Failures of Classical Free Electron Theory

Provide an example of metals that show discrepancy between theoretical predictions and experimental observations regarding electrical conductivity and electron concentration.

• Aluminum (Al) has a higher electron concentration than copper (Cu), but its electrical conductivity is lower.

• Copper (Cu) has a higher electrical conductivity than aluminum (Al) and similar electron concentration.

• Gold (Au) shows higher electrical conductivity than silver (Ag) despite lower electron concentration.

• Iron (Fe) has a lower electron concentration than nickel (Ni) but higher electrical conductivity.

What is the significance of the findings regarding the failures of classical free electron theory?

• They confirm that classical free electron theory is entirely accurate.

• They highlight the discrepancies between theoretical predictions and experimental observations, leading to the conclusion that classical free electron theory fails to accurately describe the behavior of metals.

• They suggest that classical free electron theory is the only valid theory for metals.

• They indicate that classical free electron theory is only applicable at very high temperatures.

What does the experimental data show about the relationship between electrical conductivity (σ) and electron concentration (n)?

• There is a direct relationship between electrical conductivity (σ) and electron concentration (n).

• There is no direct relationship between electrical conductivity (σ) and electron concentration (n).

• Electrical conductivity (σ) increases with decreasing electron concentration (n).

• Electrical conductivity (σ) is independent of electron concentration (n).

How is electrical conductivity (σ) expressed in terms of electron concentration (n) according to classical free electron theory?

• σ = ne²τ/m, where 'n' is the electron concentration.

• σ = n²eτ/m, where 'n' is the electron concentration.

• σ = neτ/m², where 'n' is the electron concentration.

• σ = ne²/mτ, where 'n' is the electron concentration.

What is the relationship between electrical conductivity (σ) and temperature (T) according to classical free electron theory?

• σ is proportional to T

• σ is proportional to 1/T

• σ is proportional to 1/√T

• σ is independent of T

What is the experimentally observed relationship between electrical conductivity (σ) and temperature (T)?

• σ is directly proportional to temperature T (σ ∝ T)

• σ is inversely proportional to temperature T (σ ∝ 1/T)

• σ is independent of temperature T (σ ∝ constant)

• σ increases with increasing temperature T (σ ∝ T^2)

What does the discrepancy between equations (1) and (2) indicate about classical free electron theory?

• It shows that classical free electron theory is completely accurate.

• It indicates that classical free electron theory does not agree with experimental observations, leading to its failure.

• It suggests that classical free electron theory is only applicable at low temperatures.

• It proves that classical free electron theory is the only valid theory for electron behavior.

What are the electron concentrations and conductivities for Copper (Cu) and Aluminum (Al)?

• Copper (Cu): Electron concentration = 8.45 x 10²⁸ m⁻³, Conductivity = 5.88 x 10⁷ Ωm⁻; Aluminum (Al): Electron concentration = 18.06 x 10²⁸ m⁻³, Conductivity = 3.65 x 10⁷ Ωm⁻.

• Copper (Cu): Electron concentration = 9.00 x 10²⁸ m⁻³, Conductivity = 6.00 x 10⁷ Ωm⁻; Aluminum (Al): Electron concentration = 15.00 x 10²⁸ m⁻³, Conductivity = 4.00 x 10⁷ Ωm⁻.

• Copper (Cu): Electron concentration = 7.50 x 10²⁸ m⁻³, Conductivity = 5.00 x 10⁷ Ωm⁻; Aluminum (Al): Electron concentration = 20.00 x 10²⁸ m⁻³, Conductivity = 3.00 x 10⁷ Ωm⁻.

• Copper (Cu): Electron concentration = 8.00 x 10²⁸ m⁻³, Conductivity = 5.50 x 10⁷ Ωm⁻; Aluminum (Al): Electron concentration = 17.00 x 10²⁸ m⁻³, Conductivity = 3.80 x 10⁷ Ωm⁻.