Question

A metal crystallizes in a bcc unit cell having unit cell volume \(2.5\times 10^{-23} \text{cm}^3\). Find the number of unit cells in 18 g metal if the density of metal is \(7.2 \text{g cm}^{-3}\).

• A. \(1.0\times 10^{23}\)
• B. \(2.0\times 10^{23}\)
• C. \(0.5\times 10^{23}\)
• D. \(1.5\times 10^{23}\)

Hint:

Find the volume of the sample from the density, then divide by the volume of one unit cell.

Answer 1

The Correct Option is A

Step 1: Approach
Work with proportions between the volume of the sample and the volume of one cell.

Step 2: Sample volume
From $\rho=\dfrac{m}{V}$, we get $V = 18/7.2 = 2.5$ cm$^3$.

Step 3: Cell count
One cell is $2.5\times10^{-23}$ cm$^3$. The count is
\[ \frac{2.5}{2.5\times10^{-23}} = 10^{23} \]

Step 4: Note on the trap
Option (B) gives $2\times10^{23}$, which is the number of atoms (2 per bcc cell), not of unit cells. The question asks for unit cells, so the answer is (A).

Final Answer:
The sample contains $1.0\times10^{23}$ unit cells, option (A). \[ \boxed{1.0\times10^{23}} \]