Question

Calculate the number of unit cells in 0.79 g metal if product of density and volume of unit cell is 1.58 $\times$ 10$^{-22}$ g.

• A. 3.96 $\times$ 10$^{21}$
• B. 1.72 $\times$ 10$^{21}$
• C. 4.46 $\times$ 10$^{21}$
• D. 5.0 $\times$ 10$^{21}$

Hint:

The mass of a unit cell is the product of its density and its volume.

Answer 1

The Correct Option is D

Step 1: Concept
Mass of one unit cell = Density ($\rho$) $\times$ Volume of unit cell ($V$).
Given $\rho \times V = 1.58 \times 10^{-22}$ g.
Step 2: Formula
Number of unit cells = $\frac{\text{Total Mass}}{\text{Mass of one unit cell}}$.
Step 3: Calculation
$N = \frac{0.79}{1.58 \times 10^{-22}} = 0.5 \times 10^{22} = 5.0 \times 10^{21}$.
Step 4: Conclusion
The number of unit cells is 5.0 $\times$ 10$^{21}$.
Final Answer:(D)