A cubic solid is made by atoms A forming close pack arrangement, B occupying one. Fourth of tetrahedral void and C occupying half of the octahedral voids. What is the formula of compound.

Answer

To determine the formula of the compound formed by atoms A, B, and C in a cubic solid, we can follow these steps:

### Step 1: Determine the number of A atoms in the close-packed arrangement.
- In a face-centered cubic (FCC) arrangement, the contribution of atoms is calculated as follows:
- There are 6 face-centered atoms, each contributing \( \frac{1}{2} \) (since each face atom is shared between two unit cells).
- There are 8 corner atoms, each contributing \( \frac{1}{8} \) (since each corner atom is shared among eight unit cells).

Calculation:
\[ \text{Contribution from face atoms} = 6 \times \frac{1}{2} = 3 \]
\[ \text{Contribution from corner atoms} = 8 \times \frac{1}{8} = 1 \]
\[ \text{Total A atoms} = 3 + 1 = 4 \]

### Step 2: Calculate the number of B atoms occupying tetrahedral voids.
- In a close-packed structure, the number of tetrahedral voids is twice the number of atoms.

Calculation:
\[ \text{Number of tetrahedral voids} = 2 \times 4 = 8 \]
- B occupies one-fourth of the tetrahedral voids:
\[ \text{B atoms} = \frac{1}{4} \times 8 = 2 \]

### Step 3: Calculate the number of C atoms occupying octahedral voids.
- The number of octahedral voids is equal to the number of atoms in the close-packed structure.

Calculation:
\[ \text{Number of octahedral voids} = 4 \]
- C occupies half of the octahedral voids:
\[ \text{C atoms} = \frac{1}{2} \times 4 = 2 \]

### Step 4: Write the formula of the compound.
- Now we can summarize the contributions of each atom:
- A: 4
- B: 2
- C: 2

Thus, the formula of the compound is:
\[ \text{Formula} = A_4B_2C_2 \]

### Final Answer:
The formula of the compound is \( A_4B_2C_2 \).

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