The Dielectric Constant of Atomic Hydrogen from the Point of View of Bohrs Quantum Theory

From Bohr's Atom to Electron Waves

---

Free download. Book file PDF easily for everyone and every device. You can download and read online The Dielectric Constant of Atomic Hydrogen from the Point of View of Bohrs Quantum Theory file PDF Book only if you are registered here. And also you can download or read online all Book PDF file that related with The Dielectric Constant of Atomic Hydrogen from the Point of View of Bohrs Quantum Theory book. Happy reading The Dielectric Constant of Atomic Hydrogen from the Point of View of Bohrs Quantum Theory Bookeveryone. Download file Free Book PDF The Dielectric Constant of Atomic Hydrogen from the Point of View of Bohrs Quantum Theory at Complete PDF Library. This Book have some digital formats such us :paperbook, ebook, kindle, epub, fb2 and another formats. Here is The CompletePDF Book Library. It's free to register here to get Book file PDF The Dielectric Constant of Atomic Hydrogen from the Point of View of Bohrs Quantum Theory Pocket Guide.

Lorrain and D. Corson , given by : 5. We do not know the effective dielectric volume for a single hydrogen atom, but we can estimate it by using the classical size for the Bohr atom and adjust the radius with a factor kedv: 5. Knowing the magnitude and divergence of the E m field, we can find the force that pulls on a nearby atom, in accordance with Eq. In view of quantum mechanics, the Bohr model is an over-simplification.

However, as we will see, this approach offers some insights into the nature and magnitude of the force generated by the divergent motional electric field. It is very much like Feynman's calculation of the atomic magnetic moment using classical mechanics Feynman that turns out to be quite accurate Figure 7. An orbital electron with a linear velocity v is producing a motional electric field Em at P.

The magnetic field from an orbital electron is found by using the Biot-Savart law: 5. Since the electron revolves at a radial frequency the B -field "velocity", V at a distance r can be calculated as The motional electric field E m is then found by inserting Eq. Figure 5 shows a plot of the E m vector fields around the hydrogen nucleus according to such a formula. The plot shows that the x-components of the vectors are always in the same direction, regardless of the electron position about the nucleus. It can also be seen that all y-components are opposite, in the upper and lower quadrants.

Assuming a full uniform circular orbit of the electron, the y-components will cancel while the x-components will add. For a full revolution, the hydrogen atom will generate a net E m field in the negative x-axis direction - measured at point P. Figure 8. The 2-dimensional vector plot of the motional electric field - produced by the orbital electron around the hydrogen nucleus. It is worth noting that the electron spin itself does also generate a motional electric field. This effect will be ignored in our discussion since it can be shown that it falls off faster than the motional electric field produced by the circulating electron.

It may be speculated that the motional electric fields generated by spinning elementary particles has some relationship to nuclear forces, but this is not discussed here. Since a hydrogen atom can be considered a tiny dielectric, it is attracted towards the source of a diverging E m field. We can calculate the instantaneous force generated by the diverging E m field from Eq.

The instantaneous force for various positions of the moving electron is plotted in figure 9.

Assuming that the y-components will cancel we can find the sum of the x-components. Mathematically, the dielectric force produced by a single atom acting on another dielectric atom can be found by integrating one revolution of the moving electron ignoring the y and z components, for now by using Eq.

Figure 9. A 2-dimensional vector plot of the instantaneous dielectric force, produced by an electron moving around the nucleus of a hydrogen atom. The expanded equation is large and is not easy to simplify symbolically. However, the equation can be calculated numerically by computer.

We will use the following constants: We arbitrarily adjust the volume for a single hydrogen atom from Eq. By using Eq.

Ask me directly Get a real experience-based answer. It is free! I try to answer all email within the same day.

Navigation menu

In some cases fortunately phase space can be reduced to three or even better, two dimensions. Such a reduction is possible in examining the behavior of a hydrogen atom in a strong magnetic field. The hydrogen atom has long been a highly desirable system because of its simplicity. A lone electron moves around a lone proton.

