Question
Download Solution PDFA compound is made up of three elements X, Y and Z. X atoms are present at each corner of the unit cell, Y atoms are present on each edge and Z atoms are present in the centre of each face. The formula of the compound is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- Atoms at the edge of a unit cell:
- In a crystal lattice, an edge of a unit cell is shared by four other unit cells.
- One is the adjacent unit cell and the other two are on the layer just above the unit cell.
- So each edge contributes to one-fourth of an atom in a unit cell.
- There are 12 edges per unit cell, thus a total number of atoms becomes 12 × 1/4 = 3.
- Atoms at the corners of a unit cell:
- The corner atoms are shared via 8 cubes, so the contribution from each corner is 1/8.
- Total number of atoms on the corner of a cube = 8
- The total number of atoms from corners is 8 × 1/8 = 1.
- Atoms at the face of a unit cell:
- Each face is shared by two unit cells.
- the contribution from each face is thus 1/2.
- There are six faces in a cube, so the total contribution from the faces of the cube = 3
Calculation:
- The atoms present at the corners are X.
- Contribution from all the corners = 1.
So, the total number of X atoms = 1.
- Y atoms are present at the edges.
- Total number of atoms at edges = 3,
So the number of Y atoms = 3.
- The total contribution from all 6 faces is 3.
- Z atoms are present at the faces.
So total number of Z atoms = 3.
Hence, the formula of the compound is XY3Z3.
Last updated on May 5, 2025
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