Question:
Calculate the volume occupied by a particle in fcc unit cell if volume of unit cell is 1.6 \(\times\) 10\(^{-23}\) cm\(^3\).
Calculate the volume occupied by a particle in fcc unit cell if volume of unit cell is 1.6 \(\times\) 10\(^{-23}\) cm\(^3\).
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For FCC: Volume of one atom $= \frac{0.74 \times V_{cell}}{4}$.
Updated On: Apr 26, 2026
- 5.44 \(\times\) 10\(^{-24}\) cm\(^3\)
- 2.96 \(\times\) 10\(^{-24}\) cm\(^3\)
- 8.37 \(\times\) 10\(^{-24}\) cm\(^3\)
- 6.15 \(\times\) 10\(^{-24}\) cm\(^3\)
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The Correct Option is B
Solution and Explanation
Step 1: Concept
Packing efficiency of FCC $= 74% = 0.74$.
Total volume of all particles in unit cell $= 0.74 \times \text{Volume of unit cell}$.
Step 2: Total particle volume
Total Volume $= 0.74 \times 1.6 \times 10^{-23} = 1.184 \times 10^{-23} \text{ cm}^3$.
Step 3: Volume of one particle
In FCC, number of atoms per unit cell $(Z) = 4$.
Volume of one particle $= \frac{1.184 \times 10^{-23}}{4} = 0.296 \times 10^{-23} = 2.96 \times 10^{-24} \text{ cm}^3$.
Final Answer: (B)
Packing efficiency of FCC $= 74% = 0.74$.
Total volume of all particles in unit cell $= 0.74 \times \text{Volume of unit cell}$.
Step 2: Total particle volume
Total Volume $= 0.74 \times 1.6 \times 10^{-23} = 1.184 \times 10^{-23} \text{ cm}^3$.
Step 3: Volume of one particle
In FCC, number of atoms per unit cell $(Z) = 4$.
Volume of one particle $= \frac{1.184 \times 10^{-23}}{4} = 0.296 \times 10^{-23} = 2.96 \times 10^{-24} \text{ cm}^3$.
Final Answer: (B)
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