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* 10^(-3)\, (kg)/(cm^(3)) )*(10^(2)\, (cm)/(m))^(3) \\ = 2.4142 * 10^(-25) \, kg`

Calculate the number of atoms in a sample of mass 1.40 g.

`N = (1.40 \time 10^(-3) kg)/(2.4142 * 10^(-25) \, (kg)/(atom) ) =5.8 * 10^(21) \, atoms`

Answer: 5.8 x 10²¹ atoms