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Dual Op Amp
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How would three P orbitals, X,Y,Z, in the same subshell, give the electrons different quantum energies?
Dual Op Amp said:How would three P orbitals, X,Y,Z, in the same subshell, give the electrons different quantum energies?
This is correct. It is a kind of crystal field splitting.marlon said:When you would apply an extern electric field, the three orbitals will position themselves in three different ways, each corresponding to a different energy-level.
These statements are false in classical mechanics, as demonstrated onso-crates said:At a given energy, a circular path has minium angular momentum and that is why S orbitals with appear spherical. The more eccentric the orbit (more elliptical) the more angular momentum it posseses at a given energy. Thus as l increases, orbitals get more eccentric and spike-like.
I agree, but the classical analogy is useful when one wants to explain why s-orbitals at the same time have a high electron density at the nucleus and extend further from the center of the atom.reilly said:A classical orbit with zero angular momentum is impossible -- there are two ways to get a L=0 state: a particle at rest, a particle in linear motion incident on the proton/CM.
Pieter Kuiper said:I agree, but the classical analogy is useful when one wants to explain why s-orbitals at the same time have a high electron density at the nucleus and extend further from the center of the atom.
Of course, that is the way to calculate the expectation value of the electron distance to the nucleus. The outcome is n^2 times the Bohr radius.ZapperZ said:Again, we need to be a bit careful here. While it is true that the radial wavefunction R_nl for l=0 has a probability density that peaks at r=0, if we want to say anything about the electron position, then what is relevant is the product of rR_nl. This is because you need to actually find the probability of the average position via |<R_nl|r|R_nl>|^2.
The product rR_nl is a way to calculate the radial density P(r) for finding the the electron at a distance r from the nucleus. It is related to the probability density by [tex]r^2 |\Psi(x,y,z)|^2[/tex]. The radial probability is zero at the origin because a point has zero surface and volume.Already, you can tell that r=0, something else happens. In fact, it is ZERO at r=0. So the electron really does not have a substantial probability to be right at nucleus.
Pieter Kuiper said:In contrast to orbitals with [tex]l \neq 0[/tex], s-orbitals do have a contact density at the nucleus. This is measurable. It is responsible for the Knight shift in nuclear-magnetic-resonance experiments and for the isomer shift in Mössbauer spectroscopy.
In a very simple picture, delocalized electrons are like a free electron gas, so they are everywhere, also at the nuclei. If you put in the attractive Coulomb potential, the density at the nucleus increases, and these electrons have local s-character.ZapperZ said:I'm not sure how you can tell, based on the Knight shift measurement, that there is a "contact" density of the s-orbital electron with the nucleus. The shift in the resonance frequency, especially in metals, have NOTHING to do with any "contact" between any electrons and the nuclei in that metals. This has everything to do with the nuclear interaction with the conduction electrons, which certainly is WAY out of the nucleus since these are delocalized electrons.
You are wrong. The radial density (the chance of finding an electron in a shell with thickness dr and radius r) decreases as r decreases, simply because the volume (the surface) of the shell decreases. But the electron density of s-electrons increases towards the nucleus.The issue here is still that the expectation value of finding an s-orbital electron at the nucleus DROPS towards zero as one approaches the nucleus for a radius less than some mean value. At the very least, it is inaccurate to say that "...s-orbitals at the same time have a high electron density at the nucleus."
Pieter Kuiper said:In a very simple picture, delocalized electrons are like a free electron gas, so they are everywhere, also at the nuclei. If you put in the attractive Coulomb potential, the density at the nucleus increases, and these electrons have local s-character.
The Knight shift measures contact density of the wave function at the Fermi level, so one can only do this for metals. The isomer shift in Mössbauer is a bit easier to interpret. It "arises due to the non-zero volume of the nucleus and the electron charge density due to s-electrons within it." http://www.rsc.org/lap/rsccom/dab/mossbauerspec/part2.htm
You are wrong. The radial density (the chance of finding an electron in a shell with thickness dr and radius r) decreases as r decreases, simply because the volume (the surface) of the shell decreases. But the electron density of s-electrons increases towards the nucleus.
http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_2.html
Of course their wave functions have to be orthogonal to the wave functions of the core electrons. Close to the nucleus the wave functions of the conduction electrons in say sodium are very similar to atomic Na 3s wave functions. Qualitatively (number of radial nodes) these wave functions look like hydrogen 3s wave functions.ZapperZ said:Er... no. These delocalized electrons are everywhere in the material, but this is a "cartoon" picture as an approximation. There are no indication that they actually penetrates right to the nucleus, simply because the core-level electrons are still there! The fact that they are the outermost electrons is the reason why their atomic orbitals have been hybridized with neighboring atomic orbitals and thus, they do not retain any isolated energy levels.
Your retreat is rather ungracious.Again, there appears to be a misconception regarding R_nl and rR_nl. I have indicated that the probability density of the radial part of the wave function for all l=0 DOES peak at r = 0. However, you cannot use this to say that this then indicates that the s-electron spends MOST of its time at the nucleus, or has the highest probability of being found at the nucleus. The mathematics just does not agree with that.
