JEE Main 2023 · 25 January · morning · Single correct · +4 / −1

A cubic solid is made up of two elements X and Y. Atoms of X are present on every alternate corner and one at the center of cube. Y is at 1/3ʳᵈ of the total faces. The empirical formula of the compound is :

  1. (a) X₂Y_(1.5)
  2. (b) X₃Y₂
  3. (c) XY_(2.5)
  4. (d) X_(2.5)Y
Answer and solution

Answer (b) X₃Y₂

Solution

Chemistry ma’am · 3 steps

Multiply each atom by its share in the cell, then turn the ratio into whole numbers.

  1. Count X. A cube has 8 corners, so every alternate corner means 4 corners. Each corner atom is shared by 8 cubes, giving 4 × 1/8 = 1/2. The body-centre atom belongs fully to this cube and adds 1, so X = 1/2 + 1 = 3/2.
  2. Count Y. A cube has 6 faces, and one-third of them is 2 faces. Each face atom is shared by 2 cubes, so Y = 2 × 1/2 = 1.

    X : Y = 3/2 : 1 = 3 : 2

  3. So. The empirical formula is X₃Y₂, which is option (b).

The idea to keep. Corner counts 1/8, face 1/2, edge 1/4, body centre 1. An empirical formula always uses the smallest whole-number ratio, never fractions.

Answer from the NTA final answer key. Solution by PrepWiser.

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Asked about 40 times in JEE Main since 2020. This question is from 2023.