A quantity of 1.9 × 10⁻⁴ g of the metal having density 19 g/ml is dispersed in 1 l of water to give a sol having spherical metal particles of radius 10 nm. The approximate number of metal sol particle

Question

A quantity of 1.9 × 10⁻⁴ g of the metal having density 19 g/ml is dispersed in 1 l of water to give a sol having spherical metal particles of radius 10 nm. The approximate number of metal sol particles per cm³ of the sol is

Prashant Kotian · Accepted Answer

Correct answer: A. Volume of total metal = Mass/Density = 1.9 × 10⁻⁴ g / 19 g/cm³ = 10⁻⁵ cm³. Volume of one particle = (4/3)πr³ = (4/3) × 3.14 × (10 × 10⁻⁷ cm)³ ≈ 4.187 × 10⁻¹⁸ cm³. Total particles in 1 L = (10⁻⁵) / (4.187 × 10⁻¹⁸) ≈ 2.388 × 10¹² particles. Number of particles per cm³ (per mL) = 2.388 × 10¹² / 1000 ≈ 2.35 × 10⁹. Therefore, correct answer is A.

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