Atom, wave nature

The properties of electrons described so far (mass, charge, spin, and wave nature) apply to all electrons. Electrons traveling freely in space, electrons moving in a copper wire, and electrons bound to atoms all have these characteristics. Bound electrons, those held in a specific region in space by electrical forces, have additional important properties relating to their energies and the shapes of their waves. These additional properties can have only certain specific values, so they are said to be quantized. 

In LEED, electrons of well-defined (but variable) energy and direction of propagation diffract off a crystal surface. Usually only the elastically diffracted electrons are considered and we shall do so here as well. The electrons are scattered mainly by the individual atom cores of the surface and produce, because of the quantum-mechanical wave nature of electrons, wave interferences that depend strongly on the relative atomic positions of the surface under examination. 

The concepts which we need for understanding the structural trends within covalently bonded solids are most easily introduced by first considering the much simpler system of diatomic molecules. They are well described within the molecular orbital (MO) framework that is based on the overlapping of atomic wave functions. This picture, therefore, makes direct contact with the properties of the individual free atoms which we discussed in the previous chapter, in particular the atomic energy levels and angular character of the valence orbitals. We will see that ubiquitous quantum mechanical concepts such as the covalent bond, overlap repulsion, hybrid orbitals, and the relative degree of covalency versus ionicity all arise naturally from solutions of the one-electron Schrodinger equation for diatomic molecules such as H2, N2, and LiH. 

In an atom, an electron moves at very high speeds—on the order of 2 million meters per second—and therefore exhibits many of the properties of a wave. An electron s wave nature can be used to explain why electrons in an atom are... 

Was this your answer Moving According tode Broglie, particles of matte1 behave like waves by virtue of their motion.The wave nature of electrons in atoms is pronounced because electrons move at speeds of about 2 million meters per second. 

The wave nature of electrons explains so many previously unexplained facts for the following reason. If waves are confined to a finite region of space, iliey form characteristic shapes and patterns that are specific to (lie nature of the confinement. [Figure 8 in the entiy on Chemical Elements shows waves in space confined to the neighborhood of a central point.] Only those and no other patterns can develop in this sort of confinement. But this is just the confinement that electrons suffer when they are confined around the atomic nucleus by electric attraction. The electron waves in atoms must assume some of these patterns. The simple patterns are lower than the more complex ones they are lower in energy. Indeed, the electrons in an atom assume the lowest possible patterns. 

Wavefunctions of electrons in atoms are called atomic orbitals. The name was chosen to suggest something less definite than an orbit of an electron around a nucleus and to take into account the wave nature of the electron. The mathematical expressions for atomic orbitals—which are obtained as solutions of the Schrodinger equation—are more complicated than the sine functions for the particle in a box, but their essential features are quite simple. Moreover, we must never lose sight of their interpretation, that the square of a wavefunction tells us the probability density of an electron at each point. To visualize this probability density, we can think of a cloud centered on the nucleus. The density of the cloud at each point represents the probability of finding an electron there. Denser regions of the cloud therefore represent locations where the electron is more likely to be found. 

A note of caution The Bohr theory, even when improved and amplified, applies only to hydrogen and hydrogen-like species, such as He+ and Li+. The theory explains neither the spectra of atoms containing even as few as two electrons, nor the existence and stability of chemical compounds. The next advance in the understanding of atoms requires an understanding of the wave nature of matter. 

A little-known paper of fundamental importance to modern atomic theory was published by Hantaro Nagaoka in 1904 [10]. Apart from oblique citation, it was soon buried and forgotten. With hindsight it deserved better than that. It contained the seminal ideas underlying the nuclear model of the atom, the standing-wave nature of orbital electrons and radiationless stationary states. It was so far ahead of contemporary thinking that later imitators either failed to appreciate its significance, or pretended to be unaware of it. 

The electron which responds to both quantum and classical potential fields exhibits this dual nature in its behaviour. Like a photon, an electron spreads over the entire region of space-time permitted by the boundary conditions, in this case stipulated by the classical potential. At the same time it also responds to the quantum field and reaches a steady, so-called stationary, state when the quantum and classical forces acting on the electron, are in balance. The best known example occurs in the hydrogen atom, which is traditionally described to be in the product state tpH = ipP ipe, hence with broken holistic symmetry. In many-electron atoms the atomic wave function is further fragmented into individual quantum states for pairs of electrons with paired spins. 

If one considers the wave nature of light, one may think that the photon size is roughly equal to its wavelength (say 500 nm) however, when the photon is absorbed by an atom, it "disappears" within a body of radius 0.5 nm this is a manifestation of the intricacies of the wave-particle duality, which are discussed in Section 3.39. 

S. Inouye et al., Phase-Coherent Amphfication of Atomic Matter Waves, Nature 402, 641-644 (1999). 

An important feature of the band system is that electrons are delocalised or spread over the lattice. Some delocalisation is naturally expected when an atomic orbital of any atom overlaps appreciably with those of more than one of its neighbours, but delocalisation reaches an extreme form in the case of a regular, 3-dimensional lattice. We can understand this best if we choose to think of the wave nature of electrons, and from that point of view we can formulate band theory as follows. 

I ve been using marbles and atom-size insects as an analogy for electrons, but I don t want to leave you with the misconception that electrons can only be thought of as solid objects. In the introduction to this book and in the first chemistry book, I discussed how we can think of electrons (and all particles, for that matter) as collections of waves. It is this wave nature of electrons that is the basis for quantum mechanics, which is the math we use to come up with the uncertainty principle. So, while it is often convenient to consider electrons to be tiny, solid objects, you should always be aware of the model of electrons as waves. 

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