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Introducing the Quantum World: The First Model: the Bohr Atom

Erasmus Profile Erasmus : A blackbody is a body that radiates energy applied to it such that energy input equals energy output.
Planck in studying blackbody radiation found that light waves could only gain or lose by finite amounts related to their frequency. These finite amounts were called quantum.

 

BlackBody Radiation

The problem that Planck was trying to solve was that the greatest amount of energy that was radiated from a blackbody was near the middle of the electromagnetic spectrum (visible light), instead of increasing with the higher frequency (or lower wavelength), as classical physics suggested.

Erasmus Profile Erasmus : Classical physics suggested that the higher the frequency (or the lower the wavelength), the higher the temperature would be. Classical physics predicted that the black body radiation would exponentially increase with temperature. But measurements suggested that the radiation intensity started to decrease towards ultraviolet, instead of increasing exponentially, becoming infinitely large. This is known as the “ultraviolet catastrophe

Planck explained that the only way the blackbody spectrum would work, was if the blackbody was made up of oscillators that could only emit light (photon energy) in discrete chunks, so that the electromagnetic energy could only be emitted in a quantized form, meaning discrete values, instead of a continuous set of values.

Kinkajou Profile Kinkajou : An analogy of this situation would be walking up some stairs; you increase in potential energy for every step you walk. But you can only take a whole number of steps – you can’t walk up 1.5 number of steps, therefore the potential energy you receive is discrete, not continuous.
Goo Goo : Energy in atomic electrons has only a discrete set of values, or quantized values.

Erasmus Profile Erasmus : Therefore, Planck proposed that light and other electromagnetic waves were emitted in discrete packets of energy called “quanta”, which were multiples of a certain constant – Planck’s constant. He came up with the formula

E = nhf
Where E is any possible energy, n is any integer (and can only be an integer), h is Planck’s constant, and f is the frequency of radiation. The Planck constant is 6.62*10-34 m2kg/s.

 In 1905, Einstein hypothesized that instead of thinking of light as a wave, it was really a stream of photons, each with a discrete amount of energy  Albert Einstein used this observation from an experiment called the photoelectric effect  and won his Nobel Prize in the process.

Essentially an atom possesses a finite number of energy states in which electron can exist. When energy via a photon impacts on electron, only a photon of a frequency/energy level that matches the energy difference between energy states can be absorbed by the electron, lifting it to a high energy level. This energy is reradiated at specific wavelengths – quanta of energy.

 

Kinkajou Profile Kinkajou : Tell us about the Photoelectric effect.

PhotoElectric Effect

Erasmus Profile Erasmus : The photoelectric effect is the phenomenon when certain metals are exposed to light, they eject electrons. This is because there are negatively charged electrons on the surface of the metal that are attracted to the positive charges in the nucleus of the metal, and when you send light of the same frequency (or photons), it can knock some of the surface electrons off.

Einstein took a light source and pointed it towards a metal surface. He noticed that only light above a certain frequency (or below a certain wavelength) caused electrons to be given off by the surface. Above that frequency, the higher the frequency of the light, the higher the energy of the surface electrons given off. Einstein also saw that the electrons were emitted instantaneously, with no delay whatsoever, which could not happen if the light was a wave sweeping over the metal. This could only happen if the electron emissions were caused by individual particles of light.

The next development was the Bohr Atom model in 1913. It essentially showed the electrons in an atom orbiting an atomic nucleus in discrete positions. We now call these discrete positions: Orbitals or Valences. An electron could exist only in anyone of a number of discrete positions around an atomic nucleus.

This theory explained the spectral lines of atoms. The emission of light absorbed by Hydrogen Orbitals

Some of the orbital shells of a Hydrogen atom. The energy levels of the orbitals are shown to the right.

 

 

Kinkajou Profile Kinkajou : Tell Us About the Electron Shells of Atoms -
say Hydrogen Atoms to keep it simple.

Erasmus Profile Erasmus : Hydrogen, like all atoms, provides very distinctive lines when the frequency of its spectral output are measured as electron changes between orbitals.  These electromagnetic waves come in the form of packets, or photons that are absorbed or emitted by an electron. Photons are absorbed if the electron takes energy to move away from the hydrogen nucleus and emitted if the electron moves closer to the hydrogen nucleus.

