Question

The compound forming ccp structure contains $9.6\times10^{23}$ atoms. Find the number of tetrahedral voids formed in it.

• A. $1.00\times10^{24}$
• B. $1.68\times10^{24}$
• C. $1.92\times10^{24}$
• D. $1.56\times10^{24}$

Hint:

For $N$ packing atoms: Tetrahedral Voids = $2N$, Octahedral Voids = $N$. Therefore, the total number of voids combined is $3N$!

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We are given the total number of atoms forming a cubic close-packed (ccp) crystal lattice. We need to calculate the total number of tetrahedral voids generated within this entire crystal.

Step 2: Detailed Explanation:
In any close-packed solid structure (whether it is hexagonal close-packed hcp or cubic close-packed ccp/fcc), there is a direct mathematical relationship between the number of lattice constituent atoms and the number of generated interstitial voids:
Let the total number of atoms forming the close-packed lattice be $N$.
- The number of Octahedral Voids formed is exactly equal to $N$.
- The number of Tetrahedral Voids formed is exactly double that, which is $2N$.
We are given the number of atoms:
$N = 9.6 \times 10^{23}$
Using the rule for tetrahedral voids:
$\text{Number of Tetrahedral Voids} = 2 \times N$
$\text{Number of Tetrahedral Voids} = 2 \times (9.6 \times 10^{23})$
$\text{Number of Tetrahedral Voids} = 19.2 \times 10^{23}$
To match standard scientific notation formats, shift the decimal place:
$19.2 \times 10^{23} = 1.92 \times 10^{24}$

Step 3: Final Answer:
The number of tetrahedral voids is $1.92\times10^{24}$, matching option (c).