Final answer:
The number of areas of electron density refers to regions where electrons exist within an atom or a material, including those from bonds and lone pairs. In metals, the electron number density can be equated to atoms per unit volume. Understanding these regions' electron density is crucial for analyzing material properties.
Step-by-step explanation:
When discussing the number of areas of electron density, we are often referring to the concept in chemistry where each area represents a region in an atom where electrons are likely to be found. These regions can include lone pairs, single bonds, double bonds, triple bonds, and electron clouds from adjacent atoms. The density of states (g(E)), Fermi factor (F), and electron number density (n(E)) are all factors that help to define these regions quantitatively.
To calculate the number of free electrons in a metal like copper, we look at the atomic structure which provides one free electron per copper atom. Thus, the number of free electrons in copper is equal to the number of copper atoms per unit volume (m³). The density of states can be derived from the solution to Schrödinger's equation, indicating the quantum states per unit energy interval in the material.
At the Fermi energy (EF), there is a sharp decrease in electron number density as stated by quantum theory. The behavior of electron density and density of states is crucial for understanding electrical conductivity and the properties of materials at different energy levels.