Electron as wave

Although scientists talk about the dual wave and particle properties of electrons, many nonscientists still believe that electrons are only tiny particles. Rooted as we are in the macroscopic world, it can be difficult for some to picture a particle as also being a wave. One look at the accompanying picture, however, should help change that. What looks like ripples surrounding two barely submerged pebbles in a pool of water is really the surface of a copper crystal. 

Although they are true believers in the wave nature of electrons, the physicists at the IBM Al-maden Research Center in San Jose, California, were genuinely surprised when their scanning tunneling microscope (STM) produced this image of the copper surface. We looked at the surface with all these waves and thought, Is our machine bro- 

Recalling that p = mv and assuming that the electron mass is constant (ignoring any relativistic corrections), we have 

if we know the electron s position with a minimum uncertainty of 5 X 10-13 m, the uncertainty in the electron s velocity is at least 1 X 108 m/s. This is a very large number in fact, it is the same magnitude as the speed of light (3 X 108 m/s). At this level of uncertainty we have virtually no idea of the velocity of the electron. 

This means there is a very small (undetectable) uncertainty in our measurements of the speed of a ball. Note that this uncertainty is not caused by the limitations of measuring instruments Av is an inherent uncertainty. 

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We like to picture the atom as a miniature solar system, with the electrons orbiting around the nucleus. This solar system picture satisfies our intuition, but it does not accurately reflect today s understanding of the atom. About 1923, Louis de Broglie suggested that the properties of electrons in atoms are better explained by treating the electrons as waves rather than as particles. 

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. 

To begin with, Schrbdinger attempted to interpret corpus(il( .s, and particularly electrons, as wave packets. Although his formuhn are entirely correct, his interpretation cannot be maintained, since on the one hand, as we have already explained above, the wave packiits must in course of time become dissipated, and on the other hand the description of the interaction of two electrons as a collision of two wave packets in ordinary three-dimensional space lands us in grave difficulties. 

It could be shown, though, that the four electrons, as wave-forms, interacted and formed four average bonds that were precisely equivalent, and directed toward the apices of a tetrahedron. Thus, the Van t Hoff-Le Bel tetrahedral atom (see page 120) was explained in electronic terms. 

To sum up the argument we find a ubiquitous role played by electrons in chemical theory. Electrons-as-particles phenomena can be obtained from atoms by means of certain procedures such as the cloud chamber. Electrons as wave phenomena can be obtained from atoms by distinctive and independent procedures such as double slit experiments. But it does not follow that the electrons obtained... 

The essential and peculiar feature of the quantum mechanical model of the atom lies in its description of electrons as waves rather than particles. It is far more inmitive to think of electrons as particles, perhaps resembling tiny marbles, than to envision them as waves. But just as we ve seen for light, experimental observations led to the idea that electrons can exhibit wave-like behavior. The first evidence of the wave nature of electrons came through diffraction experiments in 1927. Diffraction was already a well-understood phenomenon of waves, so the observation of electron diffraction strongly suggested the need for a wave-based treatment of the electron. 

For the study of electrons in atoms and molecules it is more convenient to consider electrons as waves. Since the electrons are contained within atoms or molecules, the waves that describe them are standing waves, as are for instance the waves of water which move within a closed pool. The standing wave also describes the vibration of a strained wire for example on some musical instrument. Let us use the analogy of a strained wire to obtain a deeper insight into the behavior of electrons in molecules. 

Schrodinger created a mathematical model to describe electrons as waves. 

Quantimi Mechanics. By the mid-1920 s physicists had developed quantum mechanics, a powerful new theory explaining the behavior of electrons in atoms. Different forms of quantum mechanics emphasized electrons as particles (matrix mechanics) and electrons as waves (wave mechanics), and these theories were eventually shown to be equivalent. Quantum mechanics proved very successful for understanding ionic and covalent crystals, organic chemical molecules, and many other physical and chemical phenomena, but it proved unable to unlock the mysteries of superconductivity. However, in 1933 German physicist Walther Meissner discovered a superconductor s ability to repel magnetism, which provided a clue to understanding superconductivity, since study of the Meissner effect showed how transitions from normal to superconducting states are thermodynamically reversible. Other studies helped explain some of the... 

If we are going to treat electrons as waves, then we must quickly review what happens when two waves interact with each other. Two waves that approach each other can interfere in one of two possible ways—constructively or destructively. Similarly, when atomic orbitals overlap, they can interfere either constructively (Figure 1.11) or destructively (Figure 1.12). 

The main difference between the two models is that, while Bohr considered the electrons to be traditional particles whose motion could be described by the classical mechanics of Newton, the quantum mechanical model treats the electrons as waves. The wave properties of electrons provide a logical explanation for the existence of allowed orbits in Bohr s atomic model. 

Turning the discussion back to the molecular wavefunction, we see that the idea of PBCs is in line with the idea of modeling an electron in a delocalized way. Put simply, we must have PBCs to stop the electrons falling off die end of our model. We now model electrons as waves propagating through the model using continuous... 

That the description of electrons as waves is not simply a mathematical construct but is visibly real can be demonstrated by using a device called a scanning tunneling microscope (STM). This instrument allows the mapping of electron distributions in molecules at the atomic level. The picture shows an orbital image of tetracyanoethene deposited on a Ag surface, taken at 7 K. [Picture courtesy of Dr. Daniel Wegner, University of Munster, and Professor Michael F. Crommie, University of California at Berkeley]... 

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