Questions tagged [orbitals]

An orbital is the mathematical function describing the location and wave-like behaviour of an electron in either an atom ( for atomic orbitals) or in a molecule (molecular orbitals).

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Would a high energy Hydrogen atom start emanating electromagnetic radiation?

We know that the total energy of the hydrogen atom is proportional to the inverse of the square of the principal quantum number $n$: $$E_n \propto -\frac{1}{n^2}$$ So at high quantum numbers the ...
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Fine structure of chlorine - energy levels and total angular momentum $J$

The table below summarizes the energy levels of neutral chlorine with fine structure. I know that lower values of $J = L + S$ should be associated to lower energies. This is confirmed by the intuition ...
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How much energy is released in high orbital hyperfine transitions?

The famous 21 cm Hydrogen Line happens due to the hyperfine transition of the 1s electron spin in Hydrogen orbital cloud. If a hyperfine transition were to happen in other elements highest orbital ...
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What are s-bands and d-bands in band structures?

Given a band structure diagrams I can understand whether there are band gaps and what the bands are but what are s-bands and d-bands and how do I tell them apart in these diagrams? Example: I ...
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Why do electrons in an atom only occupy stationary states, without superposition?

In simple quantum mechanical problems such as the infinite square well, we solve the Time Independent Schrodinger's equation by separation of variable, effectively getting the energy eigenstates of ...
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How can the electron in a hydrogen atom have energy without angular momentum ($n>0$, $\ell=0$)? [duplicate]

Been struggling with this concept. Or is this just one of those things in quantum mechanics which attempting to understand is futile? Guess we can see it as the electron just linearly oscillating back ...
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Is my understanding of the limitations of the Bohr model related to atomic spectra correct?

I'm talking about a neutral hydrogen atom here: According to Bohr, if the electron jumps from $n=2$ to $n=1$, there'd be only one wavelength of light being emitted. However, that is not the case we ...
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What is the magnetic quantum number for $p_x$, $p_y$, $p_z$?

After tons of research, I've come to the conclusion that the $p_x$ and $p_y$ orbitals can have either $m_\ell=+1$ or $-1$, but $p_z$ is $0$. But my professor said that we can attribute any $m_\ell$ ...
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How many $\rm d$ orbitals do I have in $\rm [Ar]3d^{10}4s^1$ configuration materials?

I have noticed in a book the following band configuration for copper: But I think I read in the book that each band has 2 electrons if it is fully occupied. But in here I see only four 3d types of ...
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Is there a lowermost limit to a hybrid orbital's energy level?

Mixing of atomic orbitals is intended to lower the overall energy of the system, but there must be a fundamental limit to this. Is there any way of calculating or estimating a specific value?
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Grotrian diagram for Helium

Hi, is this Grotrian diagram for helium wrong? I can't understand how a $1s2d$ state is possible since my understanding was that the $d$ states only start at $n=3$?
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How does one calculate the Bohr energy of an electron in a non-atomic systems?

When calculating the orbital energy of an electron in a hydrogen-like atom, the orbital velocity is required. However, to derive this value, the equation given is: \begin{equation*} ZK_{e} e^{2}/r^{2} ...
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Is there a relationship between $p, d, f, d$... orbitals and $p, d$... block elements?

In the quantum mechanical model of an atom there are various orbitals around the nucleus as: $p$ orbitals, $s$ orbitals, $f$ orbital, $d$ orbital etc. And in the periodic table there are p block ...
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Modes vs. Orbitals

I'm studying some very general, mathy, not-necessarily-realistic models which can be represented with fermionic operators or bosonic ones (not both though). One thing I keep seeing is the usage of &...
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Why did Rutherford's atomic model predict a continuous emission spectrum for hydrogen?

When researching the flaws of Rutherford's atomic model, I get that one of them is that it predicts the electrons would spiral and collapse into the nucleus. However, I don't understand the second ...
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In the Bohr model of the atom, does the centripetal force balance out the electrostatic force? [closed]

Is this picture correct? It's the Bohr Model for electron moving around the nucleus. In my opinion, the centripetal force should be directed towards the center, and the electrostatic force should be ...
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Is there direct verification or proof of the orbital probability clouds of Hydrogen using Schrodinger wave function? [duplicate]

The different probability cloud shapes of the Hydrogen atom (consisting of one proton and one electron) can be solved using the spherical wave function. The answer is often summarized as follows: ...
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How did Rutherford conclude that the electrons orbited the nucleus in his planetary model? And another way to explain the mass was mostly in nucleus?

