Question:
A and B atoms in a crystal are positioned at the corners and face centers respectively. What is the formula of the crystal?
A and B atoms in a crystal are positioned at the corners and face centers respectively. What is the formula of the crystal?
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In a cubic unit cell, a corner atom contributes \(\frac{1}{8}\), a face-centered atom contributes \(\frac{1}{2}\), an edge-centered atom contributes \(\frac{1}{4}\), and a body-centered atom contributes \(1\).
Updated On: Jun 18, 2026
- \(A_2B_3\)
- \(AB_2\)
- \(AB_3\)
- \(A_2B_3\)
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The Correct Option is C
Solution and Explanation
Step 1: Count the contribution of A atoms at corners.
In a cubic unit cell, there are 8 corners.
Each corner atom contributes \[ \frac{1}{8} \] to one unit cell.
Therefore, total number of A atoms is \[ 8 \times \frac{1}{8}=1 \]
Step 2: Count the contribution of B atoms at face centers.
In a cubic unit cell, there are 6 faces.
Each face-centered atom contributes \[ \frac{1}{2} \] to one unit cell.
Therefore, total number of B atoms is \[ 6 \times \frac{1}{2}=3 \]
Step 3: Write the simplest ratio.
The ratio of A atoms to B atoms is \[ A:B = 1:3 \] Hence, the formula of the crystal is \[ AB_3 \]
Step 4: Final conclusion.
Therefore, \[ \boxed{AB_3} \] Hence, the correct option is (3).
In a cubic unit cell, there are 8 corners.
Each corner atom contributes \[ \frac{1}{8} \] to one unit cell.
Therefore, total number of A atoms is \[ 8 \times \frac{1}{8}=1 \]
Step 2: Count the contribution of B atoms at face centers.
In a cubic unit cell, there are 6 faces.
Each face-centered atom contributes \[ \frac{1}{2} \] to one unit cell.
Therefore, total number of B atoms is \[ 6 \times \frac{1}{2}=3 \]
Step 3: Write the simplest ratio.
The ratio of A atoms to B atoms is \[ A:B = 1:3 \] Hence, the formula of the crystal is \[ AB_3 \]
Step 4: Final conclusion.
Therefore, \[ \boxed{AB_3} \] Hence, the correct option is (3).
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