A binary compound has Y-atoms forming FCC unit cell and another type of X-atoms occupying \(\frac{1}{3}\)rd of tetrahedral voids. Find out the molecular formula of the compound
A binary compound has Y-atoms forming FCC unit cell and another type of X-atoms occupying \(\frac{1}{3}\)rd of tetrahedral voids. Find out the molecular formula of the compound
Correct Answer: 23
Approach Solution - 1
For 1 unit cell,
No. of particles
X = \(\frac{1}{3}\times8\)
Y = 4
∴ The formula of Ionic solid = \(X_{\frac{8}{3}}Y_4\) =\(X_2Y_3\)
Approach Solution -2
The formula of the compound can be determined as follows:
In an FCC unit cell, there are 4 atoms located at the corners and one atom at the center of each face. Thus, the total number of Y atoms in the unit cell is 4 from the corners.
In a FCC unit cell, there are tetrahedral voids and octahedral voids. Each void can accommodate one atom. The number of tetrahedral voids in a FCC unit cell is twice the number of atoms per unit cell, which is 4 in this case. Therefore, there are 8 tetrahedral voids in the unit cell. Since X atoms occupy \(\frac{1}{3}\) of the tetrahedral voids, there are \(8\times \frac{1}{3}=\frac{8}{3}\) X atoms in the unit cell.
The ratio of X atoms to Y atoms in the unit cell is therefore \(\frac{(\frac{8}{3})}{4}=\frac{2}{3}\). This means that the molecular formula of the compound is X2Y3. Therefore, option B (X2Y3) is the correct answer.
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Concepts Used:
Solid State
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Types of Solids:
Based on the nature of the order that is present in the arrangement of their constituent particles solids can be divided into two types;
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