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JEE Main 202325 JanuaryMorning Shift
Exam
JEE Main
Year
2023
Date
25 January
Shift
Morning Shift
Subject
Chemistry
Chapter
Solid State

JEE Main 2023 · 25 January · Morning Shift · Chemistry · Solid State

A cubic solid is made up of two elements X and Y . Atoms of X are...

A cubic solid is made up of two elements XX and YY. Atoms of XX are present on every alternate corner and one at the center of cube. YY is at 13rd\dfrac{1}{3}rd of the total faces. The empirical formula of the compound is

Options

  1. AX2Y1.5{X}_{2}{Y}_{1 . 5}
  2. BX1.5Y{X}_{1 . 5}Y
  3. CXY2.5{XY}_{2 . 5}
  4. DX1.5Y2{X}_{1 . 5}{Y}_{2}

Correct answer

B. X1.5Y{X}_{1 . 5}Y

Step-by-step solution

The share of the atom present at corner of the cube is 1/81 / 8. The share of the atom at face centre is 1/2.1 / 2 . Hence, the molecule can be represented as follows,

X4×18+1×1Y6×13×12{X}_{4 \times \dfrac{1}{8} + 1 \times 1}{Y}_{6 \times \dfrac{1}{3} \times \dfrac{1}{2}}

⇒X12+1Y1⇒ {X}_{\dfrac{1}{2} + 1}{Y}_{1}

⇒X23Y1⇒ X\dfrac{2}{3}{Y}_{1}

⇒X1.5Y1⇒ {X}_{1 . 5}{Y}_{1}(Empirical formula)

⇒X3Y2⇒ {X}_{3}{Y}_{2}.

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