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Questions tagged [orbitals]

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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
76 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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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
56 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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0answers
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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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2answers
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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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106 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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3answers
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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
47 views

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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0answers
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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
63 views

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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2answers
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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
49 views

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
51 views

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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2answers
644 views

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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0answers
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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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2answers
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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. ...
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When will Hund's rules fail?

I heard someone mentioned that Hund's rules do not always work. Looking at atomic spectrum: (https://qudev.phys.ethz.ch/phys4/PHYS4_lecture10v1_2page.pdf page 10 Hg spectrum) How could singlet (with ...
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1answer
86 views

$sp^3$ Hybridization wavefunctions and probability density

I have plotted a hydrogen-like sp3-hybrid orbital probability density and it looks like this: I can plot 4 overlapping probability densities in a tetrahedral shape: So far it looks OK. But when I'm ...
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1answer
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What does degeneracy and multiplicity in Term symbol mean?

$^{2S+1}L_J$ was the term symbol. I watched a video online saying $2J+1$ was the fold of degeneracy to the term symbol. Specifically, for nitrogen, the term symbol for the lowest energy was $^4S_{3/...
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Why does 'The electron density builds quadratically with distance from the nuclues.'?

I found the statement above on this useful website. http://photonicswiki.org/index.php?title=Atomic_Orbitals_and_Nodes But I am confused. Why would that be the case? Is this based on some exotic ...
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0answers
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How does the hydrogen atom actually “look like”? [duplicate]

When deriving the solutions for the "simple" quantum mechanical hydrogen problem, one normally uses spherical coordinates $(r,\theta,\phi)$, since the problem has rotational symmetry. The solution has ...
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How does an electron know whether a photon is of correct energy states? [duplicate]

Since to become excited an electron in its ground state have to absorb a particular frequency of light otherwise they will just pass through each other, I'm thinking how can the electron measure the ...
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How come the xenon $6s$ state is metastable?

I'm having some trouble puzzling out some aspects of the electronic excitation spectrum of xenon, and I'd appreciate some help with it. This classic paper ─ the first one to pioneer the use of laser-...
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$\langle r \rangle$ and orbital energy [duplicate]

Even though $\langle r_{2s} \rangle > \langle r_{2p} \rangle$ based on the following formula $$ \langle r_{n\ell} \rangle = \frac{{a}_{0}}{2}(3{n}^{2}-\ell(\ell+1)) $$ $2s$ has a lower orbital ...
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1answer
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What happens to the $3d$ and $4s$ levels during the ionisation of a transition metal?

I'm just wondering about the transition state of a transitional metal before (ex: $[\mathrm{Ar}]\, 3d^3 \,4s^2$) and after ionisation (which means $[\mathrm{Ar}]\, 3d^3 \,4s^1$) because before ...
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1answer
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Must the total orbital angular momentum quantum number $L$ be less than the principal quantum number $n$? If so, why?

I am studying LS coupling and term symbols. In my textbook, there is an exercise: Why is it impossible for a $2\ ^{2}\text{D}_{3/2}$ state to exist? The answer says, the total orbital angular ...
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4answers
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Could an electron enter the nucleus, and if so would it be captured by a proton?

I've been trying to find an answer to this question, but have come across contradictory answers, and have limited knowledge of quantum mechanics myself. Almost all the threads (here and on Quora) ...
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What are the experiments performed to determine the position of an electron inside an atom to verify the probability wave function data?

What are the experiments performed to determine the position of an electron inside the atom to verify the probability wave function data? Is it possible to do those experiments in real life?
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Understanding the radial distribution function [duplicate]

I am confused why the maximum of the radial distribution function for 2p orbital is closer to the nucleus than that for 2s orbital. Doesnt this mean that there is a higher chance of finding 2p orbital ...
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1answer
191 views

How to get the radius of Bohr from the uncertainty principle?

I would like to know how to get the following result: \begin{eqnarray} a_0=\frac{4\pi\varepsilon_0 \hbar^2}{\mu e^2} \end{eqnarray} from the beginning of the uncertainty of heisenberg. If possible, I ...
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Would an $H_2O$ Molecule actually look like this 3D representation if we could see it?

I'm trying to get a much better grasp on atoms and molecules and I am a visual learner. I found the above image here. This intuitively makes sense to me because I can see how the electron orbitals ...
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2answers
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What is the energy of an atomic orbital?

When we refer to energy of an atomic orbital what is this energy ? is potential energy ? but if is potential energy then shouldn't be considered the whole potential energy of the atom ( potential ...