A metal crystallises in a bcc lattice. Its unit cell edge length is about 300 pm and its molar mass is about 50 g mol-1. What would be the density of the metal (in g cm-3)?

Question

A metal crystallises in a bcc lattice. Its unit cell edge length is about 300 pm and its molar mass is about 50 g mol-1. What would be the density of the metal (in g cm-3)? (A) 3.1 (B) 6.2 (C) 9.3 (D) 12.4

Tardigrade Admin · Accepted Answer

a = 300 pm, Z = 2 (for bcc unit cell) M = 50 g mol-1 Density, ρ = (Z× M/NA × a3× 10-30) g cm-3 = (2× 50/NA× 1023× (300)3× 10-30) =(100/6.02× 27× 10-1) = (1000/6.02× 27) = 6.15 g cm-3 ≈ 6.2 g cm-3

Q. A metal crystallises in a bcc lattice. Its unit cell edge length is about 300 pm and its molar mass is about 50gmol−1. What would be the density of the metal (in gcm−3)?

3.1

6.2

9.3

12.4

a=300pm,Z=2 (for bcc unit cell) M=50gmol−1 Density, ρ=NA​×a3×10−30Z×M​gcm−3 =NA​×1023×(300)3×10−302×50​=6.02×27×10−1100​ =6.02×271000​=6.15gcm−3≈6.2gcm−3

Q. A metal crystallises in a bcc lattice. Its unit cell edge length is about 300 pm and its molar mass is about $50 g m o l^{- 1}$ . What would be the density of the metal (in $g c m^{- 3}$ )?