Despite the electron’s probability distribution in an atomic orbit, the energy transition states are very distinct when they move between orbitals.  The photon energy and its wavelength are measured by spectral analysis such as hydrogen’s spectral lines below.

 

Hydrogen Spectrum

Hydrogen Spectrum
The movement of electrons between these energy levels produces a spectrum. These wavelengths are at 656, 486, 434, and 410nm. These correspond to the emission of photons as an electron in an excited state transitions down to energy level n=2.

Kinkajou Profile Kinkajou : This Model is a bit old in the New Quantum World. So tell us about some of the limitations of the Bohr Atom Model.

Erasmus Profile Erasmus : Limitations of the Bohr Model.
The Bohr Model was an important step in the development of atomic theory. However, it has several limitations.
* It is in violation of the Heisenberg Uncertainty Principle. The Bohr Model considers electrons to have both a known radius and orbit, which is impossible according to Heisenberg.
* The Bohr Model is very limited in terms of size. Poor spectral predictions are obtained when larger atoms are in question.
* It cannot predict the relative intensities of spectral lines.
* It does not explain the Zeeman Effect, when the spectral line is split into several components in the presence of a magnetic field.
* The Bohr Model does not account for the fact that accelerating electrons do not emit electromagnetic radiation.

Kinkajou Profile Kinkajou : What is the Rydberg Formula?
Erasmus Profile Erasmus : The Rydberg formula explains the different energies of transition that occur between energy levels. When an electron moves from a higher energy level to a lower one, a photon is emitted. Each element has a distinct spectral fingerprint. Even a simple hydrogen atom has multiple potential quantal energy states possible for the electron in orbit around the atomic nucleus, (a proton in the case of the average hydrogen atom).

Kinkajou Profile Kinkajou : Let's move on, Progressing Into Valence Theory:
Starting with a Simple Base Example: A neutral hydrogen atom.

Energy Levels of a Hydrogen Atom

 

Erasmus Profile Erasmus : The energy levels are given in the diagram above. The x-axis shows the allowed energy levels of electrons in a hydrogen atom, numbered from 1 to 5. The y-axis shows each level's energy in electron volts (eV). One electron volt is the energy that an electron gains when it travels through a potential difference of one volt
(1 eV = 1.6 x 10E-19 Joules).

Electrons in a hydrogen atom must be in one of the allowed energy levels. To remove electrons, if an electron is in the first energy level, it must have exactly -13.6 eV of energy. If it is in the second energy level, it must have -3.4 eV of energy. An electron in a hydrogen atom cannot have -9 eV, -8 eV or any other value in between.

Let's say the electron wants to jump from the first energy level, n = 1, to the second energy level n = 2. The second energy level has higher energy than the first, so to move from n = 1 to n = 2, the electron needs to gain energy. It needs to gain (-3.4) - (-13.6) = 10.2 eV of energy to make it up to the second energy level.

The electron can gain the energy it needs by absorbing light energy. If the electron jumps from the second energy level down to the first energy level, it must give off some energy by emitting light. The atom absorbs or emits light in discrete packets called photons, and each photon has a definite energy. Only a photon with an energy of exactly 10.2 eV can be absorbed or emitted when the electron jumps between the n = 1 and n = 2 energy levels.

The energy that a photon carries depends on its wavelength. Since the photons absorbed or emitted by electrons jumping between the n = 1 and n = 2 energy levels must have exactly 10.2 eV of energy, the light absorbed or emitted must have a definite wavelength. This wavelength can be found from the equation

E = hc/wavelength

Where E is the energy of the photon (in eV), h is Planck's constant (4.14 x 10-15 eV s) and c is the speed of light (3 x 108 m/s). Rearranging this equation to find the wavelength gives
Wavelength = hc/E.

A photon with energy of 10.2 eV has a wavelength of 1.21 x 10-7 m, in the ultraviolet part of the spectrum. So when an electron wants to jump from n = 1 to n = 2, it must absorb a photon of ultraviolet light. When an electron drops from n = 2 to n = 1, it emits a photon of ultraviolet light.

The step from the second energy level to the third is much smaller. It takes only 1.89 eV of energy for this jump. It takes even less energy to jump from the third energy level to the fourth, and even less from the fourth to the fifth.

