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Questions tagged [orbitals]

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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
83 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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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
38 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
47 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
620 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)\...
1
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1answer
43 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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3answers
124 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
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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 ...
2
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0answers
82 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
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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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0answers
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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
63 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
37 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
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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
47 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 ...
3
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0answers
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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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0answers
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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 ...
3
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1answer
68 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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1answer
95 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 ...
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4answers
220 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
395 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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0answers
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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 ...
0
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1answer
87 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
218 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
59 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 ...
0
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1answer
59 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
46 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
41 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?
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1answer
39 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
77 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 ...
0
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1answer
37 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
47 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
35 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&...
1
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1answer
39 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 ...
3
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1answer
246 views

String behavior in electron orbitals?

It feels like this should be a incredibly easy question to find an answer to, but I’m coming up zeroes in my search - if I’ve overlooked a parallel question please feel free to close this. ...
2
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1answer
73 views

Ground state of Beryllium (${\rm Be}$)

Why is the ground state of Beryllium (${\rm Be}$) with electronic configuration $[{\rm He}]2s^2$ is $^1S_0$ and not $^3S_1$? The state $^3S_1$ has higher spin multiplicity.
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0answers
55 views

What is the point of talking about three axes for hydrogen orbitals?

The hydrogen orbitals are usually described using polar coordinates ($\Psi(r, \theta, \varphi)$). I understand that $r$ is the distance from the center of the atom, but how are the angles defined? ...
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2answers
76 views

Do empty orbitals have energy?

Suppose we have the Na (Sodium) atom. It has half-filled the 3s orbital and unfilled 3p orbital. Does the empty 3p orbital have energy? also does the energy of 3p change if an electron occupy it?
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Completely Non-classical Spin-orbit Interaction [closed]

Question: What is the reason for spin-orbit interaction without just assuming that the electron moves on a circular path around a nucleus? Every explanation for spin-orbit coupling that I have read ...
0
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2answers
61 views

How are line spectra explained after rejecting/improving Bohr's theory?

I learned that Bohr explained line spectra by postulating that electrons can only be at certain discrete distances from the nucleus. Later, this theory was refuted/improved by de Broglie and ...
0
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1answer
38 views

Quantum mechanics: orbitals with opposite signs in the magnetic quantum number

In quantum mechanics, the orbitals, psi (n, l, m) and psi (n, l, -m) have opposite signs in the magnetic quantum number but they have the same absolute value. (i) Are the probability density ...
2
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1answer
56 views

Relation of Hydrogen orbitals to its spectral series?

I'm looking for the link between the Rydberg formula for hydrogen spetcral series $$\frac{1}{\lambda_{\mathrm{vac}}} = R\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$$ and this image. Is it right to ...
2
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0answers
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A question about almost stationary orbits

For an orbit around the earth with period equal to a sidereal day with eccentricity $e=0$ and inclination $i=0$, the path on earth would be a single point on the equator. I have done some simulations ...
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3answers
203 views

What does the principal quantum number really mean? [closed]

What do principal quantum numbers actually represent? The modern structure represent that electrons do not revolve around the nucleus. It says there are no shells or orbits for electron rather there ...
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1answer
41 views

Orbitals, shapes and wave function relation

Are the shapes of orbitals like $s$ which is sphere due to wave function or due to square of the wave function?
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1answer
209 views

Electron transitions and spin [closed]

Take a single proton and electron. Write $n,\ell,m$ for the quantum numbers of the electron, and $1/2$ or $-1/2$ for its spin. The space of states of this system is the separable Hilbert space $V$ ...
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1answer
38 views

State with highest energy of Carbon atom

A possible excited state of the $C$-Atom is one with a $3s$ electron: $(1s)^2(2s)^2(2p)^1(3s)^1$. One can find out that there are the 4 possibilities $^1P_1, ^3P_2,^3P_1,^3P_0$. Why is the $^1P_1$ ...
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4answers
245 views

How do orbitals exist in an atom?

I have come across a picture online which talks about 1s,2s,2p orbitals of a sodium atom. Observation:In the picture we see some volume of space in common to two orbitals. For example:The circled(...