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Chapter 18: Problem 57

Some scientists believe that the solid hydrogen that forms at very low temperatures and high pressures may conduct electricity. Is this hypothesis supported by band theory?

Short Answer

Expert verified
Answer: Yes, it is possible for solid hydrogen formed at very low temperatures and high pressures to conduct electricity, according to band theory. This would depend on the specific conditions and the energy arrangement of the valence and conduction bands in solid hydrogen. If the energy bands overlap or are very close, it could lead to the conduction of electricity.

Step by step solution

01

Understanding Band Theory

Band theory is a model used to explain the electronic behavior of solids, specifically their ability or inability to conduct electricity. Atoms in a solid are arranged in a regular pattern called a lattice, and their valence electrons participate in the formation of a continuous band of energy levels. The distribution and nature of these bands determine the electrical conductivity of a solid.
02

Types of Energy Bands

There are two main types of energy bands: 1. Valence band: contains the valence electrons of the atoms and is mostly responsible for the chemical bonding between atoms. 2. Conduction band: contains the electrons that can move freely and participate in the conduction of electricity, if there are any. These bands can overlap, be separated by a small energy gap, or be separated by a large energy gap. The size of the energy gap (also known as the band gap) between the valence band and the conduction band determines whether a solid is a conductor, semiconductor, or insulator.
03

Band Theory and Conduction

A solid is considered to be: 1. A conductor if the valence band and the conduction band overlap, meaning that there are electrons in the conduction band available for electrical conduction. 2. A semiconductor if a small energy gap exists between the valence band and the conduction band, and electrons can be excited to the conduction band under specific conditions (e.g., increased temperature). 3. An insulator if a large energy gap exists between the valence band and the conduction band, making it almost impossible for electrons to jump from the valence band to the conduction band and contribute to electrical conduction.
04

Band Theory Application to Solid Hydrogen

Hydrogen is a diatomic gas at standard conditions (room temperature and atmospheric pressure). However, at very low temperatures and high pressures, it forms a solid with a lattice structure. In solid hydrogen, each hydrogen atom has only one valence electron, forming a filled valence band. If under specific conditions (high pressure and low temperature), the energy bands in solid hydrogen become such that there is no significant energy gap between the valence and conduction bands, or if they overlap, it is possible for the electrons to jump from the valence band to the conduction band and participate in electrical conduction, making solid hydrogen a potential conductor.
05

Conclusion

The hypothesis that solid hydrogen formed at very low temperatures and high pressures may conduct electricity can be supported by band theory. However, this would depend on the specific conditions and the energy arrangement of the valence and conduction bands in solid hydrogen. If the energy bands overlap or are very close, it could lead to the conduction of electricity.

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