Final answer:
The number density of copper is calculated by dividing the mass density by the molar mass to find the number of moles per cubic meter, which is then multiplied by Avogadro's number, resulting in a number density of 8.49 × 10²¸ atoms/m³.
Step-by-step explanation:
To determine the number density of copper, we utilize the mass density given (8.96 g/cm³, which can be converted to 8960 kg/m³), the atomic mass of copper (63.54 g/mol), and Avogadro's number (6.02 × 10²³ atoms/mol). The number density, n, represents the number of copper atoms per unit volume.
Firstly, we calculate the number of moles in one cubic meter of copper:
Number of moles = mass density / molar mass = 8960 kg/m³ / (63.54 g/mol × 1 kg/1000 g) = 141 moles/m³
Then, we calculate the number density by multiplying the number of moles by Avogadro's number:
Number density n = Number of moles × Avogadro's number = 141 moles/m³ × 6.02 × 10²³ atoms/mol
After calculating, we get:
Number density n = 8.49 × 10²¸ atoms/m³