Question

What is the number of tetrahedral voids present in \(0.5\) mole of compound forming hcp structure?

• A. \(1.223\times 10^{23}\)
• B. \(3.628\times 10^{23}\)
• C. \(4.487\times 10^{23}\)
• D. \(6.022\times 10^{23}\)

Hint:

An hcp lattice has 2 tetrahedral voids per atom, so find the number of atoms first.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
In close packing (hcp or ccp) with \(N\) atoms, there are \(N\) octahedral voids and \(2N\) tetrahedral voids.

Step 2: Number of Atoms:
\(0.5\) mol of atoms \(= 0.5 \times 6.022\times 10^{23} = 3.011\times 10^{23}\) atoms.

Step 3: Number of Tetrahedral Voids:
\[ 2N = 2 \times 3.011\times 10^{23} = 6.022\times 10^{23} \]

Step 4: Check the Other Options:
\(3.011\times10^{23}\) would be the number of atoms or octahedral voids. The other values do not match any simple multiple of \(N\). So (D) is correct.

Final Answer:
The number of tetrahedral voids is \(6.022\times10^{23}\), option (D). \[ \boxed{\text{(D) } 6.022\times 10^{23}} \]