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Questions tagged [orbitals]

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Relation between magnetic quantum number and angular momentum quantum number

The energy levels of a quantum rigid rotator are given by $$ E_{\ell}=\frac{\hbar^{2}}{2 I} \ell(\ell+1), \quad \text { for } \ell=0,1,2,3, \dots $$ It is also stated that the degeneracy of each level ...
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Constructing many-body densities from Kohn-Sham orbitals

In many electronic structure methods, one solves "effective" one-particle Schrödinger equations for one-particle wavefunctions. In my case, I have Kohn-Sham orbitals from a DFT calculation. The ...
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LCAO of molecular hydrogen represented as a vector

I wanted to ask a question about the MO of a Hydrogen Molecule, H$_{2}$. I was learning today - in my first lesson about vectors for orbital physics - about the applications of vectors in orbital ...
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Why do all atoms follow the same $n$ and $\ell$ quantization conditions as hydrogen? [duplicate]

The quantum state of an electron in a hydrogen atom is specified by 4 quantum numbers: $n$ , $\ell$, $m_\ell$, $m_s$ which can take the following values: $$n = 1, 2, 3, ... $$ $$\ell = 0, 1, 2, 3, ......
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Query about Heisenberg uncertainty principle

acoording to heisenbergy uncertainty principle if the electrons change the radius of their orbit, then it is like making transition even though the change in radius is small and they should emit ...
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Why does transition from one electron shell to another shell always produce massless photon?

When electrons transition from a higher energy state to a lower energy state (energy difference $E$), they produce massless photon with frequency $\nu$ where $ \Delta E= h \nu$ (h is Planck ...
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3answers
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Do electrons in the same orbital but different spin feel each other's Coulomb repulsion?

Or is it irrelevant, as orbitals are QM while Coulomb interactions are classical physics? What I think I understood of orbitals is that particles with the same quantum numbers cannot occupy the same ...
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What led Bohr to come up with the idea of quantization of angular momentum? How Bohr Proved this idea? [duplicate]

How did Bohr come up with the idea of quantization of angular momentum? In the proof of quantization of angular momentum we use de Broglie wavelength concept and de Broglie wavelength concept was ...
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1answer
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In De Broglie's Explanation for Bohr's Quantization Condition, why do we not use 2πr = n λ/2, why do we use 2πr = n λ?

In de Broglie's explanation for Bohr's quantization condition, why do we not use $2\pi r = n\lambda/2$, why do we use $2\pi r = n\lambda$? We know that in waves on strings, for standing waves ...
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What exactly does it mean for an element to experimentally violate the Madelung ordering rule?

The Madelung ordering rule says that as you increase the atomic number of a neutral atom, the electron orbitals fill up in order of increasing value of $n+l$, and in increasing order of $n$ within a ...
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Naive question on the development of quantum numbers

In my freshman Chem 101 course, we are going over the development of the atomic model upto the basic modern quantum model. I learned that the azimuthal and magnetic quantum numbers were introduced to ...
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1answer
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Difference between $nh/2π$ and $\sqrt{\ell(\ell+1)}h/2π$

My textbook mentions that the orbital angular momentum is the second formula and the angular momentum of an electron is given by $nh/2π$ in Bohr model. Please help me realise the link between these ...
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1answer
118 views

Can an electron be inside a proton?

This article has an image showing the 2S and 2P states of a hydrogen atom. The caption makes the following claim: The 2S and 2P states of hydrogen show where the electron could be found at any ...
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1answer
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Interaction between electrons in which the magnetic dipole moments interact more strongly than their electric fields

Asking a question Has anyone tried to incorporate the electrons magnetic dipole moment into the atomic orbital theory?, I was curious whether anyone has attempted to relate the intrinsic property of ...
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Determining the binding energy in the L-shell in copper

Im having trouble grasping the following problem: Calculate the binding energy in the L-shell for copper, if the binding energy for the K-shell is $ \ 1,439*10^{-15} J\ $. I know that you find the ...
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3answers
135 views

Are the electrons' orbitals the same for all atoms?

