation

For cubic crystals, dhkl=a/√(h²+k²+l²).

Relative to d100=a, the three spacings are 1:1/√2:1/√3=**1:0.71:0.58, B**.