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Chapter 11: Problem 48

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.

Short Answer

Expert verified
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 by step solution

01

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.
02

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.
03

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.
04

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.

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Most popular questions from this chapter

The Lewis structure of \(\mathrm{N}_{2}\) indicates that the nitrogento-nitrogen bond is a triple covalent bond. Other evidence suggests that the \(\sigma\) bond in this molecule involves the overlap of \(s p\) hybrid orbitals. (a) Draw orbital diagrams for the N atoms to describe bonding in \(\mathrm{N}_{2}\) (b) Can this bonding be described by either \(s p^{2}\) or \(s p^{3}\) hybridization of the \(\mathrm{N}\) atoms? Can bonding in \(\mathrm{N}_{2}\) be described in terms of unhybridized orbitals? Explain.

Construct a concept map that embodies the ideas of valence bond theory.

A molecule in which \(s p^{2}\) hybrid orbitals are used by the central atom in forming covalent bonds is (a) \(\mathrm{PCl}_{5}\) (b) \(\mathrm{N}_{2} ;\) (c) \(\mathrm{SO}_{2} ;\) (d) \(\mathrm{He}_{2}\)

Is it correct to say that when a diatomic molecule loses an electron, the bond energy always decreases (that is, that the bond is always weakened)? Explain.

Which of the following substances, when added in trace amounts to silicon, would produce a \(p\) -type semiconductor: (a) sulfur, (b) arsenic, (c) lead, (d) boron, (e) gallium arsenide, (f) gallium? Explain.
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