Question:
A compound $M_{p} X_{q}$ has cubic close packing (ccp) arrangement of X. Its unit cell structure is shown below. The empirical formula of the compound is
A compound $M_{p} X_{q}$ has cubic close packing (ccp) arrangement of X. Its unit cell structure is shown below. The empirical formula of the compound is
Updated On: Jul 13, 2024
- MX
- $MX_{2}$
- $M_{2}X$
- $M_{5} X_{14}$
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The Correct Option is B
Solution and Explanation
No.of Matoms$=\frac{1}{4}\times4+1=1+1=2$
No.of Xatoms $=\frac{1}{2}\times6+\frac{1}{8}\times8=3+1=4$
So, formula = $M_{2} X_{4} =MX_{2}$
No.of Xatoms $=\frac{1}{2}\times6+\frac{1}{8}\times8=3+1=4$
So, formula = $M_{2} X_{4} =MX_{2}$
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Concepts Used:
Unit Cells
The smallest portion of a crystal lattice which repeats in different directions to form the entire lattice is known as Unit cell.
The characteristics of a unit cell are:
- The dimensions are measured along the three edges, a, b and c. These edges can form different angles, they may be mutually perpendicular or may not.
- The angles held by the edges are α (between b and c) β (between a and c) and γ (between a and b).
Therefore, a unit cell is characterised by six parameters such as a, b, c and α, β, γ.
Types of Unit Cell:
Numerous unit cells together make a crystal lattice. Constituent particles like atoms, molecules are also present. Each lattice point is occupied by one such particle.
- Primitive Unit Cells: In a primitive unit cell constituent particles are present only on the corner positions of a unit cell.
- Centred Unit Cells: A centred unit cell contains one or more constituent particles which are present at positions besides the corners.
- Body-Centered Unit Cell: Such a unit cell contains one constituent particle (atom, molecule or ion) at its body-centre as well as its every corners.
- Face Centered Unit Cell: Such a unit cell contains one constituent particle present at the centre of each face, as well as its corners.
- End-Centred Unit Cells: In such a unit cell, one constituent particle is present at the centre of any two opposite faces, as well as its corners.