Question

Al (at. wt. 27) crystallizes in the cubic system with a cell edge of 4.05AA. Its density is 2.7g cm⁻3. Determine the atom unit cell type and calculate the radius of the Al atom.

• A. fcc, 2.432AA
• B. bcc, 2.432AA
• C. bcc, 1.432AA
• D. fcc, 1.432AA

Hint:

Common metals like Al, Cu crystallize in fcc structure.

Answer 1

The Correct Option is D

Step 1: Density relation: ρ=(ZM)/(NAa³) Substituting values gives Z=4⟹ fcc lattice.
Step 2: For fcc: 4r=√(2)a ⟹ r=frac√(2)4a
Step 3: r=frac√(2)4×4.05≈1.43AA