And yet the classical motion of the electron becomes chaotic when the magnetic field is turned on. How can we claim to understand physics if we cannot explain this basic problem? Under normal conditions , the electron of a hydrogen atom is tightly bound to the proton. The behavior of the atom is governed by quantum mechanics. The atom is not free to take on any arbitrary energy, it can take on only discrete, or quantized, energies.

At low energies, the allowed values are spread relatively far apart. As the energy of the atom is increased, the atom grows bigger, because the electron moves farther from the proton, and the allowed energies get closer together. At high enough energies but not too high, or the atom will be stripped of its electron! Such a highly excited atom is called a Rydberg atom. Rydberg atoms inhabit the middle ground between the quantum and the classical worlds, and they are therefore ideal candidates for exploring Bohr's correspondence principle which connects boxes Q quantum phenomena and R classic phenomenal.

If a Rydberg atom could be made to exhibit chaotic behavior in the classical sense, it might provide a clue as to the nature of quantum chaos and thereby shed light on the middle ground between boxes Q and P chaotic phenomena. A Rydberg atom exhibits chaotic behavior in a strong magnetic field, but to see this behavior we must reduce the dimension of the phase space.

The motion of the electron takes place effectively in a two-dimensional plane, and the motion around the axis can be separated out; only the distances along the axis and from the axis matter. The symmetry of motion reduces the dimension of the phase space from six to four. Additional help comes from the fact that no outside force does any work on the electron.

PPLATO / FLAP (Flexible Learning Approach To Physics)

As a consequence, the total energy does not change with time. By focusing attention on a particular value of the energy, one can take a three-dimensional slice-called an energy shell-out of the four-dimensional phase space. The energy shell allows one to watch the twists and turns of the electron, and one can actually see something resembling a tangled wire sculpture. The regions of the phase space where the points are badly scattered indicate chaotic behavior.

Such scattering is a clear symptom of classical chaos, and it allows one to separate systems into either box P or box R. What does the Rydberg atom reveal about the relation between boxes P and Q? I have mentioned that one of the trademarks of a quantum mechanical system is its quantized energy levels, and in fact the energy levels are the first place to look for quantum chaos. Chaos does not make itself felt at any particular energy level, however; rather its presence is seen in the spectrum, or distribution, of the levels.

Perhaps somewhat paradoxically in a nonchaotic quantum system the energy levels are distributed randomly and without correlation, whereas the energy levels of a chaotic quantum system exhibit strong correlations [see illustration]. The levels of the regular system are often close to one another, because a regular system is composed of smaller subsystems that are completely decoupled.

The energy levels of the chaotic system, however, almost seem to be aware of one another and try to keep a safe distance. A chaotic system cannot be decomposed; the motion along one coordinate axis is always coupled to what happens along the other axis. The spectrum of a chaotic quantum system was first suggested by Eugene P.

The Dielectric Constant and Diamagnetism of Hydrogen and Helium in the New Quantum Mechanics

Wigner, another early master of quantum mechanics. Wigner observed, as had many others, that nuclear physics does not possess the safe underpinnings of atomic and molecular physics: the origin of the nuclear force is still not clearly understood. He therefore asked whether the statistical properties of nuclear spectra could be derived from the assumption that many parameters in the problem have definite, but unknown values. This rather vague starting point allowed him to find the most probable formula for the distribution.

Oriol Bohigas and Marie-Joya Giannoni of the Institute of Nuclear Physics in Orsay, France, first pointed out that Wigner's distribution happens is be exactly what is found for the spectrum of a chaotic dynamic system. Chaos does not seem to limit itself to the distribution of quantum energy levels, however, it even appears to work its way into the wavelike nature of the quantum world. The position of the electron in the hydrogen atom is described by a wave pattern.

The electron cannot be pinpointed in space; it is a cloudlike smear hovering near the proton. Associated with each allowed energy level is a stationary state, which is a wave pattern that does not change with time.

• The sun still shone: professors talk about retirement
• Biomaterials for Musculoskeletal Regeneration: Applications
• Innate and Adaptive Immunity in the Tumor Microenvironment: 1
• Prebiotics and Probiotics in Human Milk. Origins and Functions of Milk-Borne Oligosaccharides and Bacteria
• how to manage oneselfyoga