JEE Main · 2022 · 28 Jul 2022 · Shift 2 · Solid State

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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)

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

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