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

Concept:
Number of unit cells present in a given volume is calculated by: \[ \text{Number of unit cells}=\frac{\text{Total volume}}{\text{Volume of one unit cell}} \] ip

Step 1: Write the given values.
\[ V_{\text{total}}=1\ \text{cm}^3 \] \[ V_{\text{cell}}=3.448\times10^{-23}\ \text{cm}^3 \] ip

Step 2: Apply the formula.
\[ N=\frac{1}{3.448\times10^{-23}} \] ip

Step 3: Calculate the value.
\[ N \approx 2.9\times10^{22} \] ip Hence, the correct answer is:
\[ \boxed{(C)\ 2.9\times10^{22}} \]