Questions tagged [orbitals]

An orbital is the mathematical function describing the location and wave-like behaviour of an electron in either an atom ( for atomic orbitals) or in a molecule (molecular orbitals).

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Would externally applied centrifuge force push electron out of an atom?

Background about me: I know nothing about physics. It occurred to me to ask the following question: Imagine a small amount of some element placed in centrifuge device that spins with very fast speed. ...
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On degeneracies of energy levels in atoms

For hydrogenic atoms the energy levels are (in cgs units): $$ E_n = -\frac{e^2Z^2}{2n^2a_0} $$ This formula shows there's no dependence on quantum numbers $l$ and $m_l$. These so-called degeneracies ...
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Why octet atom are stable? And what make atom unstable?

I have search a lot that want make octet atom stable but all I found is that it need to fill the orbit! why . Why it need to fill the orbit. And I also search that why atom which don't have octet are ...
3 votes
1 answer
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Can a light element with excited nucleus undergo internal conversion?

Internal conversion occurs when an excited nucleus ejects a low level electron from the first 2 low energy shells such as a $k$-shell electron instead of emitting gamma when returning to ground state. ...
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Different versions for the Radial Solution of the Hydrogen Atom [closed]

Initially, I'm trying to prove if the following is true $$|\psi_{n00}(r=0)|^2 =\dfrac{1}{\pi n^3a_0^3}$$ I'm looking to solve some calculations made in Introductory Quantum Optics Christopher Gerry ...
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Why is it easier to throw electrons from a higher energy shell?

From what i understand, as we increase the radius of unlike charges, the potential energy of the system also increases, so electrons in the outer shell live in a higher potential system, i.e more ...
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How did the Aufbau principle come to be? [duplicate]

How did the Aufbau principle come to be? Being that my education on chemistry doesn't go past highschool, i was never sure how the following diagram was conceived: I would like to understand how the ...
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3 answers
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Which element has the bigger atomic radius Cr or Mn?

In ncert Mn is bigger. In periodic table app, Cr is bigger.
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Tight-binding: aren't the electronic bands just the eigenvalues of the Hamiltonian?

In the tight-binding model we choose a set of atomic orbitals $\{\phi_1(\textbf{r}), ..., \phi_N(\textbf{r})\}$ and estimate a transfer matrix and hopping matrix $$ \begin{cases} S_{ij}(\textbf{k}) = \...
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Flat bands in metals

When I look at the angular momentum resolved band structure of the sodium (Na), there are two flat band at very low energies (p at around -25 eV and s at around -50 eV). What should I understand from ...
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„Orbital“ of an quark

Inspired by the idea of the electron orbitals ( probability of finding an electron in an atom) i was wondering what that would look like inside a proton or neutron for quarks. For simplicity consider ...
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Is it justified to take orbital as just a "dispersed region of charge" for applications in Organic chemistry?

When I read organic chemistry book in the past, it seems so a heuristic used to explain and understand reaction mechanism is that negative charge attracts positive charge (or indirectly as ...
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Why do you use $n_r = n -\ell -1$ as quantum number instead of $n$ for hydrogen atom?

I got two different quantum numbers for the same problem: Hydrogen atom without any interaction. Then, my energy is $$ E_n = -\frac{R_y}{n^2} $$ with the quantum number $n = 1, 2, 3, ....$ In another ...
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1 answer
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How to determine possible term symbols in case there are more than 2 electrons

I'm doing some exercises on $LS$ coupling during my self-study of atomic physics. I understand how to construct a table of possible microstates. I also understand how to map term symbols to those ...
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What is an orbital singlet?

For Helium atom we know there are spin singlet and spin triplet state corresponding to $S=0$ and $S=1$. But what if the electrons are more than two and what does singlet mean for orbital degree of ...
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Does laser trap atom cooling change the electron shell levels?

Do the electron orbits change during the cooling of the atom in a laser trap? When cooling down, do the electrons come closer to the nucleus of the atom or do they move away? Or do the electrons leave ...
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1 answer
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Expansion of the Bohr-Sommerfeld Model to any atomic/molecular system

I know that the Bohr model of the atom was modified by Sommerfeld to include elliptical orbits, and that the resulting Bohr-Sommerfeld theory has long been put aside in favor of quantum mechanics. ...
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Is there a limit of electrons a single hydrogen atom can have?