Goo Goo : What would happen if the electron gained enough energy to make it all the way to 0 eV?

Erasmus Profile Erasmus : The electron would then be free of the hydrogen atom. The atom would be missing an electron, and would become a hydrogen ion.

Kinkajou Profile Kinkajou : The table below shows the first five energy levels of a hydrogen atom.

Energy Levels of Hydrogen Atom

Erasmus Profile Erasmus : The energy levels are much more complex and difficult for larger atoms with many electrons. And there’s more. The energy levels of neutral helium are different from the energy levels of singly ionized helium!
The energy levels are regarded as basic routine information. They are published in sources such as the CRC Handbook of Chemistry.

 

Hydrogen Spectrum Orbital Energies

Kinkajou Profile Kinkajou : Tell us about Hydrogen Orbital Transitions
Erasmus Profile Erasmus : Another set of data demonstrating proof of the wave equations is the transitional energies and wavelengths for an electron in a hydrogen atom that moves between orbitals. In this case, it is a difference in energy between two positions relative to the nucleus, where ni is the initial orbital and nf is the final orbital.
The table below shows the calculations of the above transition (3->2) through to an electron in the ninth orbital transitioning to the second orbital (9->2). 

Hydrogen transition Energies

Erasmus Profile Erasmus : When Complex electron shell structures exist in bigger atoms, it becomes obvious that electron shells can in fact overlap in terms of energy level.
The Aufbau principle states that electrons fill lower-energy atomic orbitals before filling higher-energy ones (Aufbau is German for "building-up"). By following this rule, we can predict the electron configurations for atoms or ions.

 

Aufbau Principle

Erasmus Profile Erasmus : There are a number of exceptions to the rule; for example palladium (atomic number 46) has no electrons in the fifth shell, unlike other atoms with lower atomic number.

The Aufbau principle dictates the manner in which electrons are filled in the atomic orbitals of an atom in its ground state. It states that electrons are filled into atomic orbitals in the increasing order of orbital energy level. According to the Aufbau principle, the available atomic orbitals with the lowest energy levels are occupied before those with higher energy levels.

 

A diagram illustrating the order in which atomic orbitals are filled is provided below. Here, ‘n’ refers to the principal quantum number and ‘l’ is the azimuthal quantum number.

Aufbau Orbital Filling

Erasmus Profile Erasmus : The Aufbau principle can be used to understand the location of electrons in an atom and their corresponding energy levels. For example, carbon has 6 electrons and its electronic configuration is 1s22s22p2.

Also, the manner in which electrons are filled into orbitals in a single subshell must follow Hund’s rule, i.e. every orbital in a given subshell must be singly occupied by electrons before any two electrons pair up in an orbital.

Kinkajou Profile Kinkajou : Tell us About the Salient Features of the Aufbau Principle


* According to the Aufbau principle, electrons first occupy those orbitals whose energy is the lowest. This implies that the electrons enter the orbitals having higher energies only when orbitals with lower energies have been completely filled.

* The order in which the energy of orbitals increases can be determined with the help of the (n+l) rule, where the sum of the principal and azimuthal quantum numbers determines the energy level of the orbital.

* Lower (n+l) values correspond to lower orbital energies. If two orbitals share equal (n+l) values, the orbital with the lower n value is said to have lower energy associated with it.
* The order in which the orbitals are filled with electrons is: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, and so on.

Kinkajou Profile Kinkajou : Any Exceptions to the Aufbau principle? Surely not everything is that easy?


Erasmus Profile Erasmus :Orbiatls Irregularity

 (as suggested by the Aufbau principle). This exception is attributed to several factors such as the increased stability provided by half-filled subshells and the relatively low energy gap between the 3d and the 4s subshells.

The energy gap between the different subshells is illustrated below.

Half-filled subshells feature lower electron-electron repulsions in the orbitals, thereby increasing the stability. Similarly, completely filled subshells also increase the stability of the atom. Therefore, the electron configurations of some atoms disobey the Aufbau principle (depending on the energy gap between the orbitals).

 

Orbitals Energy Map

For example, copper is another exception to this principle. This can be explained by the stability provided by a completely filled 3d subshell.

