Question

Calculate the number of unit cells present in 0.6 g metal if the product of density and unit cell volume is \(3.6 \times 10^{-22} \mathrm{~g}\).

• A. \(1.666\times 10^{21}\)
• B. \(3.333\times 10^{21}\)
• C. \(2.499\times 10^{21}\)
• D. \(4.833\times 10^{21}\)

Hint:

Density times unit cell volume equals the mass of one unit cell.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
Density \(=\dfrac{\text{mass of unit cell}}{\text{volume of unit cell}}\), so density \(\times\) volume \(=\) mass of one unit cell.

Step 2: Mass of One Unit Cell
Mass of one unit cell \(=3.6\times10^{-22}\ \text{g}\).

Step 3: Calculation
Number of unit cells \(=\dfrac{0.6}{3.6\times10^{-22}}=1.666\times10^{21}\).

Step 4: Compare the options
Option (A).

Final Answer:
There are \(1.666\times10^{21}\) unit cells. \[ \boxed{\text{(A) }1.666\times 10^{21}} \]