The mass number of atom of gold is 197 and the density is 19.7 gm per cm³.The radius of the gold is approximately (given that N = 6*10²³)
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atomic mass of gold is 197 amu. it means, mass of one mole of gold is 197g.
given, density of gold is 19.7g/cm³
so, volume of one mole of gold atom = 197g/19.7g/cm³ = 10cm³
here it is given that Avogadro's number is 6 × 10²³
so, volume of one mole of gold atom = volume of 6 × 10²³ atoms of gold. = 10 cm³
or, volume of each gold atom = (10/6) × 10^-23 cm³ = (5/3) × 10^-23 cm³
if we assume atom is spherical, then volume of each gold atom , V = 4/3 πr³ , where r is radius of gold atom.
so, 4/3πr³ = (5/3) × 10^-23 cm³
or, r³ = (50/4π) × 10^-24 cm³
or, r³ = 3.98 × 10^-24 cm³
or, r = × 10^-8 cm
or, r ≈ 1.5847 × 10^-8 cm = 1.5847 × 10^-10 m = 1.5847 A°
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