For multi-electron atoms, n is a poor indicator of electron's energy. Energy spectra of some shells interleave.

The states crossed by same red arrow have same value. The direction of the red arrow indicates the order of state filling.

Aufbau Integer and Orbital Filling

It is sometimes stated that all the electrons in a shell have the same energy, but this is an approximation. However, the electrons in one subshell do have exactly the same level of energy, with later subshells having more energy per electron than earlier ones. This effect is great enough that the energy ranges associated with shells can overlap.

 

Kinkajou Profile Kinkajou : So tell us about IONISATION and how it affects Binding Energy

Atomic Binding Energy

Erasmus Profile Erasmus : The graph above shows the binding energy for electrons in different shells in neutral atoms. The ionization energy is the lowest binding energy for a particular atom.

 

Ionization energy of atoms, denoted Ei, is measured by finding the minimal energy of light quanta (photons) or electrons accelerated to a known energy that will kick out the least bound atomic electrons. The measurement is performed in the gas phase on single atoms.

Electron binding energy is a generic term for the energy needed to remove an electron from a particular electron shell for an atom or ion.

 

Kinkajou Profile Kinkajou : Let's talk about trends in the Valences across the Periodic Table


Erasmus Profile Erasmus : Generally, the (n+1)th ionization energy of a particular element is larger than the nth ionization energy. When the next ionization energy involves removing an electron from the same electron shell, the increase in ionization energy is primarily due to the increased net charge of the ion from which the electron is being removed. Electrons removed from more highly charged ions experience greater forces of electrostatic attraction; thus, their removal requires more energy.

In addition, when the next ionization energy involves removing an electron from a lower electron shell, the greatly decreased distance between the nucleus and the electron also increases both the electrostatic force and the distance over which that force must be overcome to remove the electron. Both of these factors further increase the ionization energy.

Some values for elements of the third period are given in the following table:

Successive ionization energy values / kJmolE-1
(96.485 kJ/mol = 1 eV

Large jumps in the successive molar ionization energies occur when passing noble gas configuration. The first two molar ionization energies of magnesium (stripping the two 3s electrons from a magnesium atom) are much smaller than the third, which requires stripping off a 2p electron from the neon configuration of Mg2+. That electron is much closer to the nucleus than the 3s electron removed previously.

Ionization energies peak in noble gases at the end of each period in the periodic table of elements and, as a rule, dip when a new orbital is starting to be filled.

Atomic Ionisation Energies

Erasmus Profile Erasmus : Ionization energy is also a periodic trend within the periodic table. Moving left to right within a period, or upward within a group, the first ionization energy generally increases, with exceptions such as aluminium and sulphur in the table above. As the nuclear charge of the nucleus increases across the period, the electron shielding remains constant, hence the atomic radius decreases, and the electron cloud becomes closer towards the nucleus because the electrons, especially the outermost one, are held tighter by the higher effective nuclear charge. Similarly on moving upward within a given group, the electrons are held in lower-energy orbitals, closer to the nucleus and therefore are more tightly bound.

Ionisation Energies

Erasmus Profile Erasmus : In chemistry and atomic physics, an electron shell may be thought of as an orbit followed by electrons around an atom's nucleus. The closest shell to the nucleus is called the "1 shell" (also called the "K shell"), followed by the "2 shell" (or "L shell"), then the "3 shell" (or "M shell"), and so on farther and farther from the nucleus. The shells correspond to the principal quantum numbers (n = 1, 2, 3, 4 ...) or are labelled alphabetically with the letters used in X-ray notation (K, L, M, …).

Each shell can contain only a fixed number of electrons: The first shell can hold up to two electrons, the second shell can hold up to eight (2 + 6) electrons, the third shell can hold up to 18 (2 + 6 + 10) and so on.
Each shell consists of one or more subshells, and each subshell consists of one or more atomic orbitals.

The existence of electron shells was first observed experimentally in Charles Barkla's and Henry Moseley's X-ray absorption studies.

Kinkajou Profile Kinkajou : SUBSHELLS : So these are part of an orbital or valence?


