Atoms of an element 'A' occupy tetrahedral voids in the hexagonal close packed (hcp) unit cell lattice formed by the element 'B'. The formula of the compound formed by 'A' and 'B' is

Options

A. `A_(2)B`
B. `AB_(2)`
C. `A_(4)B_(3)`
D. `A_(2)B_(3)`

Answer

To find the formula of the compound formed by elements A and B, we can follow these steps:

### Step 1: Understand the Structure
The question states that element A occupies tetrahedral voids in a hexagonal close packed (hcp) lattice formed by element B.

### Step 2: Determine the Number of Atoms in HCP
In a hexagonal close packed (hcp) structure, the number of atoms per unit cell is 6. This means that there are 6 atoms of element B in the unit cell.

### Step 3: Calculate the Number of Tetrahedral Voids
In a close packed structure, the number of tetrahedral voids is twice the number of atoms present in the unit cell. Therefore, for 6 atoms of B:
\[ \text{Number of tetrahedral voids} = 2 \times 6 = 12 \]

### Step 4: Determine the Occupation of Tetrahedral Voids
It is given that 2/3 of the tetrahedral voids are occupied by atoms of element A. Thus, the number of tetrahedral voids occupied by A is:
\[ \text{Occupied tetrahedral voids} = \frac{2}{3} \times 12 = 8 \]

### Step 5: Establish the Ratio of Atoms A to B
Now we have:
- Number of atoms of A = 8 (from the occupied tetrahedral voids)
- Number of atoms of B = 6 (from the hcp structure)

The ratio of the number of atoms of A to B is:
\[ \text{Ratio of A to B} = \frac{8}{6} = \frac{4}{3} \]

### Step 6: Write the Formula
From the ratio of atoms, we can write the formula of the compound as:
\[ \text{Formula} = A_4B_3 \]

### Final Answer
The formula of the compound formed by A and B is \( A_4B_3 \).

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