Question

The mass of an atom present in unit cell is \(4.4 \times 10^{-23} \mathrm{~g}\) and the product of density and volume of unit cell is \(1.792 \times 10^{-22} \mathrm{~g}\). What is the type of cubic unit cell?

• A. Body centred unit cell
• B. Face centred unit cell
• C. Base centred unit cell
• D. Simple cubic unit cell

Hint:

The mass of the unit cell equals density times volume, and it equals the number of atoms Z times the mass of one atom.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Mass of a unit cell \(=\rho\times a^3=Z\times m\), where Z is the number of atoms per unit cell and m is the mass of one atom.

Step 2: Given Data
\(m=4.4\times10^{-23}\text{ g}\) and \(\rho a^3=1.792\times10^{-22}\text{ g}\).

Step 3: Calculation
\(Z=\dfrac{1.792\times10^{-22}}{4.4\times10^{-23}}=4.07\approx4\)

Step 4: Identify the Cell
Z = 4 corresponds to a face centred cubic unit cell.

Final Answer:
The unit cell is face centred cubic. \[ \boxed{\text{(B) }\text{Face centred unit cell}} \]