Question

Calculate the number of atoms present per unit cell if product of density and volume of unit cell is \(1.8 \times 10^{-22} \mathrm{~g}\).

[Mass of an atom \(=4.5 \times 10^{-23} \mathrm{~g}\) ]

• A. 1
• B. 2
• C. 4
• D. 6

Hint:

Density times unit cell volume gives the mass of one unit cell. Divide it by the mass of one atom.

Answer 1

The Correct Option is C

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

Step 2: Calculation
\(Z=\dfrac{\rho a^3}{\text{mass of one atom}}=\dfrac{1.8\times 10^{-22}}{4.5\times 10^{-23}}\)

Step 3: Result
\(Z=\dfrac{18}{4.5}=4\)

Step 4: Compare the options
A value of 4 atoms per unit cell matches the third option (face-centred cubic).

Final Answer:
The unit cell contains 4 atoms. \[ \boxed{\text{(C) }4} \]