Question

How many tetrahedral voids are present in 0.4 mole of a compound that forms hcp structure?

• A. $4.8 \times 10^{23}$
• B. $3.011 \times 10^{23}$
• C. $1.2 \times 10^{23}$
• D. $2.4 \times 10^{23}$

Hint:

To solve this instantly without full calculation, remember that the total number of tetrahedral voids per mole is exactly $2 \times N_A \approx 12 \times 10^{23}$. Multiplying this straight by the given moles gives: $0.4 \times 12 \times 10^{23} = 4.8 \times 10^{23}$.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The goal is to calculate the total number of tetrahedral voids present in a sample containing 0.4 moles of a compound that crystallizes in an hcp lattice.

Step 2: Key Formula or Approach:
In any close-packed structure (hcp or ccp), the number of tetrahedral voids is exactly twice the number of constituent particles (2N), where N = moles × Avogadro's number.

Step 3: Detailed Explanation:
First calculate N = 0.4 × 6.022 × 10²³ = 2.4088 × 10²³ particles. Then the tetrahedral voids count is 2N = 2 × 2.4088 × 10²³ = 4.8176 × 10²³, which rounds to 4.8 × 10²³.

Step 4: Final Answer:
The total number of tetrahedral voids is 4.8 × 10²³, matching option (A).