Erasmus Profile Erasmus : Each shell is composed of one or more subshells, which are themselves composed of atomic orbitals. For example, the first (K) shell has one subshell, called 1s; the second (L) shell has two subshells, called 2s and 2p; the third shell has 3s, 3p, and 3d; the fourth shell has 4s, 4p, 4d and 4f; the fifth shell has 5s, 5p, 5d, and 5f and can theoretically hold more in the 5g subshell that is not occupied in the ground-state electron configuration of any known element.  The various possible subshells are shown in the following table:

 

Valence Subshells

* The second column is the azimuthal quantum number (L) of the subshell. The precise definition involves quantum mechanics, but it is a number that characterizes the subshell.

* The third column is the maximum number of electrons that can be put into a subshell of that type. For example, the top row says that each s-type subshell (1s, 2s, etc.) can have at most two electrons in it. In each case the figure is 4 greater than the one above it.

* The fourth column says which shells have a subshell of that type. For example, looking at the top two rows, every shell has an s subshell, while only the second shell and higher have a p subshell

* The final column gives the historical origin of the labels s, p, d, and f. They come from early studies of atomic spectral lines. The other labels, namely g, h and i, are an alphabetic continuation following the last historically originated label of f.

Kinkajou Profile Kinkajou : How Many electrons can exist in each shell?


Erasmus Profile Erasmus : Each subshell is constrained to hold 4L + 2 electrons at most, namely:
* Each s subshell holds at most 2 electrons
* Each p subshell holds at most 6 electrons
* Each d subshell holds at most 10 electrons
* Each f subshell holds at most 14 electrons
* Each g subshell holds at most 18 electrons

Electron energy levels are dictated by the valence or orbital energy levels.
Splitting occurs due to the spin up / spin down effects on the electron. This is the basis of the Hydrogen line. This is approximately 1x10-3 eV.

HYPERFINE structure splitting occurs due to interactions between electron clouds. This occurs with energies of the order of 1x10-4 eV. There can be some additional effects due to the atomic nucleus itself spinning around its own axis.

Kinkajou Profile Kinkajou : Show us this stuff for the periodic table.