In the Geiger-Marsden Experiment, I get how he knew that the nucleus was positively charged, and I'm assuming he knew it was small because the scattering through large angles only happened every 8000 ...
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Azimuthal quantum number for $sp^3$ hybridization

The $s$ orbital corresponds to $l=0$. The $p$ orbital corresponds to $l=1$. For an electron in an $sp^3$ hybridization orbital, what is $l$?
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Why isn't the molecule of water linear straight?

When you see models of water you see something like this: The hydrogens in the water molecule become negatively charged because the oxygen pulls electrons more. So why don't they repel and move to ...
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1answer
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Can different electron orbitals within the same atom be entangled?

Could the electron in the outer shell orbital be entangled with an electron within the inner S orbit of the atom? If so, how would this affect the properties of such an atom, such as emission and ...
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Can micro black hole hold electron and create atom?

Protons have a positive charge and hold negatively charged electrons in atoms. Thanks, quantum mechanics rules electrons don't fall to the nucleus. If we substitute the atomic nucleus with a micro ...
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On which quantum numbers the energy eigenvalues of a multielectron system depends?

We usually read the case for a hydrogen atom where we find that the potential energy depends only on the variable $r$ and the energy eigenvalues are dependent on principal quantum number only. What ...
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Do fermions of different types have the same quantum states available to occupy?

I'm not asking whether two fermions of different types can occupy the same quantum state, cf. the Pauli exclusion principle. I'm asking whether fermions of different types would have the same options ...
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Hydrogen atom orbital projections resemble to some Chladni figures! Mathematical reasoning?

Chladni figures are formed by sprinkling salt on a vertically vibrating membrane, f.e. [. Some of them are purported to be projections of hydrogen atom orbitals f.e. 1s, 2s, 2p, 3d, etc., e.g. . One ...
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Do paired electrons have no higher order magnetic multipoles?

An electron pair consists of an up and down electron in an energetically favorable condition where their magnetic dipole moments cancel each other. However, does that also mean they have no quadrupole ...
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1answer
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Does changing energy level of electron in an atom has time duration? [duplicate]

In quantum mechanics electron in an atom is described by the wave function of probability. When the electron changes level the wave function changes to another. Is the changing electron level when it ...
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During promotion of electron in $3p$ orbital before hybridisation, why does it get promoted to $3d$ orbital and not $4s$?

During the hybridization of certain elements such as phosphorus during the formation of $\rm PCl_5$, the atom first gets changed to the excited state. In the case of $\rm PCl_5$, the paired electron ...
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Why do we need the radial probability distribution function?

I know that the radial probability distribution function gives us the probability of finding an electron between in a spherical shell of thickness $dr$ which is at a distance $r$ from the nucleus. Now ...
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Pauli Exclusion Principle Violation, Why is Energy Quantized?

The orbitals of an atom can be thought of as being formed from the probability of finding electrons in those orbitals. If the orbital is 1s (n = 1, l = 0), then it has a certain "volume" for ...
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Location of Orbital inside atom

So, I was am having a hard time understanding the location of an orbital inside an atom. I read that: Within each subshell, there are orbitals. This gives the final location of where electrons reside ...
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Is 5 km/s enough to escape Earth's gravitational field? [closed]

A particle is fired vertically upward with a speed of $15\,\mathrm{km}/\mathrm s$. With what speed will it move in interstellar space? Assume only earth's gravitational field. So this is a question ...
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How to work out the multiplicity of Uranium Hexafluoride?

Consider the uranium atom which itself has a multiplicity of 5 since it has 4 unpaired electrons, each with half a spin, and so the total spin S =2 and so 2S+1 is 5. I am trying to work out the ...
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Do all of the energy levels listed in Hydrogen Spectral Series assumed to be s ('sharp') sublevels?

