If the resistivity of copper is 1.7 ×10^-0 Ωcm, then the mobility of electrons in copper, if eac

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If the resistivity of copper is 1.7 ×10^-0 Ωcm, then the...

If the resistivity of copper is $1.7 \times 10^{-0} \Omega \mathrm{cm}$, then the mobility of electrons in copper, if each atom of copper contributes one free electron for conduction, is [The atomic weight of copper is $63.54$ and its density is $8.96 \mathrm{~g} / \mathrm{cc}]:$ (a) $23.36 \mathrm{~cm}^{2} / \mathrm{Vs}$ (b) $503.03 \mathrm{~cm}^{2} / \mathrm{Vs}$ (c) $43.25 \mathrm{~cm}^{2} / \mathrm{Vs}$ (d) $88.0 \mathrm{~cm}^{2} / \mathrm{Vs}$

If the resistivity of copper is $1.7 \times 10^{-0} \Omega \mathrm{cm}$, then the mobility of electrons in copper, if each atom of copper contributes one free electron for conduction, is [The atomic weight of copper is $63.54$ and its density is $8.96 \mathrm{~g} / \mathrm{cc}]:$
(a) $23.36 \mathrm{~cm}^{2} / \mathrm{Vs}$
(b) $503.03 \mathrm{~cm}^{2} / \mathrm{Vs}$
(c) $43.25 \mathrm{~cm}^{2} / \mathrm{Vs}$
(d) $88.0 \mathrm{~cm}^{2} / \mathrm{Vs}$

Key Concepts

Atomic Density Calculation

Atomic density is determined by using the material’s mass density and its molar mass, along with Avogadro's number. For metals where each atom contributes a conduction electron, this calculation is essential for finding the number density of electrons, which, in turn, is a key component in determining conductivity and electron mobility.

Conductivity Relation

The conductivity relation, given by ? = n e ?, connects the macroscopic electrical conductivity of a material to microscopic properties: n (the charge carrier density), e (the elementary charge), and ? (the mobility of the charge carriers). Since resistivity is the inverse of conductivity, this relation is central in linking measurable electrical properties with material parameters.

Electron Mobility

Electron mobility represents how quickly an electron can move through a conductor when subjected to an electric field. It is defined as the drift velocity per unit electric field and is influenced by factors such as scattering events, defects, and phonon interactions. Higher mobility indicates that electrons can accelerate more easily, contributing to efficient electrical conduction.

Resistivity

Resistivity is a fundamental property of materials that quantifies how strongly a given material opposes the flow of electric current. In conductors, lower resistivity means electrons can move more freely. In calculations, resistivity is inversely related to conductivity, which is useful when relating electrical conduction to the material's microscopic properties.

Free Electron Model

The free electron model is an idealized description of conduction in metals, where conduction electrons are considered to move freely within a constant potential created by the ion cores. This model simplifies the behavior of electrons in a metal and forms the basis for deriving key properties, such as the relation connecting conductivity, electron density, and electron mobility.

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