How to Calculate the Mobility of Electrons in Copper (Cu)?

To calculate the mobility of electrons in copper, we can use the formula:

• σ = n * e * μ

Where:

• σ is the conductivity (5.9 x 10^-5 Ω^-1 m^-1),
• n is the charge carrier concentration (number of electrons per unit volume),
• e is the charge of an electron (approximately 1.6 x 10^-19 C),
• μ is the mobility of the charge carriers.

To find n, we first need to calculate the number of atoms in a cubic meter of copper. We can use the density and atomic mass of copper:

• Density of Cu = 8.96 g/cm³, which is equal to 8960 kg/m³,
• Atomic mass of Cu = 63.5 g/mol, which is equal to 0.0635 kg/mol.

Using Avogadro’s number (approximately 6.022 x 10²³ atoms/mol), the number of atoms per cubic meter can be calculated:

• n = (density of Cu) / (atomic mass of Cu) * Avogadro’s number

Calculating n:

n = (8960 kg/m³) / (0.0635 kg/mol) * (6.022 x 10²³ atoms/mol)
≈ 8.49 x 10²⁸ electrons/m³

Now we can rearrange the conductivity equation to solve for mobility (μ):

• μ = σ / (n * e)

Substituting the known values:
σ = 5.9 x 10⁵ Ω^-1 m^-1
n ≈ 8.49 x 10²⁸ electrons/m³
e ≈ 1.6 x 10^-19 C

Now plug in the values:

• μ = (5.9 x 10⁵) / (8.49 x 10²⁸ * 1.6 x 10^-19)

Calculating this gives:

μ ≈ 4.39 x 10^-3 m²(V.s)^-1

So, the mobility of electrons in copper is approximately 4.39 x 10^-3 m²(V.s)^-1.