The mass density of silver at room temperature is 10.5 ×10^3 kg / m^3 and its atomic mass is 10

step 1 The given problem, density of silver is given as row is equal to 10 .5 into 10 dash 3 kilogram p

The mass density of silver at room temperature is 10.5 ×10^3...

The mass density of silver at room temperature is $10.5 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ and its atomic mass is $108 \mathrm{~g} / \mathrm{mol}$. If we assume there is one free electron per silver atom, what is the free-electron density for silver, in electrons $/ \mathrm{m}^{3}$ ? How does your answer compare to the free-electron density for copper given in Example $25.1 ?$

Key Concepts

Avogadro's Constant

Avogadro's constant is the number of atoms, molecules, or particles in one mole of a substance. It is a fundamental constant that provides the link between the macroscopic scale (grams or kilograms) and the microscopic scale (individual atoms or molecules), allowing conversion from moles to number of particles.

Free Electron Model

The free electron model considers the conduction electrons in a metal as being nearly free to move throughout the material. In many simple metals, it is assumed that there is one free electron per atom, which directly allows the calculation of the free-electron density by multiplying the atomic number density by the number of conduction electrons per atom.

Mass Density and Number Density

This concept involves relating the macroscopic mass density of a material to the microscopic number of atoms present per unit volume. By knowing the mass density and the molar mass of the material, one can calculate the number of moles per unit volume, and then, using Avogadro's constant, determine the number density of atoms.

Comparative Analysis of Electron Densities

This concept pertains to comparing the electron densities of different metals. Differences in mass density and atomic mass between materials lead to variations in the number of atoms per unit volume, and consequently, the free-electron density. Such comparisons help in understanding the electrical and thermal properties of the metals.

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