Questions tagged [orbitals]

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3
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1answer
51 views

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
148 views

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
76 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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1answer
27 views

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
106 views

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
2k 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
110 views

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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1answer
47 views

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
62 views

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
810 views

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
380 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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0answers
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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
156 views

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
3k views

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 ...
1
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1answer
51 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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2answers
391 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
45 views

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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2answers
180 views

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
432 views

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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1answer
492 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
61 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
865 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
62 views

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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2answers
721 views

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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0answers
116 views

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
53 views

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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0answers
100 views

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
278 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
606 views

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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2answers
42 views

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
78 views

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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0answers
40 views

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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0answers
92 views

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-...
2
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1answer
86 views

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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3answers
642 views

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 ...
2
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4answers
506 views

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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3answers
471 views

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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1answer
1k 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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3answers
795 views

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
138 views

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 ...
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1answer
211 views

Can electron jump from $n=2$ to $n=3$?

Assume Bohr's Model. Lets not consider latest modern theory. Consider a Hydrogen atom in ground state (n=1). It excites to next level n=2. It will stay here for 10^-8 seconds. Now we supply more ...
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0answers
73 views

Term Symbols of Carbon Atom [duplicate]

For a neutral Carbon Atom, the electron (ground) configuration is $1s^2$$2s^2$$2p^2$. I am told that the term symbols $^{3}S_{1}$ and $^{3}D_{1,2,3}$ are forbidden by Pauli Exclusion Principle. May ...
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2answers
50 views

Force to step down atomic level of an electron?

How much force is needed to step down atomic level of an electron? Where does it gets it energy to overcome the orbits to step up?
3
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1answer
47 views

Why does $2p$ have highest RDF at $4a_{0}$?

I was reading notes from my first class in Quantum Physics that I received and left confused at the following statement: For each principal quantum number $n$, the orbital set with the highest $\...
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0answers
99 views

Quantum numbers $n$ and $\ell$ relation in many electrons atom [duplicate]

Solving the Schrodinger equation for hydrogen atom we arrive to the conclusion that quantum numbers $n$ and $\ell$ have the relation $$\ell=0,1,...,n-1.$$ Now,since we can not solve the Schrodinger ...
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1answer
63 views

Electronic configuration

In chemistry the lithium electronic configuration is $$1s^22s^1 \, .$$ Can we prove this using approximation method like perturbation theory that this the ground state and not for example $1s^22p^...
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1answer
77 views

Bad value for sphere of influence with Venus [closed]

I would like to get value of sphere of influence than Wikipedia for Venus: on https://en.wikipedia.org/wiki/Sphere_of_influence_%28astrodynamics%29 It is indicated for Venus: $S_{\text{OI}}=0.616\,\...
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1answer
39 views

Given the wavefunction of an electron in hydrogen, what possible energies can it obtain and what are the probabilities of those energies? [closed]

we are given, $$\psi(\textbf{r})=A\left[R_{2,1}(r)Y_{1,-1}(\theta,\phi)+iR_{2,1}(r)Y_{1,0}(\theta,\phi)+2R_{2,1}(r)Y_{1,1}(\theta,\phi)\right]$$ we can rewrite this as: $$\left|\psi(\textbf{r})\right&...
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1answer
144 views

A dreidel on a spinning table

In the spirit of the holidays. Let's assume that a dreidel is spinning counter-clockwise at frequency $f$ on a table. From external point of view, what will I see if I rotate the table clockwise at ...

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