A Hall effect experiment uses a silver bar 3.50 μm thick. When the bar carries a current of 1.42

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A Hall effect experiment uses a silver bar 3.50 μm thick....

A Hall effect experiment uses a silver bar $3.50 \mu \mathrm{m}$ thick. When the bar carries a current of $1.42 \mathrm{~A},$ a perpendicular magnetic field of $0.155 \mathrm{~T}$ results in a Hall potential difference of $6.70 \mu \mathrm{V}$. (a) Use these data to determine the density of conduction electrons in silver. (b) How many conduction electrons are there per atom of silver? [Note: The density of silver is $\left.10,490 \mathrm{~kg} / \mathrm{m}^{3} .\right]$

Key Concepts

Hall Effect

The Hall effect is a phenomenon observed in current?carrying conductors or semiconductors when they are placed in a magnetic field perpendicular to the current flow. Under these conditions, the magnetic Lorentz force deflects the moving charge carriers to one side of the material, resulting in a transverse voltage (the Hall voltage) across the conductor. This effect is crucial in determining properties such as the type (negative electrons or positive holes) and density of charge carriers in the material.

Conduction Electron Density

Conduction electron density refers to the number of free electrons per unit volume in a conducting material. The Hall effect provides a method to measure this density by relating the observed Hall voltage, the applied magnetic field, and the current through the material. Knowledge of the conduction electron density is essential for understanding a material's electrical conductivity and overall electronic behavior.

Lorentz Force

The Lorentz force is the force exerted on a moving charged particle in the presence of electric and magnetic fields. In the context of the Hall effect, this force acts perpendicular to both the direction of current flow and the magnetic field, causing the charge carriers to accumulate on one side of the conductor. This accumulation generates the Hall voltage and provides key insights into the dynamics and density of charge carriers.

Atomic Density and Conduction Electrons per Atom

Atomic density relates the macroscopic density of a material to the number of atoms present per unit volume by using the material's molar mass and Avogadro’s number. By comparing the conduction electron density obtained from the Hall effect with the atomic density, one can estimate how many conduction electrons are contributed by each atom. This ratio is fundamental in characterizing the electronic structure and bonding in metals.

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