Is there a limit of electrons a single hydrogen atom can have? If so what is it? why? Is the the answer to why scalable to helium?
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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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Why electrons in an atom don't radiate photons?

Consider the $s$ orbital of an helium atom. The electron can be anywhere around (or even in) the nucleus. Electrons, like all charges, create electric fields. When the atom interacts with other atoms ...
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Intuition for the $\Delta m = 0,\pm 1$ dipole selection rule

The selection rules for hydrogen are: $\Delta l=\pm1$ and $\Delta m=0,\pm1$. The first makes intuitive sense because of the conservation of angular momentum and the fact that a photon has spin 1. But ...
3 votes
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Can the pilot wave theory explain why the circumference of an orbit has to be an integer multiple of the wavelength of the electron orbiting it?

Consider the atomic model proposed by Bohr. The velocity of an electron at any orbit is given by the following equation: $$v= n \dfrac{h}{2\pi mr}$$ Now, this equation stems from the fact that, quote, ...
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How does an electron move in the $p$ orbital?

This is my first time learning about orbitals and I am very confused over how do electrons move around the nucleus in the $p$ orbital. Wouldn't it have to move out of the orbital where probability of ...
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Why silver reflectivity decreases at around 350

This picture is from the site:https://www.zmescience.com/other/feature-post/gold-color-relativity/ I was wondering why the reflectivitiy of silver goes to 0 at around 350 nm. I understand why for gold ...
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How to normalize cartesian gaussian type basis sets?

I am currently working on my graduation paper each high school student in Switzerland has to write. I chose quantum mechanics. To be more specific Hartree-Fock-Theory. I understand all the theory ...
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Normalization-Formula for contracted Gaussian Orbitals

I am trying to write a python script that implements the Hartree-Fock-Routine. I am currently working on generating the basis-functions. While doing my research I found this website that explains how ...
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Do electrons with the same fundamental quantum number (ex: $n=1$), have the same average distance from nucleus?

For example, in the silicon atom, do the electrons located in $3s$ and $3p$, with $n=3$, have the same distance to the nucleus? I think in the diagram below, the arrangement of the electrons relative ...
1 vote
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Identifying number of node of an arbitrary wave function

Given an arbitrary wave function, what is the most general way to identify number of its nodes? By arbitrary, I mean we don't have any predefined conditions (like wave function of an atom, a harmonic ...
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Is central field approximation perfect for alkalis?

In my atomic theory lecture notes it always says the central field approximation is 'excellent' for alkali atoms due to the spherical symmetry of the core electrons and the $s$-shell of the valence ...
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Do electrons in same orbital shell (ex: $3p$) have the same energy level?

Due to Pauli exclusion principle, each quantum state can be occupied by no more than one electron in a electron system. However, why there is more than one electron in the same energy level in the ...
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Existence of Subshell structures for molecules [closed]

For Hydrogen atom, we could explicitly solve Schrodinger's Equation, a partial differential equation. Using reparametrization, we arrive at series solution using Frobenius method. From this we see ...
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Explanation passage in Griffith's - Angular momentum of carbon

In subsection 5.22 "The periodic table", chapter 5 about identicals particles he states: The electrons in the orbitals (1s)&(2s) have no orbital angular momentum ($l=0$), so they shouldn't ...
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What is the shape of the path that electron makes in an atom?

If electrons make no transition to any of the other orbital or a shape, then what is the shape pf the path it makes while revolving around the nucleus? Does it have to do anything with the ...
3 votes
2 answers
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Physical Intuition for thermodynamic limit of the average occupancy, $\langle N\rangle$, of an orbital

Say your allowed occupancies for an orbital are $0, 1, 2$, and the values of energy associated with these occupancies are $0, \epsilon, 2 \epsilon$. Give an expression for the ensemble average ...
1 vote
1 answer
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What causes the electric field in a Daniell Cell?

