Question

What is the number of atoms present per unit cell of aluminium having edge length \(4~\text{\AA}\)? (Given: Density of Al = \(2.7~\text{g cm}^{-3}\), Atomic mass of Al = 27)

• A. 8
• B. 1
• C. 2
• D. 4

Hint:

FCC unit cells always contain 4 atoms per unit cell.

Answer 1

The Correct Option is D

Step 1: Use density formula for unit cell.
\[ \rho = \frac{Z \times M}{a^3 \times N_A} \] Step 2: Substitute given values.
\[ 2.7 = \frac{Z \times 27}{(4 \times 10^{-8})^3 \times 6.022 \times 10^{23}} \] Step 3: Solve for \(Z\).
On solving, we get: \[ Z = 4 \] Step 4: Conclusion.
Thus, aluminium unit cell contains 4 atoms, confirming FCC structure.