Q. A metal has a fcc lattice. The edge length of the unit cell is 404 pm. The density of the metal is 2.72 g cm⁻³. The molar mass of the metal is (NA = Avogadro's constant = 6.02 × 10²³ mol⁻¹)
A) 40 g mol⁻¹
B) 30 g mol⁻¹
C) 27 g mol⁻¹
D) 20 g mol⁻¹
Explanation
[Solution from source] M = ρa³Nₐ/Z with Z = 4 for fcc, a = 404 pm = 4.04 × 10⁻⁸ cm: a³ = 6.594 × 10⁻²³ cm³. M = 2.72 × 6.594 × 10⁻²³ × 6.02 × 10²³/4 ≈ 27.0 g mol⁻¹ (aluminium). Answer (3).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.