Final answer:
The density of mobile electrons in copper is calculated by dividing the density of copper by its atomic mass and then multiplying by Avogadro's number; this represents the number of free electrons per cubic meter.
Step-by-step explanation:
The density of mobile electrons in copper metal can be calculated using known values such as the density of copper (8.95 g/cm³), the atomic mass of copper (63.54 g/mol), and Avogadro's number (6.02 × 10²³ atoms/mol). Since copper contributes one free electron per atom, the density of mobile electrons equals the number of copper atoms per cubic meter. Using the density of copper, atomic mass, and Avogadro's number, we can calculate the number of atoms per cubic meter, which gives us the density of mobile electrons.
We calculate this by first converting the density of copper to kg/m³ (8.95 g/cm³ equals 8.95 × 10³ kg/m³) and then using this formula:
n = (density of copper / atomic mass of copper) × Avogadro's number
Here, n is the number of free electrons per cubic meter in copper.