Metal M crystallizes into a FCC lattice with the edge length of 4.0 × 10⁻⁸ cm. The atomic mass of the metal is _____ g/mol. (Nearest integer).
(Use: Nₐ = 6.02 × 10²³ mol⁻¹, density of metal, M = 9.03 g cm⁻³)
(Use: Nₐ = 6.02 × 10²³ mol⁻¹, density of metal, M = 9.03 g cm⁻³)
Answer: 87
Solution
For FCC lattice, Z = 4. Using the density formula: d = (Z × M)/(Nₐ × a³), where a = 4.0 × 10⁻⁸ cm. Rearranging: M = (d × Nₐ × a³)/Z = (9.03 × 6.02 × 10²³ × (4.0 × 10⁻⁸)³)/4 = (9.03 × 6.02 × 10²³ × 64 × 10⁻²⁴)/4 ≈ 87 g/mol.
JEE Main · 2022 · 28 Jul 2022 · Shift 2 · Integer answer