The radius of an atom of gold (Au) is about 1.35 A. a) how many gold atoms would

Question

The radius of an atom of gold (Au) is about 1.35 A. a) how many gold atoms would have to be lined up to span 2.5 mm? b) If the atom is assumed to be a sphere, what is the volume in cm^3 of a single Au atom? The radius of an atom of gold (Au) is about 1.35 A. a) how many gold atoms would have to be lined up to span 2.5 mm? b) If the atom is assumed to be a sphere, what is the volume in cm^3 of a single Au atom? The radius of an atom of gold (Au) is about 1.35 A. a) how many gold atoms would have to be lined up to span 2.5 mm? b) If the atom is assumed to be a sphere, what is the volume in cm^3 of a single Au atom?

Explanation / Answer

a)
diameter = 2*r = 2*1.35 = 2.70 A
distance = 2.5 mm = 2.5*10^7 A

use:
number of Atom = distance / diameter
= (2.5*10^7)/(2.70)
= 9.3*10^6

Answer: 2.70

b)
r = 1.35 A = 1.35*10^-8 cm

use:
V = (4/3)*pi*r^3
= (4/3)*pi*(1.35*10^-8 cm)^3
= 1.03*10^-23 cm^3
Answer: 1.03*10^-23 cm^3

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