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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What does it mean when the $1s$ and $2s$ orbitals overlap?
The shape of the $s$ orbital is spherical. Consequently the $1s$ orbital will be a sphere with nucleus as its center while $2s$ will be a similar but bigger sphere.
Now orbitals represent the space in ...
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Is third photoelectric effect law wrong? [closed]
1.Ionization energy equals minimal energy electron needs to overcome atom’s Coulombs and gravitational fields.
Ionization energy depends on which state atom currently is. For ground state ionization ...
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Why are atoms not being ionized during stimulated emission?
To ionize atom at some state, as understand, it must receive the energy of that state, so for a hydrogen atom, being in the ground state it $13.6\ eV$. In the second state, the ionization energy is ...
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What if atom receives energy higher than $\Delta_1$ but lower than$\Delta_2$? [duplicate]
Considering an atom at ground state 0.
To be excited to state 1, it needs to get, as understand $E_e = E_0 - E_1$.
What if, atom at $E_0$ interacts with photon, which energy is higher than $E_0 - E_1$,...
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What does electron actually do in quantum mechanics?
I know that electrons are considered waves in quantum mechanics and it has a probability density region of where it could be found. But what does it actually do ? Does it stay at one part or move to ...
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What prevents an electron from emitting a photon and staying at the same orbital?
I understand that electrons cannot join already filled orbitals. I also understand that in case there's a hole in a lower orbit [1], an electron can emit a photon and change its orbit (e.g., L->K).
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Schrodinger's equation solutions for hydrogen in a strong magnetic field
I've read that in the vicinity of a neutron star, the magnetic fields are so strong that (other environmental factors aside) conventional chemistry breaks down because orbitals/electron configurations ...
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Band structure of Graphene and Tight Binding
Consider the $sp^2$ hybridization of Carbon in Graphene depicted in the following picture:
When considering the LCAO TB method, one would expect conduction properties to be determined by the ...
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Solving Hydrogen atom with ladder operators
Start with a system I fairly understood, the harmonic oscillator.
Here all possible states fulfilling the eigenvalue-equation $H |n\rangle = E_n |n\rangle$ are given by
$$|n\rangle = \dfrac{1}{\sqrt{n!...
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Is the $1s$ state of Hydrogen eigenfunction of all the three of the Hamiltonian, the orbital angular momentum $\vec L$, and $L_z$?
Let $H$ be the Hamiltonian, $\vec L$ the orbital angular momentum, and $L_z$ its projection on the z-axis.
Is the 1s state of Hydrogen an eigenfunction of all the three operators? I suppose it should ...
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What does band inversion mean for occupation?
I am thinking about Topological Insulators at the moment and am not clear about how to understand the occupation of the inversed band.
I understand that due to energetic and symmetry reasons the ...
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Teaching the Standing Wave Model vs Bohr's Model [closed]
In an introductory teaching level, what are the advantages and the disadvantages to teach the standing wave model of the hydrogen atom, (as in PSSC Physics textbook, 7th edition) versus the Bohr's ...
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Confusion regarding Bohr Radius
The bohr radius is derived by setting the centripetal force of electron to equal the coulomb force.
$$\frac{mv^2}{r}=\frac{kq_1q_2}{r^2}.$$
The electron is not a particle orbiting the electron ...
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Understanding of Band Inversion in $\rm Bi_2Se_3$ Topological Insulator [closed]
I'm currently trying to understand Fig. 2 in this Paper (http://dx.doi.org/10.1103/PhysRevB.82.045122) which aims to explain the origin of band inversion in Bi2Se3. I really want to get an ...
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Will removing an outermost electron from the outermost orbital of an atom change the orbital geometry?
Does $\text{He}^+$ and $\text{He}$ have different orbitals?
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Linear combination of atomic orbitals (LCAO) justification for molecular orbitals (MO) done in this MIT solid state chemistry lecture
In this series on solid state chemistry by MIT, 11:00-13:00 in this lecture, LCAO for molecular orbitals is justified by the fact that Schrodinger's equation is linear (and therefore the superposition ...
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Interference of atomic orbitals: In what field do atomic orbitals oscillate? [closed]
I am learning molecular orbital theory for chemical applications. To understand why molecular orbitals can be antibonding, destructive interference aka out-of-phase interference of the orbital ...
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What is $\vec{q}$ in this expression?
So I am having trouble following and understanding what $\vec{q}$ is in this evaluation. Here is my attempt at a solution:
Since the solution is for 2P to 1s transition it must be in the form of ...
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Why does a transition between 2 $s$-orbitals work for cesium's clock transition?
I have a small question about the cesium's clock transition. According to the information on the Wiki: https://en.wikipedia.org/wiki/Caesium_standard, the chosen transitions are two hyperfine ground ...
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How are the orbitals named?
l = 0 to (n-1).
l is azimuthal quantum number.
n is principal quantum number.
for,
l = 0 , it is s.
l = 1 , it is p.
…
l = 99, it is what?
What is the name given to it?
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Negative quantum number $L$ for one of the states of Carbon
The carbon atom has its in its final subshell $2p$ simply two electrons. These electrons must be in a state given by:
$$\left|{2,1,m_l,m_s}\right.\rangle$$
Where $m_l=-1, 0, 1$, and $m_s=\dfrac{1}{2}, ...
