Question

Calculate the number of atoms present in 1 g of an element if it forms fcc unit cell structure. [$\rho \times \text{a}^3 = 6.8 \times 10^{-22} \text{ g}$]}

• A. $7.125 \times 10^{21}$
• B. $4.548 \times 10^{21}$
• C. $6.815 \times 10^{21}$
• D. $5.882 \times 10^{21}$

Hint:

Number of atoms in $m$ grams $= \frac{Z \times m}{\rho \times a^3}$.

Answer 1

The Correct Option is D

Step 1: Identify Given
Mass of unit cell $= \rho \times a^3 = 6.8 \times 10^{-22} \text{ g}$.
Number of atoms in FCC unit cell ($Z$) $= 4$.
Step 2: Calculate Number of Unit Cells
Number of unit cells in 1 g $= \frac{1}{\text{Mass of one unit cell}}$
Number of unit cells $= \frac{1}{6.8 \times 10^{-22}}$
Step 3: Calculate Number of Atoms
Total atoms $= \text{Number of unit cells} \times Z$
Total atoms $= \frac{1}{6.8 \times 10^{-22}} \times 4$
Total atoms $= \frac{4}{6.8} \times 10^{22} \approx 0.5882 \times 10^{22} = 5.882 \times 10^{21}$.
Final Answer: (D)