Are the electronic orbitals of an atom always quantified in the same way (i.e. the same energy required to reach the next level), or does each atom have its own values for each level? If the ...
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1answer
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Why is order of electron orbital filling not completely sequential? [duplicate]

Orbitals fill in the following order, 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, etc. Its a nice pattern that many elements follow, but there are exceptions to. For example: V: 1s2 ... 4s2 ...
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What is a pseudo wave and how to calculate it?

In a description of the density of states in https://wiki.fysik.dtu.dk/gpaw/documentation/pdos/pdos.html I find the term pseudo (partial) wave (in the section Molecular Orbital PDOS). What is it and ...
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Has anyone tried to incorporate the electrons magnetic dipole moment into the atomic orbital theory?

The Pauli exclusion principle is related to the electrons spin. The quantum numbers are complete only with the spin quantum number. I am curious whether anyone has attempted to relate the intrinsic ...
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2answers
77 views

Path of an electron around a nucleus [duplicate]

I have just started reading about quantum mechanics and i stumbled upon this silly question - Quantum mechanical model of an atom says that path of an electron around the nucleus is uncertain. Then ...
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1answer
66 views

What was the origin of Bohr-Sommerfeld's quantization rules?

What made Bohr and Sommerfeld think momentum and angular momentum is quantized? What is the meaning of momentum quantization in harmonic oscillator? Can we imagine it (by some classical example)?
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Can the spectra of helium atom be solved by Schrodinger equation?

Can the Schrodinger equation work out the spectra of helium atom, not all, but part of them?
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Has man ever observed the spectrum of a single hydrogen atom?

Were there this kind of experiment done before? The spectrum we observed is radiated by huge number of hydrogen atoms in the gas, not by single hydrogen atom. I know it's very hard to test a single ...
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2answers
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Why Bohr atom model is still being tought in high school? [duplicate]

Bohr atom model is still the textbook content of today's high school physics. We all know that the Bohr model is only suitable for single electron hydrogen atom, not suitable for other atoms. For ...
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Do electrons really perform instantaneous quantum leaps?

This is not a duplicate, non of the answers gives a clear answer and most of the answers contradict. There are so many questions about this and so many answers, but none of them says clearly if the ...
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Crystal Field Theory (CFT) in $s$-$p$ orbitals system

Crystal Field Theory (CFT) is a model that describes the breaking of degeneracies of electron orbital states, usually d or f orbitals (Source: wiki). My doubts: Is it possible to have CFT effect in ...
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1answer
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Why don't all electrons contribute to total orbital angular momentum of an atom?

There are 47 electrons in a Silver atom, but talking about its orbital angular momentum we only take the outermost valence electron which occupies the 5s orbital. Why don't the remaining inner 46 ...
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0answers
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How to calculate orbital densities/shapes of atoms in 3D?

When we read about orbitals, I'm sure we are all used to seeing illustrations of them by drawing some contour "along" the probability density function so that the electron's position is equiprobable ...
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51 views

Spacial Wavefunction Symmetries and Identical particles

I was reading this and it mentions in the 3-electron section, that for a spacial wave function to be symmetric under fermion swapping, it must be a function of even parity. Similarly for anti-symmetry ...
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How can I calculate the hyperfine structure of a $p$-orbital?

I have a little problem with the calculation of the hyperfine structure of the 3p orbital in the hydrogen atom. The Hamiltonian is: Were represents the magnetic moment of the proton and the ...
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1answer
98 views

Role of d-band in metals

I have seen that in many publications authors discuss the metals in the d-block of the periodic table (often called 'transition metals') separately from other metals (e.g. alkali metals and aluminum). ...
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1answer
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Neutral lithium ionization energy for removing an electron from the $1s$ orbital

How much energy does it take to singly ionize a neutral lithium atom by removing an electron from the $1s$ orbital?
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1answer
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In chemical compounds, where does the “magic” come from in atomic “magic numbers”?

It is well known that atoms with a full electron shell are more stable, it is one of the first facts taught in a middle school Chemistry course: "An element whose atoms have no electrons outside ...
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1answer
63 views

What is so special about Paschen, Balmer and Lyman series?

I'm reading McIntyre's QM book and I see the same diagram ever so often: He goes on to say: I don't understand what he is trying to say with the last sentence. It seems he is saying, that ...
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How to deduce the SK (Slater-Koster model) integral for two-center with px, py orbital?

