Find the mobility (in cm2/volt-sec) of e- in copper assuming that each atom contributes one free e^- for conduction.
Resistivity of copper is 2.7 x 10^-6 ohm-cm.
Atomic weight of copper is 63.54.
Density of copper = 8.96 gm/cm³
Avogadro's number = 6.025 x 10²³
Electronic charge = 1.6 x 10^-19 coulomb.
Correct answer is '27.25'. Can you explain this answer?

Question

Find the mobility (in cm2/volt-sec) of e- in copper assuming that each atom contributes one free e^- for conduction.
Resistivity of copper is 2.7 x 10^-6 ohm-cm.
Atomic weight of copper is 63.54.
Density of copper = 8.96 gm/cm³
Avogadro's number = 6.025 x 10²³
Electronic charge = 1.6 x 10^-19 coulomb.

Correct answer is '27.25'. Can you explain this answer?

Answer

Answer

Given:
Resistivity of copper (ρ) = 2.7 x 10^-6 ohm-cm
Atomic weight of copper (A) = 63.54
Density of copper (ρ) = 8.96 gm/cm^3
Avogadro's number (N) = 6.025 x 10^23
Electronic charge (e) = 1.6 x 10^-19 coulomb

Formula:
The mobility (μ) of a charge carrier is given by the equation:
μ = σ / (n * e)
where σ is the electrical conductivity, n is the charge carrier concentration, and e is the electronic charge.

Solution:
Step 1: Calculate the charge carrier concentration (n):
The charge carrier concentration (n) can be calculated using the formula:
n = N * (ρ / A) * (1 / ρ)
where N is Avogadro's number, ρ is the density, and A is the atomic weight.

Substituting the given values into the formula:
n = (6.025 x 10^23) * (8.96 gm/cm^3) * (1 cm^3 / 63.54 gm)
n = 8.493 x 10^22 cm^-3

Step 2: Calculate the electrical conductivity (σ):
The electrical conductivity (σ) can be calculated using the formula:
σ = 1 / ρ
where ρ is the resistivity.

Substituting the given value into the formula:
σ = 1 / (2.7 x 10^-6 ohm-cm)
σ = 3.703 x 10^5 (ohm-cm)^-1

Step 3: Calculate the mobility (μ):
The mobility (μ) can be calculated using the formula:
μ = σ / (n * e)
where σ is the electrical conductivity, n is the charge carrier concentration, and e is the electronic charge.

Substituting the calculated values into the formula:
μ = (3.703 x 10^5 (ohm-cm)^-1) / ((8.493 x 10^22 cm^-3) * (1.6 x 10^-19 coulomb))
μ ≈ 27.25 cm^2/V-sec

Therefore, the mobility of electrons in copper is approximately 27.25 cm^2/V-sec.

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