Pieter Kuiper said:Of course their wave functions have to be orthogonal to the wave functions of the core electrons. Close to the nucleus the wave functions of the conduction electrons in say sodium are very similar to atomic Na 3s wave functions. Qualitatively (number of radial nodes) these wave functions look like hydrogen 3s wave functions.
The clearest indication that s-symmetry wave functions penetrate core-level electron clouds comes from the periodic table: the energy of the 4s orbital in potassium and calcium is lower than the energy of their 3d orbitals. This energy difference is due to the stronger coulomb interaction of the nucleus with the 4s electrons. The 3d electrons are in circular orbits (classically speaking) and do not get that close to the atom's core.
Your retreat is rather ungracious.
I never said "most of its time". I made the comparison with comets. Most of the time they are frozen at distances beyond Pluto. But once in a while they come for a short time close to the sun.
I just said that the probability density of s-electrons is high at the nucleus.
And earlier you said that was inaccurate.
Let me concede this trivial truism, and end my discussion with you.ZapperZ said:If you are using this argument, then you cannot ignore the expectation value calculations, which clearly stated that at r=0, |<r>|^2 is zero!
The octet rule is a chemical idea from before quantum mechanics with "cubical atoms" and things like that.Dual Op Amp said:I'm saying quantum physics states that no two electrons can have the same energy, and since the higher the shell, the more energy, no two electrons can exist in the same subshell. except for the fact that two electrons can spin in the opposite direction. Yet, there are a total of 3 P orbitals in an octec obeying atom, that's 6 electrons, not 2.
Dual Op Amp said:Okay, now I'm getting it.
N, is the energy or shell of the electron.
L, is the angular momentum of an electron, L is determined by L=n-1.
M, is the orientation or orbital of the electron.
Ms, is the spin of the elctron.
Are you saying there is something wrong with what Dual Op Amp says here?so-crates said:Not quite. L is the orbital 'type' (s, p, d, f).
Pieter Kuiper said:Are you saying there is something wrong with what Dual Op Amp says here?
Now that I understand this, I realize this was a great explanation.The Pauli principle states that no two electrons can have the same set of principle quantum numbers. These numbers are n, l, m_l, and m_s.
n is the principle quantum number that would be identified as the energy level, starting at 1. This is the first number in your electron configuration. For example hydrogen with a configuration of 1s2. The 1 is the principle quantum number.
l is your angular quantum number. Its range is 0...n - 1. This represents your “s,p,d,f” orbitals. For an s orbital, l = 0, for a p orbital, l = 1, and so forth. This number represents the angular momentum of the orbit. At a given energy, a circular path has minium angular momentum and that is why S orbitals with appear spherical. The more eccentric the orbit (more elliptical) the more angular momentum it posseses at a given energy. Thus as l increases, orbitals get more eccentric and spike-like.
m_l is the magnetic quantum number, whose range is -l(“l” not one)... -1, 0, 1 ... l. We see here that for l = 1 (the p orbital), l can be either -1, 0 or 1. Thus at the we have three different p orbitals which are conveniently called x, y and z.
m_s is the spin magnetic quantum number, also called "electron spin", which can be +/- 1/2.
The key here is that unless the atom is in a magnetic field, you cannot distinguish between the different m_l and m_s values.
Also keep in mind we are talking about individual atoms and not molecules. For molecules, things get more complicated with hybridized orbitals and bonding/anti-boding orbitals.
This i s NOT because of Coulomb repulsion.Dual Op Amp said:I think it's because electrons repell each other, but they are attracted to the proton. So, they orbit around it in shells, to stay away from each other, but to get as close to the nucleus as possible. Maybe that explains quantum physics. Maybe that explains why no two electrons can have the same quantum numbers.
When you get to molecules its a whole different ball game, because your electron orbitals are no longer isolated to the atom, but you must include BOTH atoms. You start to have "bonding" orbitals and "antibonding" orbitals. This is why, for example, the emission spectra of (plain old oxygen) is different than it is for , (ozone), because the electrons in these molecules are allowed different energy levels
3 P orbitals are a type of atomic orbital that are shaped like dumbbells and are associated with the energy level of the third principal quantum number (n=3). They are found in the electron shell of an atom and can hold up to 6 electrons.
Quantum energies of 3 P orbitals are explored through various experimental techniques such as spectroscopy, which involves studying the interactions between matter and electromagnetic radiation. These experiments provide information about the energy levels and transitions of electrons within the 3 P orbitals.
Exploring quantum energies of 3 P orbitals allows us to better understand the behavior of electrons in atoms and molecules. This information is crucial in fields such as chemistry, materials science, and quantum physics, and can also lead to advancements in technology.
3 P orbitals have a different shape and orientation compared to other types of orbitals, such as s and d orbitals. They also have different energy levels and can hold a different number of electrons. Additionally, the 3 P orbitals have a higher energy than the 2 P orbitals, but lower energy than the 4 P orbitals.
Understanding quantum energies of 3 P orbitals has many practical applications, such as in the development of new materials and drugs, as well as in the design of electronic devices. It also helps in predicting the chemical reactivity and properties of molecules, which is essential in fields like pharmaceuticals and nanotechnology.