Problem 48 - General Chemistry: Principles and Modern Applications

Question

Magnesium is an excellent electrical conductor even though it has a full \(3 s\) subshell with the electron configuration: [Ne]3s^. Use band theory to explain why magnesium conducts electricity.

Step-by-Step Solution

Answer

Magnesium conducts electricity because in its crystalline state, the energy band corresponding to the 3s orbital is only half-filled. This allows the electrons to move to the empty states, conducting electricity, when an electric field is applied.

Step 1: Recap of Band Theory

Band theory is a principle in solid state physics that describes how energy levels of electrons in a solid material depend on the electrons' momentum. In a single atom, electrons occupy specific energy levels. When multiple atoms are close together, their electronic orbitals overlap, forming energy bands. These bands can either be filled OR partially filled with electrons. It's important to note- materials will conduct electricity if these bands are partially occupied.

Step 2: Analyze Electron Configuration of Magnesium

Let's look at the electron configuration of magnesium which is [Ne]3s2. This indicates that the outermost shell has 2 electrons in the 3s orbital.

Step 3: Determine the Filling of Energy Bands

These 2 electrons might give an impression that magnesium shouldn't conduct electricity because it appears to have a filled energy level. However, in a solid state, the 3s band of magnesium does not contain just 2 energy levels but a large number of very closely spaced energy levels due to overlap forming an 'energy band'. The band corresponding to the 3s orbital is only half-filled because magnesium has one electron per atom in this band.

Step 4: Conclude with the Conductivity

Hence, despite having a full 3s subshell in individual atom, the 3s band in crystalline magnesium is only half-filled. This means there are plenty of empty energy states available to which the electrons can jump when an electric field is applied, allowing magnesium to conduct electricity effectively.

Key Concepts

Magnesium Electron Configuration

Understanding the electron configuration of magnesium is key to grasping its conductive properties. Magnesium, represented as "Mg" on the periodic table, is an element that has the electron configuration:

• [Ne]3s²

The "[Ne]" part signifies the core electrons that match the electron configuration of neon, a noble gas. The "3s²" indicates two electrons in the 3s orbital. This configuration is particularly interesting because it suggests a filled 3s orbital when looking at magnesium as a single, isolated atom. However, this is not the whole story.
When magnesium atoms are part of a solid structure, the interaction with other atoms alters the energy levels. Instead of discrete energy levels, the electrons become part of energy bands."

Electrical Conductivity

Electrical conductivity is a measure of how well a material can allow the flow of electric current. For a material to be a good conductor, it needs to have electrons that can move freely within an energy band. In metals, this movement becomes possible when the outer energy bands are only partially filled.

Although the electron configuration of magnesium suggests a full 3s subshell, this doesn't describe its behavior in a bulk, solid state. Due to the metallic bonding and the arrangement of atoms in a lattice, ionic cores create numerous closely spaced energy levels forming energy bands. This produces a band where electrons can easily move.

• Partially filled or overlapping bands are essential for conductivity.
• Free electrons can jump into empty energy states when an electric field is applied.

For magnesium, the 3s band is not fully occupied in its solid form, allowing for excellent electrical conductivity.

Energy Bands

Energy bands are crucial in understanding the conductive properties of metals like magnesium. When atoms come together to form a solid, their individual electron orbitals interact and overlap.
This interaction results in the formation of energy bands, which are ranges of energy levels that electrons can occupy.

Band theory explains these phenomena in solid state physics. In magnesium:

• The 3s orbital of each atom becomes part of a large, continuous band of energy levels.
• These energy levels are much more numerous and closely spaced than in an isolated atom's discrete energy levels.

Even though a single magnesium atom seems to have a full 3s orbital, the band theory reveals that in a crystalline structure, the 3s band hosts only one electron per energy level. With a partially filled band, electrons can freely move, allowing magnesium to conduct electricity efficiently when a voltage is applied.