Question

Calculate the number of unit cell in \(1 \text{ cm}^3\) volume of metal if volume of unit cell is \(3.448 \times 10^{-23} \text{ cm}^3\)

• A. \(2.5 \times 10^{22}\)
• B. \(3.2 \times 10^{22}\)
• C. \(2.9 \times 10^{22}\)
• D. \(3.7 \times 10^{22}\)

Hint:

Whenever total volume and unit cell volume are given, just divide: \[ \frac{\text{Total volume}}{\text{Unit cell volume}} \] to get the number of unit cells.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The number of unit cells in a given volume of a crystal is found by dividing the total volume by the volume occupied by a single unit cell.
Step 2: Key Formula or Approach:
\[ \text{Number of unit cells} = \frac{\text{Total Volume}}{\text{Volume of one unit cell}} \] Step 3: Detailed Explanation:
Given:
Total Volume = \(1 \text{ cm}^3\)
Volume of one unit cell = \(3.448 \times 10^{-23} \text{ cm}^3\)
Calculation:
\[ \text{Number of unit cells} = \frac{1}{3.448 \times 10^{-23}} \] \[ \text{Number of unit cells} \approx 0.290 \times 10^{23} \] \[ \text{Number of unit cells} = 2.9 \times 10^{22} \] Step 4: Final Answer:
The number of unit cells is \(2.9 \times 10^{22}\).