Erasmus Profile Erasmus : List of elements with electrons per shell

Z Element No. of electrons/shell Group
1 Hydrogen 1 1
2 Helium 2 18
3 Lithium 2, 1 1
4 Beryllium 2, 2 2
5 Boron 2, 3 13
6 Carbon 2, 4 14
7 Nitrogen 2, 5 15
8 Oxygen 2, 6 16
9 Fluorine 2, 7 17
10 Neon 2, 8 18
11 Sodium 2, 8, 1 1
12 Magnesium 2, 8, 2 2
13 Aluminium 2, 8, 3 13
14 Silicon 2, 8, 4 14
15 Phosphorus 2, 8, 5 15
16 Sulphur 2, 8, 6 16
17 Chlorine 2, 8, 7 17
18 Argon 2, 8, 8 18
19 Potassium 2, 8, 8, 1 1
20 Calcium 2, 8, 8, 2 2
21 Scandium 2, 8, 9, 2 3
22 Titanium 2, 8, 10, 2 4
23 Vanadium 2, 8, 11, 2 5
24 Chromium 2, 8, 13, 1 6
25 Manganese 2, 8, 13, 2 7
26 Iron 2, 8, 14, 2 8
27 Cobalt 2, 8, 15, 2 9
28 Nickel 2, 8, 16, 2 10
29 Copper 2, 8, 18, 1 11
30 Zinc 2, 8, 18, 2 12
31 Gallium 2, 8, 18, 3 13
32 Germanium 2, 8, 18, 4 14
33 Arsenic 2, 8, 18, 5 15
34 Selenium 2, 8, 18, 6 16
35 Bromine 2, 8, 18, 7 17
36 Krypton 2, 8, 18, 8 18
37 Rubidium 2, 8, 18, 8, 1 1
38 Strontium 2, 8, 18, 8, 2 2
39 Yttrium 2, 8, 18, 9, 2 3
40 Zirconium 2, 8, 18, 10, 2 4
41 Niobium 2, 8, 18, 12, 1 5
42 Molybdenum 2, 8, 18, 13, 1 6
43 Technetium 2, 8, 18, 13, 2 7
44 Ruthenium 2, 8, 18, 15, 1 8
45 Rhodium 2, 8, 18, 16, 1 9
46 Palladium 2, 8, 18, 18 10
47 Silver 2, 8, 18, 18, 1 11
48 Cadmium 2, 8, 18, 18, 2 12
49 Indium 2, 8, 18, 18, 3 13
50 Tin 2, 8, 18, 18, 4 14
51 Antimony 2, 8, 18, 18, 5 15
52 Tellurium 2, 8, 18, 18, 6 16
53 Iodine 2, 8, 18, 18, 7 17
54 Xenon 2, 8, 18, 18, 8 18
55 Caesium 2, 8, 18, 18, 8, 1 1
56 Barium 2, 8, 18, 18, 8, 2 2
57 Lanthanum 2, 8, 18, 18, 9, 2 3
58 Cerium 2, 8, 18, 19, 9, 2  
59 Praseodymium 2, 8, 18, 21, 8, 2  
60 Neodymium 2, 8, 18, 22, 8, 2  
61 Promethium 2, 8, 18, 23, 8, 2  
62 Samarium 2, 8, 18, 24, 8, 2  
63 Europium 2, 8, 18, 25, 8, 2  
64 Gadolinium 2, 8, 18, 25, 9, 2  
65 Terbium 2, 8, 18, 27, 8, 2  
66 Dysprosium 2, 8, 18, 28, 8, 2  
67 Holmium 2, 8, 18, 29, 8, 2  
68 Erbium 2, 8, 18, 30, 8, 2  
69 Thulium 2, 8, 18, 31, 8, 2  
70 Ytterbium 2, 8, 18, 32, 8, 2  
71 Lutetium 2, 8, 18, 32, 9, 2  
72 Hafnium 2, 8, 18, 32, 10, 2 4
73 Tantalum 2, 8, 18, 32, 11, 2 5
74 Tungsten 2, 8, 18, 32, 12, 2 6
75 Rhenium 2, 8, 18, 32, 13, 2 7
76 Osmium 2, 8, 18, 32, 14, 2 8
77 Iridium 2, 8, 18, 32, 15, 2 9
78 Platinum 2, 8, 18, 32, 17, 1 10
79 Gold 2, 8, 18, 32, 18, 1 11
80 Mercury 2, 8, 18, 32, 18, 2 12
81 Thallium 2, 8, 18, 32, 18, 3 13
82 Lead 2, 8, 18, 32, 18, 4 14
83 Bismuth 2, 8, 18, 32, 18, 5 15
84 Polonium 2, 8, 18, 32, 18, 6 16
85 Astatine 2, 8, 18, 32, 18, 7 17
86 Radon 2, 8, 18, 32, 18, 8 18
87 Francium 2, 8, 18, 32, 18, 8, 1 1
88 Radium 2, 8, 18, 32, 18, 8, 2 2
89 Actinium 2, 8, 18, 32, 18, 9, 2 3
90 Thorium 2, 8, 18, 32, 18, 10, 2  
91 Protactinium 2, 8, 18, 32, 20, 9, 2  
92 Uranium 2, 8, 18, 32, 21, 9, 2  
93 Neptunium 2, 8, 18, 32, 22, 9, 2  
94 Plutonium 2, 8, 18, 32, 24, 8, 2  

 

 

 

Kinkajou Profile Kinkajou : What is Electron-momentum spectroscopy (EMS)? Is it Important?

Erasmus Profile Erasmus : We show the collision geometry of the EMS experiment. Two analysers detect the emerging particles over a range of angles. If two electrons are detected at the same time, they would originate from the same event. From the measured momenta and energies we can infer the binding energy and momentum of the target electron before the collision. In the picture, we show the target geometry, and the approximate energies of the incident and detected electrons.

Electron Momentum Spectroscopy

The technique that measures quantities most closely related to the wave function is electron-momentum spectroscopy (EMS).  Here the kinetic energies and momenta of an incident electron and two outgoing electrons, detected in time coincidence, are observed and recorded for a large number of events.

For each event the sum of the kinetic energies and momenta of the two outgoing electrons is different from the kinetic energy and momentum of the incident electron. The energy difference is the binding energy of the target electron.

