Question

The atomic radius of a gold atom is 144×10^-12. The volume of a gold atom can be calculated using the volume of a sphere. The density of gold is 19.3 g/cm^3. How many atoms are present in a sample of gold with a mass of 1.40g using the info provided

Answer 1

Given:
Atomic radius of gold = 144 x 10⁻¹² m = 144 pm 
Density of gold = 19.3 g/cm³ = 19.3 x 10⁻³ kg/cm³
Mass of gold sample = 1.40 g = 1.4 x 10⁻³ kg

Calculate the volume of an atom. 
v = [(4π)/3]*(144 x 10⁻¹² m)³ = 1.2508 x 10⁻²⁹ m³

Calculate the mass of an atom.
$m=(1.2508\tmes10^{-29}\,m^{3})*(19.3\times 10^{-3}\, \frac{kg}{cm^{3}} )*(10^{2}\, \frac{cm}{m})^{3} \\ = 2.4142 \times 10^{-25} \, kg$

Calculate the number of atoms in a sample of mass 1.40 g.
$N = \frac{1.40 \time 10^{-3} kg}{2.4142 \times 10^{-25} \, \frac{kg}{atom} } =5.8 \times 10^{21} \, atoms$

Answer:  5.8 x 10²¹ atoms