Question:
In a crystal lattice, anions A form hcp array. \(\dfrac{2}{3}\) of the tetrahedral voids are occupied by cations C. What is the formula of crystal?
In a crystal lattice, anions A form hcp array. \(\dfrac{2}{3}\) of the tetrahedral voids are occupied by cations C. What is the formula of crystal?
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In close-packed structures, if there are \(N\) atoms or ions, then octahedral voids are \(N\) and tetrahedral voids are \(2N\).
Updated On: Jun 18, 2026
- \(C_3A_4\)
- \(C_4A_3\)
- \(C_2A_3\)
- \(C_3A_2\)
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The Correct Option is B
Solution and Explanation
Step 1: Use the relation between anions and tetrahedral voids.
If the number of anions in close packing is \(N\), then the number of tetrahedral voids is \[ 2N \] Here, anions \(A\) form hcp array.
So, if the number of anions \(A\) is \[ N \] then tetrahedral voids are \[ 2N \]
Step 2: Calculate the number of cations occupying tetrahedral voids.
Given that \[ \frac{2}{3} \] of the tetrahedral voids are occupied by cations \(C\).
Therefore, number of cations \(C\) is \[ \frac{2}{3}\times 2N \] \[ =\frac{4N}{3} \]
Step 3: Find the ratio of cations and anions.
Number of cations \(C\) is \[ \frac{4N}{3} \] Number of anions \(A\) is \[ N \] Thus, \[ C:A=\frac{4N}{3}:N \] Multiplying by 3, \[ C:A=4:3 \]
Step 4: Write the formula.
The formula of the crystal is \[ C_4A_3 \]
Step 5: Final conclusion.
Therefore, \[ \boxed{C_4A_3} \] Hence, the correct option is (2).
If the number of anions in close packing is \(N\), then the number of tetrahedral voids is \[ 2N \] Here, anions \(A\) form hcp array.
So, if the number of anions \(A\) is \[ N \] then tetrahedral voids are \[ 2N \]
Step 2: Calculate the number of cations occupying tetrahedral voids.
Given that \[ \frac{2}{3} \] of the tetrahedral voids are occupied by cations \(C\).
Therefore, number of cations \(C\) is \[ \frac{2}{3}\times 2N \] \[ =\frac{4N}{3} \]
Step 3: Find the ratio of cations and anions.
Number of cations \(C\) is \[ \frac{4N}{3} \] Number of anions \(A\) is \[ N \] Thus, \[ C:A=\frac{4N}{3}:N \] Multiplying by 3, \[ C:A=4:3 \]
Step 4: Write the formula.
The formula of the crystal is \[ C_4A_3 \]
Step 5: Final conclusion.
Therefore, \[ \boxed{C_4A_3} \] Hence, the correct option is (2).
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