Erasmus Profile Erasmus : The experiment therefore estimates, from the number of target electrons in each small energy–momentum range, the probability of finding an electron in that range. This is the energy–momentum density of target electrons

Each orbital is often calculated as a function of the position of the electron, but it is mathematically equivalent to the orbital represented as a function of the electron momentum.

All the orbitals give the density of the orbitals per unit energy interval and thus the energy–momentum density which we compare with experiment.

Although both coordinate and momentum representations contain identical information, we are more accustomed to visualizing things in coordinate space. We therefore first describe atomic orbitals in momentum space, form an idea of how the orbitals form a chemical bond, and show how the hydrogen-molecule bond can be observed by EMS.

 

 

Momentum Space Orbital Mapping

Two other techniques determine momentum information about electrons in materials.
Compton scattering determines energy-summed and partially momentum-integrated probabilities.

Angle-resolved photoelectron spectroscopy determines the band dispersion relations in terms of energy and crystal momentum for electrons in a single crystal with a flat surface.
Crystal momentum is essentially a set of quantum numbers characterizing the orbital at a particular energy. It is a property of the crystal lattice.

EMS determines the density of the electrons as a function of their energy and real momentum, irrespective of crystal structure. It applies to gaseous, amorphous or polycrystalline materials as well as to single crystals.

Erasmus Profile Erasmus : Three-dimensional plots of the probability density lo(x,y ,0)12 in coordinate space and the probability density JO(px ,py,0)j2 in momentum space are shown for the 1s, 2s, and 2py orbitals of the hydrogen atom.

Note that in momentum and coordinate space the orbitals have the same symmetry.
The importance of EMS is in giving a visual perspective of the information about the shape of an electron orbital. Electron Orbitals have unusual shapes and are not necessarily round.

Elecron Orbiatl Map recreations

Kinkajou Profile Kinkajou : What is so critical about Electron Momentum Spectroscopy?

 

Erasmus Profile Erasmus : Consider the electron as a particle wave surrounding the atomic nucleus. It becomes obvious that the electron has a range of possible momentum values as it travels around the atomic nucleus. That's a problem.

Kinkajou Profile Kinkajou : Why should that be a problem?

Erasmus Profile Erasmus : What this says is that there are times when an electron could be in a higher energy situation as it moves and times when it could be in a low energy situation. The problem is where does the energy go when it hits a low energy phase and where does it come back from when it hits a higher energy point. The system is a closed system with 'One' definite fixed energy level. So other energy levels are 'Not' possible.

The only solution is to accept that the proton and the electron in a Hydrogen Atom are in a stable situation. The hypothesis is then that if energy varies in 3DT ( three dimensions plus time) spacetime, it must be buffered or equalised by energy in x3DT spacetime. (This is spacetime outside of our visible and experienced world: hence the 'x').

Electron Orbital TravelOur answer is that a 'Rel" forms in x3DT spacetime to hold the energy fluctuation related to the electron's orbital vagaries.

This suggests that a relationship exists in x3DT spacetime, to some extent like an elastic cord which in real time buffers the energy and momentum of the electron. When the electron is close to the atomic nucleus, (the Proton), the magnetic dipole moment of the electron is low and hence energy and momentum in 3DT spacetime is low. The relationship "Rel" holds energy in its buffer in x3DT spacetime and the energy in this buffer is high.

And Vice Versa. When the electron is furthest from the atomic nucleus, (the Proton), the magnetic dipole moment of the electron is high and hence energy and momentum in 3DT spacetime is high. The relationship "Rel" releases energy in its buffer in x3DT spacetime and the energy in this buffer is low.

Electron Orbital Binding
The electron is bound on one side
by the nuclear binding energy of the Gluons confining the 3 quarks of the proton, and on the other side
by electromagnetic force.
If the electron is given enough energy to achieve ionisation, it becomes free of the proton.

The electron essentially rattles around the proton in a tightly confined valence or orbital - an energy valley- which nonetheless allows some variability of electron position or momentum. But there needs to be some mechanism for maintaining strict energy conservation no matter what the position or momentum of the electron may be.

 

This situation must occur with predictable regularity in a stable system. There are no forces operating to cause this. There are no changes in electrostatic force that would give a push/pull result and strong and weak interactions seem irrelevant.

The only 'force' that could be involved in this situation is gravity. Gravity is not a 'force' so it cannot be responsible.