I would like to get the Slater-Koster integrals from formula: $$ \sum{R_j}expi\textbf{k}\cdot(R_j-R_i)\int\psi^*_n(\textbf{r}-\textbf{R}_i)H\psi_m({r}-\textbf{R}_j)d\nu, $$ (1) where the sum is ...
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1answer
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Prove acceleration in orbit with newtons second law

I want to prove that the acceleration in a orbit at a given point r=(x,y) is $a=-\frac{GM}{R^3}r$ (My professor said this can be proven by newtons second law, but he never explained in detail how). I ...
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2answers
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About the size of the orbitals $s$, $p$, $d$, etc, in $H$ atom

Can we define a size for the H atom orbitals which are not spherically symmetric, e.g. $p, d$ etc? For example, is it meaningful to say that the $(n+1)p$ orbital is larger in its extent than $np$ ...
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1answer
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What is this angular momentum coupling notation? $\langle \ell 2 m_\ell 0|\ell 2\ell' m'_\ell\rangle \langle \ell 2 0 0|\ell 2\ell' 0\rangle$

I'm reading this unsigned powerpoint presentation of the Nilsson model in nuclear structure physics. On p. 15, they have this: $$\langle \ell'm'_\ell|Y_{20}|\ell m_\ell\rangle = i^{\ell-\ell'}\sqrt{\...
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2answers
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Why do electrons revolve around the nucleus? [duplicate]

Why do electrons revolve around the atom's nucleus? Where does it get the energy for the revolution? Do the electrons stop revolving at absolute zero temperatures?
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1answer
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Why can there be more than one electron in an energy level if electrons are fermions?

By the Pauli-Exclusion Principle, no two electrons can be in the same quantum state. So, how can both be in the same energy eigenstate? Atom orbitals certainly have more than one electron per energy ...
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Band formation in diamond

Why is it that in the band diagram of diamond does the sp3 hybridised orbital split into two forming valence band and conduction band? I thought that these sp3 hybridised orbital forms 4n bonding and ...
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In the pilot-wave theory, is the quantum potential moving electrons randomly inside atoms?

As we know, in the pilot-wave theory (Bohmian mechanics), particles are guided on certain trajectories by the wavefunction. Here (In Bohmian mechanics, do electrons move inside an atom?) I asked about ...
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Do atomic orbitals “pulse” in time?

I understand that atomic orbitals are solutions to the time-independent Schrödinger equation, and that they are are analogous to standing waves ("stationary states"). However, even a standing ...
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2answers
136 views

If angular momentum of an electron in $s$-orbital is zero, then is it true that the electron doesn't move?

If the electron does move, then what is the factor that leads angular momentum of the electron in s-orbital to be zero?
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What are the prerequisites for a free electron and an atom/ion to recombine?

I'm mostly interested about recombination not in plasma (e.g., recombination of beta particles with atoms that they pass by), although the rules are probably the same. Say, there's a free electron ...
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3answers
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Shape of orbitals in atoms with multiple electrons

I found this statement when browsing the Wikipedia article for atomic orbitals: "Orbitals of multi-electron atoms are qualitatively similar to those of hydrogen." Is this true? Googling around I ...
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When an electron around an atom drops to a lower state, is 100% of the energy converted to a photon?

Let's say we have an electron around atom. Let's say the electron drops into a lower electron shell. Is 100% of the energy difference converted to a photon? Does the atom recoil at all? Is the any of ...
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1answer
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Atomic model - absorption [duplicate]

I have a question regarding the absorption of light in e.g. hydrogen atoms: I didn't quite understand how the electron knows that it can only absorb photons of the right energy. I thought that when ...
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Question about Electric Dipole Transition Selection Rules [duplicate]

I learned that the selection rules for electric dipole transition in a hydrogen-like atom is \begin{align} \delta l & = \pm1 \\ \delta j & =0,\pm1 \\ \delta m_j & =0,\pm1 \end{align} I ...
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Aufbau principle and quantum number $n$ (Bohr) [duplicate]

When we have to check the energy of electron we look for $n+\ell$ as in filling of electrons A/t aufbau? Or is just simply higher then value of $n$ then more the energy of electron? Because when we ...