When reading about the hydrogen spectral series (Lyman, Balmer, etc.) I noticed that nowhere are suborbital or sublevels (azimuthal) mentioned; only principal quantum numbers n .... Are there any p or ...
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Is the atomic shell model valid considering electron-electron interaction?

In atomic physics the shell model is motivated by starting looking at the H-atom. Solving Schrödinger's equation leads to atom orbitals labled by quantum numbers n,l,m. Taking Pauli's principle into ...
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What happens to an electron if given quantized energy to jump to a full orbital?

Let's consider the element neon. Its ground-state electron configuration is: $1s^2 2s^2 2p^6$. What would happen if enough energy was given for one electron in the $1s$ orbital to jump to the $2s$ ...
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If free electrons have classical trajectories, then why don't bound electrons around the nuclei have it too?

I have read this question: Changes to chemical properties of elements due to relativistic effects are more pronounced for the heavier elements in the periodic table because in these elements, ...
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2answers
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Do $2s$ and $2p$ orbitals have same energy?

While solving the Schrodinger equation for the H atom, we get $E_n$ depending exclusively on $n$ (actually on $\frac{1}{n^2}$). Then I thought 2s and 2p orbitals must have the same energy. But while ...
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Why are $L=S=0$ in full shells? Spectroscopic notation

There are some threads on this question but I'm still not understanding this considering the following scenario: If we take for example Helium in its ground state so $1s^2$. Here obviously $L=0$, but ...
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Why does the $2p$ orbital have lower energy than $2s$? [duplicate]

I know there already are questions about this. But I find some error there. So, I asked again.... The answers I have read mostly point out that electrons in 2s orbital have a higher probability to be ...
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Does energy change with change in position of electron (in quantum model)?

In the quantum model of atom, an electron has a probability of being found anywhere in the space (except nodes). Now suppose a first shell electron ($n=1$) is present at a distance $r1$ from the ...
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Why does the energy of an atomic orbital depend on the proximity to charges?

I was recently reading about Crystal field theory and especially crystal field splitting in the context of transition metals in coordination complexes. Here is what I think I have understood – or what ...
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How do particles that exist only as a cloud of probabilities have actual rates of speed?

I recently asked a question about why relativistic effects come into play only with the superheavy elements. The top answer I got was pretty good and I understand most of it, but the answer brought up ...
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Why do "relativistic effects" come into play, when dealing with superheavy atoms?

I have now read on the Wikipedia pages for unbihexium, unbinilium, and copernicium that these elements will not behave similarly to their forebears because of “relativistic effects”. When I read about ...
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Confusion about ionised atom, free electron, conduction band, donor energy level and acceptor energy level

I have some confusion about the concept of some electronic bands and energy levels. Beyond valance band, For an atom, can having at least one electron in the conduction band mean that the atom has ...
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Submerged shells, why are the valence electrons not in the outermost shell?

The valence shell of an atom, is the set of orbitals which are energetically accessible for accepting electrons to form chemical bonds. For various atoms, the valance electrons are submerged beneath ...
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Is the Larmor precession of $s$-orbital electrons constant, heedless of additional electronic orbitals as they get added from one element to another?

Understanding how the frequency required in NMR changes from element to element, even if all of them depend on the Larmor precession of the proton, I was wondering if they same applied to electron ...
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What is the meaning of negative energy?

In Bohr's model I studied that energy of an electron in the $nth$ shell is given by: $$E_{n}=-13.6 × \frac{Z^2}{n^2} eV.$$ Clearly, the energy of the electron comes out to be negative. But what is the ...
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Do the magnetic fields of paired electrons vanish everywhere, or do they form a magnetic circuit within the orbital?

As far as I can tell, that paired electrons produce opposing magnetic dipole moments does not rule out the possibility that they produce a toroidal moment. Is it possible in quantum mechanics that ...
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What exactly are quantum numbers and how do we obtain them? [duplicate]

While studying atomic orbitals, I came to know about the quantum numbers $n, l, m$ and $s$. I studied that solving the Schrödinger wave equation for atoms gives us the allowed energy levels of the ...

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