Electron sea

Figure Bl.25.6. Energy spectrum of electrons coming off a surface irradiated with a primary electron beam. Electrons have lost energy to vibrations and electronic transitions (loss electrons), to collective excitations of the electron sea (plasmons) and to all kinds of inelastic process (secondary electrons). The element-specific Auger electrons appear as small peaks on an intense background and are more visible in a derivative spectrum.

Figure 12.1 shows a slice through such a solid the cations are to be thought of as a rigid lattice, and the electrons form a gas. I have deliberately drawn the cations as large objects for two reasons. First, the very early models such as that due to Drude tried to treat the electron sea as a perfect gas. It was eventually recognized that the electrons would collide with the cations and with each other an uncomfortable number of times. In any case, many of the predictions of the Dmde model turned out to be demonstrably flawed. 

Figure 9.1 Id illustrates a simple model of bonding in metals known as the electron-sea model. The metallic crystal is pictured as an array of positive ions, for example, Na+, Mg2+. These are anchored in position, like buoys in a mobile sea of electrons. These electrons are not attached to any particular positive ion but rather can wander through the crystal. The electron-sea model explains many of the characteristic properties of metals ...

In Chapter 9, we considered a simple picture of metallic bonding, the electron-sea model The molecular orbital approach leads to a refinement of this model known as band theory. Here, a crystal of a metal is considered to be one huge molecule. Valence electrons of the metal are fed into delocalized molecular orbitals, formed in the usual way from atomic... 

This type of argument leads us to picture a metal as an array of positive ions located at the crystal lattice sites, immersed in a sea of mobile electrons. The idea of a more or less uniform electron sea emphasizes an important difference between metallic bonding and ordinary covalent bonding. In molecular covalent bonds the electrons are localized in a way that fixes the positions of the atoms quite rigidly. We say that the bonds have directional character— the electrons tend to remain concentrated in certain regions of space. In contrast, the valence electrons in a metal are spread almost uniformly throughout the crystal, so the metallic bond does not exert the directional influence of the ordinary covalent bond. 

FIGURE 1.53 A block of metal consists of an array of cations (the spheres) surrounded by a sea of electrons. The charge of the electron sea cancels the charges of the cations. The electrons of the sea are mobile and can move past the cations quite easily and hence conduct an electric current. 

Consider an electrophile immersed in an idealized zero-temperature free electron sea of zero chemical potential, which could be an approximation to its binding environment in a protein, a DNA coil, or a surface. It will become saturated with electrons, to the point that its chemical potential increases to zero, thereby becoming... 

If the electron sea provides enough electrons, the electrophile will become saturated with electrons according to Equation 13.3... 

Metals are solid at room temperature, except for mercury. This tells us that the attractive forces between metal atoms are strong. The valence electrons of metal atoms can easily move from the free orbitals of one atom to another. These electrons that can move freely between atoms form an electron sea . An attractive force occurs between the negatively charged sea of electrons and the positively charged nuclei. Metal atoms are held together because of this attractive force. This is called the metallic bond. 

Because of the attraction between the electron sea and the positively charged sodium nuclei, a metallic bond is formed. Because of these freely moving electrons in the electron sea, metals are good conductors of heat and electricity. They can be drawn into wires and can be hammered into shape easily. 

Na has one valence electron and Ca has two valence electrons therefore the total charge of the electron sea in Ca is greater than that of Na. So the metallic Ca bonds are stronger than those in Na, and therefore Ca melts at a higher temperature. 

Al(s) and Hg(s) are metals and consist of metal ions in an electron sea. Although their physical phases are different, they conduct electricity because of the freely moving electrons that make up the electron sea. 

The holes are not really empty in a real metal, because atoms and ions do not have sharp edges. The electron sea extends into the holes. 

To understand those properties, we need to look at the bonding in metals. We ll consider two theoretical models that are commonly used the electron-sea model and the molecular orbital theory. 

In the electron-sea model, a metal crystal is viewed as a three-dimensional array of metal cations immersed in a sea of delocalized electrons that are free to move throughout the crystal (Figure 21.6). The continuum of delocalized, mobile valence electrons acts as an electrostatic glue that holds the metal cations together. 

The electron-sea model affords a simple qualitative explanation for the electrical and thermal conductivity of metals. Because the electrons are mobile, they are free to move away from a negative electrode and toward a positive electrode when a metal is subjected to an electrical potential. The mobile electrons can also conduct heat by carrying kinetic energy from one part of the crystal to another. Metals are malleable and ductile because the delocalized bonding extends in all... 

FIGURE 21.6 Two- dimensional representation of the electron-sea model of a metal. An ordered array of cations is immersed in a continuous distribution of delocalized, mobile valence electrons. The valence electrons do not belong to any particular metal ion but to the crystal as a whole. 

Two bonding models are used for metals. The electron-sea model pictures a metal as an array of metal cations... 

Describe the electron-sea model of the bonding in cesium metal. Cesium has a body-centered cubic structure. 

How does the electron-sea model account for the malleability and ductility of metals ... 

Cesium metal is very soft, and tungsten metal is very hard. Explain the difference using the electron-sea model. 

Sodium melts at 98°C, and magnesium melts at 649°C. Account for the higher melting point of magnesium using the electron-sea model. 

What properties of metals are better explained by band theory than by the electron-sea model ... 

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