Question

# A compound formed by elements A and B has a cubic structure in which A atoms are at the corners of the cube and B atoms are at the face centres. The formula of the compound will be ___________.

A

${A}_{4}{B}_{3}$

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B

${A}_{2}B$

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C

$A{B}_{3}$

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D

${A}_{2}{B}_{3}$

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Solution

## The correct option is C $A{B}_{3}$The explanation for the correct answer:-Option (C) $A{B}_{3}$ Step 1: Given data The compound has a cubic structure in which A atoms are at the corners of the cube and B atoms are at the face centres.Step 2: Calculating the number of atoms of componentsNumber of atoms A present per unit cell = $\left(1/8\right)x8$$=1$Number of atoms B present per unit cell = $6x\left(1/2\right)$$=3$Step 3: Deriving components formula So, the ratio of A: B = $1:3$Therefore, the formula is ${\mathrm{AB}}_{3}$, option (C) is the correct answer.

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