Given: mass number of gold = 197, density of gold = 19.7g cm-3, Avogadro’s number = 6 × 10^23. The radius of the gold atom is approximately:

Q. Given: mass number of gold = 197, density of gold = 19.7g cm-3, Avogadro’s number = 6 × 1023. The radius of the gold atom is approximately:

(a) 1.5 × 10-8 m

(b) 1.5 × 10-9 m

(c) 1.5 × 10-10 m

(d) 1.5 × 10-12 m

Ans: (c)

Sol: Density , ρ = Mass/Volume

Volume V = mass/ρ = 197/19.7 = 10cm3
Volume of one atom = 10/6.023×1023 = (5/3) × 10-23 cm3

If R be the radius of atom then,

(4/3)πR3 = (5/3) ×10-23

R3 = (5/4π)× 10-23

R = 1.5×10-10  m

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