Now we believe gravity is a property of matter. But this example shows us a system oscillating in and out of 'stability' and hence having the capacity to generate something like gravity as a by-product of its oscillation.

The effect of gravity in stabilising the electron's movement is wrong. When the electron has lowest energy / lowest momentum and is closest to the nucleus, the effect of gravity is maximal. So the energy balance is down. When the electron has highest energy / highest momentum and is furthest from the nucleus, the effect of gravity is minimal. The energy balance is high.

The big problem is the low energy closest to the nucleus. A stable situation should have a high buffer energy when the electron is furthest from the nucleus.

 

So let's look at the example of the 'Rel'. Link to prior discussion.

Two bits of neutral matter that come together combine into a collection of matter in a gravity well. Energy is missing from this interaction final totally. The energy of the interaction we concluded can only exist in a 'Rel' in x3DT. The energy is missing in the 3DT frame of reference.

Let's analyse this situation with a view to the two particles being the electron orbiting its nuclear proton. When the two particles are closest: lowest energy / lowest momentum in 3DT , the 'Rel" energy is highest. When the two particles are most separated: highest energy / highest momentum in 3DT, the 'Rel' energy is lowest.

THIS IS STABLE and STABILISING.

The final part of the balancing equation is that gravity is created to displace the electron back into a stable orbit.

THIS WORKS.

 

So consider the idea of force or energy. It complicates the example. We get a much more elegant solution if we propose that gravity is a displacement. The electron displaces closer and further away from the nucleus in 3DT. There is a matching push / pull displacement in x3DT.

Goo Goo : So your conclusions from this Thought Experiment?

 

Erasmus Profile Erasmus : Atoms are inherently unstable unless there is a system inbuilt to equalise the electron's displacement changes around the atomic nucleus. It must be suspected that in every atom , a relationship or 'Rel' exists between the negative electrons and the positive atomic nucleus.

This system oscillates regularly and may be the reason why gravity is a property of matter.

If we think of gravity as a force arising from this atomic engine, we are creating matter and energy as gravity is generated by the oscillations of the system. If we think of gravity as a displacement in spacetime, energy balance holds and there are no breaches to the rules for Conservation of Mass or Energy. The 'Rel' holds the energy of the system, generatinga sping like effect stabilising the electron's orbit / orbital.

Gravity appears to act as a force and follows force rules, but in reality is actually a displacement in spacetime.

 

Kinkajou Profile Kinkajou : Are Specific Atoms mor prone to generate more gravity than others?

Short Periodic Table

Erasmus Profile Erasmus : I Think Yes.

Atoms with 's' orbitals have electrons following a predominantly tightly defined and hyperstable path around the proton/nucleus.

Atoms with p orbitals are likely to have the electrons orbiting as a standing half wave in one arm of the "propellor" orbital shape, with occasional bleed through of the half standing wave into the other half of the propellor(becoming a full standing wave). This electron inherently oscillates near and far from the nucleus which would give a maximum amount of momentum / energy change to the electron relative to the atomic nucleus.

There would be a maximum of 6 'p' electrons to match the 3 axes/ 6 directions giving 90 degrees separation of each orbital for maximum stability.

Atoms with maximum 'f' orbitals probably follow the same trend.

The guess would be that gravity balances the "energy / momentum" state via the "Rel' in x3DT. The balance is probably more accurately thought of in terms of 'displacement' rather than momentum / energy.

P Shell Orbital Mechanics

The p shell has a half standing wave electron predominantly in one half of the propellor with occasional bleed through of a full standing wave to the other arm of the propellor. ( I guess).

It gives some thought to the astronomical observation that suns collapse when they have burnt off much of their hydrogen/helium. Perhaps some of the collapse can be attributed to the increase in gravity as periodic elements above helium accumulate - perhaps increasing gravity as well as losing heat energy from burning H / He fuel.

Atoms like C Si Ge, P As,S Se would fit the bill.
Perhaps the ideal atom would be one of the noble gas atoms, though you would seek these in a solid state and the slightest heating effects would vaporize your engine. (Above Helium: all 's' orbitals).

As I have stated before forming polymers may well be the best path to the future rather than using pure atomic elements.

 

 

 

 

 

Erasmus Conclusions