Step 1: Understanding the Concept:
In any close-packed lattice structure (like hcp or ccp/fcc), the number of voids generated depends directly and proportionally on the number of constituent particles forming the lattice. Step 2: Key Formula or Approach:
If the total number of close-packed particles (atoms) is $N$, then by geometric derivation:
Number of octahedral voids = $N$
Number of tetrahedral voids = $2N$
Total number of voids = $N + 2N = 3N$ Step 3: Detailed Explanation:
1. Calculate the number of atoms ($N$):
Amount of compound given = $0.6 \text{ mol}$
Using Avogadro's number ($N_A \approx 6.022 \times 10^{23} \text{ mol}^{-1}$):
\[ N = 0.6 \text{ mol} \times (6.022 \times 10^{23} \text{ atoms/mol}) \]
\[ N = 3.6132 \times 10^{23} \text{ atoms} \]
2. Calculate total voids:
Total voids = $3 \times N$
\[ \text{Total voids} = 3 \times (3.6132 \times 10^{23}) \]
\[ \text{Total voids} = 10.8396 \times 10^{23} \]
3. Format the mathematical answer:
Adjusting the decimal to standard scientific notation format:
\[ \text{Total voids} = 1.08396 \times 10^{24} \approx 1.084 \times 10^{24} \]
Step 4: Final Answer:
The total number of combined voids is $1.084 \times 10^{24}$.