A metal crystallizes in such a lattice in which only 70% of the total space of the crystal is occupied by the atoms. If the atomic mass of the metal is 32 π g/mol and the atomic radius is 0.2 nm, the

Question

A metal crystallizes in such a lattice in which only 70% of the total space of the crystal is occupied by the atoms. If the atomic mass of the metal is 32 π g/mol and the atomic radius is 0.2 nm, the density of the metal is

Prashant Kotian · Accepted Answer

Correct answer: B. Packing efficiency = Z × (4/3 × π × r³) / V_cell = 0.70 => Z / V_cell = 2.1 / (4 × π × r³). Density ρ = (Z × M) / (Na × V_cell) = (2.1 / (4 × π × r³)) × (M / Na). Substituting M = 32 × π, r = 0.2 nm = 2 × 10^-8 cm, and Na = 6 × 10^23 gives ρ = (2.1 × 32 × π) / (4 × π × 8 × 10^-24 × 6 × 10^23) = 67.2 / 19.2 = 3.5 g/cm³.

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