Question:
A body centre cubic lattice is made up of two different types of atoms A and B. Atom A occupies the body centre and B occupying the corner positions. One of the corners is left unoccupied per unit cell. Empirical formula of such a solid is
A body centre cubic lattice is made up of two different types of atoms A and B. Atom A occupies the body centre and B occupying the corner positions. One of the corners is left unoccupied per unit cell. Empirical formula of such a solid is
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Corner atoms contribute $\frac{1}{8}$ each; body centre contributes 1.
Updated On: Apr 23, 2026
- AB
- A$_2$B$_3$
- A$_5$B$_7$
- A$_8$B$_7$
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The Correct Option is D
Solution and Explanation
Concept:
In cubic lattices:
• Body centre atom contributes 1 atom
• Each corner atom contributes $\frac{1}{8}$
Step 1: Number of A atoms:
A occupies body centre: \[ A = 1 \]
Step 2: Number of B atoms:
Total corners = 8, but 1 is vacant → 7 occupied \[ B = 7 \times \frac{1}{8} = \frac{7}{8} \]
Step 3: Find simplest ratio:
\[ A : B = 1 : \frac{7}{8} \] Multiply by 8: \[ A : B = 8 : 7 \] Conclusion:
Empirical formula = A$_8$B$_7$
• Body centre atom contributes 1 atom
• Each corner atom contributes $\frac{1}{8}$
Step 1: Number of A atoms:
A occupies body centre: \[ A = 1 \]
Step 2: Number of B atoms:
Total corners = 8, but 1 is vacant → 7 occupied \[ B = 7 \times \frac{1}{8} = \frac{7}{8} \]
Step 3: Find simplest ratio:
\[ A : B = 1 : \frac{7}{8} \] Multiply by 8: \[ A : B = 8 : 7 \] Conclusion:
Empirical formula = A$_8$B$_7$
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