Can you help me with the following by any chance?

The radius of an atom of gold(Au) is about 1.35 angstroms.

a)Express the distance in nanometers and in picometers

b)How many gold atoms would have to be lined up to span 1.0mm?

c)If the atom is assumed to be a sphere, what is the volume in cm^3 of a single Au atom?

### 1 Answer

(a) 1.35 angstrom x (1 nanometer / 10 angstrom) = 0.135 nanometers

1.35 anstrom x ( 100 picometers / 1 angstrom) = 135 picometers

(b) diameter = 2 x 1.35 = 2.70 angstrom

Number of gold atoms in 1mm = (1mm / 2.7 angstrom) x ( 10^7 angstrom / 1 mm) = 3703703

(c) Volume of 1 gold atom = 4/3 πr³

= 4/3 π (1.35 angstrom)³ x ( 10^-8 cm / 1 angstrom)³ = 1.03 x 10^-23 cm³