Questions tagged [orbitals]

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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
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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
60 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
52 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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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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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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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
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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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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
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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
165 views

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
120 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 ...
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2answers
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Discrete energy levels of electrons in isolated atom

My question is a duplicate of this. Please consider the equation $\nabla^2\psi + (2m/\hbar^2)[E-V]\psi=0$ (1) Potential of electron revolving hydrogen atom is given as $V=\frac{-e}{4\pi\...
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How many pions can be accomodated in an orbital?

electrons have a spin of 1/2 and 2 electrons are accomodated in an orbital pions have a spin of 0 so how many pions can be accomodated in an orbital? i thought that since no two electrons (or pions) ...
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Orbital angular momentum quantum numbers - subtracted?

Reading Griffiths' Quantum Mechanics. We have the electronic confirmation of Carbon as $$(1s)^2 (2s)^2 (2p)^2$$ in the ground state. He says There are two electrons with orbital angular ...
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3answers
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Expectation value of $x,y,z$ for general $nlm$ state of hydrogen atom

How to calculate expectation value of $\langle x\rangle, \langle y\rangle,\langle z\rangle$ for the general $\psi_{nlm}$ state? $x$ has $\sin(\theta)\cos(\phi)$ angular part which can be expressed as $...
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How to use Dyall basis sets for radial wave functions?

I have found the dyall basis set coefficients on the homepage http://dirac.chem.sdu.dk/basisarchives/dyall/ Does anyone in the forum has experience for using for example the "5p" basis set? I only ...
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1answer
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De Broglie explanation of Bohr's second postulate. discrepancy of 2 times?

I am reading how de Broglie justified the 2nd postulate of Niels Bohr (i.e. angular momentum of an electron to be integral multiple of $\frac{h}{2\pi}$). I get his explanation of electron acting like ...
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1answer
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Pauli exclusion principle for non-stable states

If an electron partially occupy $1s$ orbital, can other electron occupy $1s$ partially, too?
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Probabilities in non-stationary states

I'm confusing myself. Let's represent some state in the eigenbasis for Hydrogen: $$|\psi\rangle = \sum_{n,l,m}|n,l,m\rangle\langle n,l,m|\psi\rangle.$$ Now denote the initial state by $\psi(t=0)\...
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1answer
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Why does a stable orbit of $H$ atom contain an integer number of de Broglie wavelengths? [duplicate]

I was trying to understand why a stable orbit of a hydrogen atom has to satisfy that the orbit length must be a multiple of de Broglie wavelength. I have seen some related questions like This. But ...
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3answers
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Is the $2p\rightarrow2s$ transition possible?

Selection rules in one electron atoms are: $\Delta n=$ any $\Delta l=\pm1$ $\Delta m_l=0,\pm1$ $\Delta s=0$ Parity must change Under strong spin orbit interaction: $\Delta j=0,\pm 1$, but $j=0\...
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Spectroscopic notation for $As$

I’m wondering if I’m approaching hund’s Rules for Arsenic correctly (Ar): (Ar)$(3d)^{10}(4s)^{2}(4p)^{3}$ I started with HR1: Maximize the spin. I have 6 orbitals so I can put one electron in the ...
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Why do nodes exist in wavefuncions of electrons? [duplicate]

Nodes are points in space around a nucleus where the probability of finding an electron is zero. However, is there a reason for the existence of Nodes? I'm looking for an intuitive explanation if ...
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Generating random position for electron within 3D orbitals

Apologies in advance if this is the wrong StackExchange to ask this question in... if it is not, please don't just down-vote, let me know where else to go and I will gladly. I'm just trying to learn. ...