Q13 / 150 · MHT CET 2026 (20 April Shift 2) · Chemistry
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 $7.2\ \text{g cm}^{-3}$.
- Correct answerA$1.0 \times 10^{23}$
- B$2.0 \times 10^{23}$
- C$0.5 \times 10^{23}$
- D$1.5 \times 10^{23}$
Solution
Total volume of the metal is given by the ratio of mass to density.
$V_{\text{total}} = \dfrac{\text{Mass}}{\text{Density}} = \dfrac{18}{7.2} = 2.5\ \text{cm}^3$
The number of unit cells is the total volume divided by the volume of one unit cell.
$\text{Number of unit cells} = \dfrac{V_{\text{total}}}{V_{\text{unit cell}}} = \dfrac{2.5}{2.5 \times 10^{-23}} = 1.0 \times 10^{23}$
Answer: $1.0 \times 10^{23}$
$V_{\text{total}} = \dfrac{\text{Mass}}{\text{Density}} = \dfrac{18}{7.2} = 2.5\ \text{cm}^3$
The number of unit cells is the total volume divided by the volume of one unit cell.
$\text{Number of unit cells} = \dfrac{V_{\text{total}}}{V_{\text{unit cell}}} = \dfrac{2.5}{2.5 \times 10^{-23}} = 1.0 \times 10^{23}$
Answer: $1.0 \times 10^{23}$
Hence, the correct answer is option: 'A'.