Question:
A compound formed by elements A and B crystallizes in a cubic structure where A atoms are at the corner of the cube and B atoms are at the center of the cube. What is the formula of the compound?
A compound formed by elements A and B crystallizes in a cubic structure where A atoms are at the corner of the cube and B atoms are at the center of the cube. What is the formula of the compound?
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Count each corner atom as one-eighth and the body centre atom as one whole.
Updated On: Oct 1, 2026
- \(\text{AB}\)
- \(\text{A}_2\text{B}\)
- \(\text{AB}_2\)
- \(\text{A}_2\text{B}_2\)
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
In a cubic unit cell, a corner atom is shared by 8 cells, so only one-eighth of it belongs to the cell. A body-centre atom lies wholly inside.
Step 2: Detailed Explanation:
A atoms at 8 corners: \(8 \times \dfrac{1}{8} = 1\).
B atom at the body centre: \(1\).
Ratio A : B = 1 : 1, so the formula is AB.
Step 3: Why the other options are wrong.
\(\text{A}_2\text{B}\) and \(\text{AB}_2\) would need a 2 : 1 or 1 : 2 ratio. \(\text{A}_2\text{B}_2\) is just AB written as a multiple, not the simplest formula.
Final Answer:
The simplest formula is AB, option (A). \[ \boxed{\text{AB}} \]
In a cubic unit cell, a corner atom is shared by 8 cells, so only one-eighth of it belongs to the cell. A body-centre atom lies wholly inside.
Step 2: Detailed Explanation:
A atoms at 8 corners: \(8 \times \dfrac{1}{8} = 1\).
B atom at the body centre: \(1\).
Ratio A : B = 1 : 1, so the formula is AB.
Step 3: Why the other options are wrong.
\(\text{A}_2\text{B}\) and \(\text{AB}_2\) would need a 2 : 1 or 1 : 2 ratio. \(\text{A}_2\text{B}_2\) is just AB written as a multiple, not the simplest formula.
Final Answer:
The simplest formula is AB, option (A). \[ \boxed{\text{AB}} \]
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