Calculation of Free Electrons per Unit Volume

To calculate the number of free electrons per unit volume of a metallic wire, we need to consider the following formula:

n = N * Z * ρ / A

where n is the number of free electrons per unit volume, N is the Avogadro number, Z is the number of valence electrons per atom, ρ is the density of the metal, and A is the atomic mass number.

Given Data

Density of the metallic wire, ρ = 10^4 kg/m^3
Atomic mass number, A = 100
Number of free electrons per atom, Z = 1

Calculation

We can substitute the given data in the above formula to get the number of free electrons per unit volume:

n = (6.022 * 10^23) * (1) * (10^4) / (100)

n = 6.022 * 10^21 electrons/m^3

Therefore, the number of free electrons per unit volume of the metallic wire is 6.022 * 10^21 electrons/m^3.

Explanation

The given data provides the density of the metallic wire, which is used to calculate the number of atoms per unit volume. The atomic mass number is used to calculate the mass of one atom. The number of free electrons per atom is also given, which is used to calculate the total number of free electrons per unit volume.

The formula used in the calculation takes into account all these factors and provides the number of free electrons per unit volume of the metallic wire. This value is important in understanding the electrical conductivity of the metallic wire, as the free electrons are responsible for carrying the electrical charge through the wire.

Overall, this calculation provides a basic understanding of the properties of metallic wires and the factors that affect their electrical conductivity.