I would like to know what causes the e-field in a Daniell cell. From a chemistry point of view, I do understand that this is initiated by a redox reaction in which Gibbs free energy is decreased. The ...
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Single-particle wavefunction in Slater determinant

The ground state of $N$ non-interacting fermions can be written using a Slater determinant as: $$ \Phi_{GS}(\textbf{r}_{1}, ..., \textbf{r}_{N}) = \frac{1}{\sqrt{N!}} \begin{vmatrix} \phi_{\mu_{1}}(\...
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About why electrons in atom don't radiate(considering wave nature also) [duplicate]

It's said in textbooks that electrons won't radiate and fall into nucleus because matter wave of it's form a standing wave but could somebody explain why being a standing wave it doesn't radiate, even ...
3 votes
2 answers
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How does $s$ subshell not have a node in the center despite the nucleus being there?

In most images of $1s$ subshell I see that there's no node shown at the center, and even the formula $n-\ell-1$ gives 0 as the answer. But, isn't the nucleus experimentally proven to be at the center? ...
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How many $\rm d$ orbitals do I have in $\rm [Ar]3d^{10}4s^1$ configuration materials?

I have noticed in a book the following band configuration for copper: But I think I read in the book that each band has 2 electrons if it is fully occupied. But in here I see only four 3d types of ...
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How to think about speed or velocity of an electron (in an atom)?

One answer to this question explains that "velocity of electrons has no meaning" while another says that "it can be argued that they don't move around atoms at all". And then in another post it is ...
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Splitting of $sp$-System due to LS coupling

How do I explain the splitting of $sp$-system due to LS interaction? I think it is due to the magnetic field created due to the orbital motion of the electron, and that magnetic field splits the ...
1 vote
1 answer
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Are atoms still unstable in 4 spatial dimensions when the physical size of nuclei is accounted for?

Per this answer, depending on a dimensionless parameter hydrogen atoms in 4 spatial dimensions can be either unbound (i.e., nonexistent), stably bound dependent on boundary conditions, or unstable ...
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The uncertainty principle and the quantization of electron momentum in orbitals - Why are larger energy gaps considered more uncertain?

I am a chemist trying to understand how the uncertainty principle can be applied to the mechanics of atomic and molecular orbitals in order to have better intuitions about stability and reactivity. ...
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Pauli exclusion principle and quantum state

Wikipedia says that two identical fermions cannot occupy the same quantum state. My question is what does this quantum state means? In classical mechanics, this means that the two particles cannot ...
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Are the shapes of atomic orbitals direct consequence of the Schrödinger equation?

I am trying to understand whether the shapes of the orbitals are inevitable given the standard model. They would probably change if we change the fine tuning of the fundamental physical constants, ...
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What is the standard explanation for tungstens abnormal high Pauling electronegativity?

The electronegativity of tungsten does not follow the common trend along the periodic table.
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Hydrogen atom quantum numbers distribution

The wave function of the hydrogen atom is given by $\psi_{n \ell m} \left( r, \theta, \varphi \right) = R_{n \ell} Y_{\ell}^{m} (\theta, \varphi)$ which depend on the quantum numbers $n, \ell, m$. I ...
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How many states are possible for two (indistinguishable) electrons with $n=2$ in an atom if we forget Pauli’s exclusion principle?

I have been told I can use $^8C_2 = 28$ to obtain the answer to this question, but I am doubtful of this result since I obtain $21$ by simply writing out the possible states as ($ml_{1}$, $ms_{1}$, $...
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Can the cases of multiple fermions in any spherically potential be approximated by the Schrodinger Equation for a single fermion?

In this video https://www.youtube.com/watch?v=tq_y1qOmUBE&t=783s it's mentioned that the structor of atoms of multiple particles can be approximated using the Schrodinger Equation of the Hydrogen ...
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How can an $n=25$ Rydberg state exist in a solid? What does the wave function look like?

Phys.org's April 15, 2022 Ancient Namibian stone could hold key to future quantum computers begins: A special form of light made using an ancient Namibian gemstone could be the key to new light-based ...

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