In Chrysoberyl, a compound containing Beryllium, Aluminium and oxygen, oxide ions form cubic close packed structure. Aluminium ions occupy \(\frac{1}{4}\)th of octahedral voids. The formula of the compound is
- BeAlO4
- BeAl2O4
- Be2AlO2
- BeAlO2
The Correct Option is B
Approach Solution - 1
Step 1: Analyze the CCP structure
In a cubic close-packed structure, the oxide ions (O²⁻) form the close-packed arrangement, which leaves octahedral voids. The number of octahedral voids is equal to the number of oxide ions in the structure.
Step 2: Consider the Aluminium ions
We are told that aluminium ions (Al³⁺) occupy 1/4th of the octahedral voids in the CCP structure. This means that for every 4 oxide ions, there is 1 aluminium ion occupying an octahedral void.
Step 3: Determine the ratio of ions
- The ratio of Al to O is 1:4 because Al occupies 1/4th of the octahedral voids.
- The beryllium ions (Be²⁺) are likely in tetrahedral voids in the structure.
Step 4: Construct the formula
Given that there are 4 oxygen ions (O²⁻) for every aluminium ion (Al³⁺), the number of Be ions will balance the structure. The most likely formula for the compound would be BeAl₂O₄.
Final Answer: The formula of the compound is BeAl₂O₄.
Approach Solution -2
In the given compound, the oxide ions form a cubic close-packed structure. The aluminum ions occupy 1/4th of the tetrahedral voids and the beryllium ions occupy 1/4th of the octahedral voids.
- In a cubic close-packed structure, the number of tetrahedral voids and octahedral voids are both equal to 4.
- Aluminum occupies 1/4th of the tetrahedral voids, so it will occupy 1 tetrahedral void.
- Beryllium occupies 1/4th of the octahedral voids, so it will occupy 1 octahedral void.
- There are 4 oxide ions in the unit cell.
Therefore, the formula of the compound is \(BeAl₂O₄\).
Correct answer is (B): \(BeAl₂O₄\)
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