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Spectroscopic Notation - Does $n^{2S+1} L_J$ describe a Single Electron, or the state of multiple Electrons?
I was introduced to spectroscopic notation as $n^{2S+1} L_J$ (with L = "S, P, D..").
And the meaning that n stands for the principal quantum number (energy level, as known from the hydrogen ...
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Why do electrons orbit the nucleus instead of just sticking to it? [duplicate]
If the electron stays on the nucleus because of electrostatic charge, why do they spin around instead of just staying there?
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What is the form of general expression (one expression) for the eigenfunctions of discrete and continuous spectra of motion in the Coulomb potential?
Eigenvalues of motion in the Coulomb potential have a discrete spectrum and a continuous spectrum. The eigenwave functions have the form:
For discrete spectrum radial functions(in mathematica code):
<...
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Why does an electron "orbiting" an atomic nucleus have to be described as a standing wave? [duplicate]
"However, if one describes the electron by a matter wave, a stationary state of the atom in which the electron does not leave the atom must include a standing wave." Why?
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What would have to happen for atomic subshells to have even orbitals instead of odd orbitals?
The orbitals in the subshells, due to ℓ and mℓ, are always odd: 1, 3, 5…
• ℓ = 0 equals 1 orbital (s) of mℓ = 0.
• ℓ = 1 equals 3 orbitals ($p_z$, $p_x$ and $p_y$) of mℓ ={–1, 0, 1}.
• ℓ = 2 equals 5 ...
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Does the azimuth angle matter for determining the electron density for atomic orbitals?
The only place in the expression for the wavefunction where the azimuth angle $\phi$ is used is in the equation for the spherical harmonics, and in the spherical harmonics there is only a single ...
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Is the electron considered to be at rest within an atom?
According to older models of the atom, the electron moved around the nucleus at great speeds. If this were so, would this not mean under the laws of special relativity that it would cause significant ...
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Difference between average position of electron and average separation between proton and electron [closed]
I'm not sure to understand what is the difference between those 2 terms in the hydrogen atom.
The average position $\langle \hat{\bf r} \rangle$ is written $\langle \Psi^{*}|\hat {\bf r}|\Psi \rangle$,...
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Understanding of the M1 transition $2s \to 1s$
I found a few articles [1] that mention the following dipole magnetic (M1) transition:
$$
2 ^{2}s_{1/2} \rightarrow 1 ^{2}s_{1/2}
$$
where a state is desribe by the notation $n ^{2S+1}L_J$ with $n$ ...
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Why the closest to the nucleus electron has lower energy (contrary to Heisenberg)?
According to shell theory the lowest energy electrons are on the $s$ level and are closest to the nucleus. This means they are localized in a smaller volume then other outer shell electrons and ...
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How a single $p_x$ orbital transform under $C_{4v}$ point group?
How a single $p_x$ atomic orbital transform under $C_{4v}$ point group?
Background
I'm trying to understand how atomic orbitals hybridize on a lattice plane, e.g. NaCl (111) plane. For this purpose, ...
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Why is the bending mode of carbon dioxide harmonic?
Here's a simple classical model of a carbon dioxide molecule:
This gif illustrates the "bending mode" vibration.
If the carbon atom moves a small distance $\mathrm{d}x,$ then the springs' ...
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What is the difference between $σ$ and $π$ bond and $σ$ and $π$ bands?
In the paper I am reading, it says:
"as in the case of the single layer, the π band is formed in bilayer graphene and the π band is half-filled if the sample is not doped."
I know the σ ...
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Meaning of quantum orbitals with $\ell=0$
My question is simple:
Does a quantum eigenstate with orbital angular momentum $\ell=0$ meaning that the velocity of the particle is only radial when measured?
What is the experimental method to ...
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Bound states and negative energy [duplicate]
I have read online that the hydrogen atom's energy level is given by $$E=-13.6eV$$
where $eV$ represents electron volts. The notes say that the energy is negative because the electron is bound to the ...
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Kinetic energy of electrons
Electrons are in orbit around the nucleus. I have two questions about this:
Where does the energy for them to orbit come from?
Is chemical energy another word the kinetic energy of these electrons?
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Is all information of the quantum numbers $m\ell$ lost in a superposition?
I have learned that to create real spherical harmonics, a superposition of degenerate spherical harmonic eigenfunctions can be created using ±ml. For example, the px and py (l = 1) spherical harmonics ...
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Would externally applied centrifuge force push electron out of an atom?
Background about me: I know nothing about physics.
It occurred to me to ask the following question:
Imagine a small amount of some element placed in centrifuge device that spins with very fast speed. ...
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On degeneracies of energy levels in atoms
For hydrogenic atoms the energy levels are (in cgs units):
$$
E_n = -\frac{e^2Z^2}{2n^2a_0}
$$
This formula shows there's no dependence on quantum numbers $l$ and $m_l$. These so-called degeneracies ...
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Why is it easier to throw electrons from a higher energy shell?
From what i understand, as we increase the radius of unlike charges, the potential energy of the system also increases, so electrons in the outer shell live in a higher potential system, i.e more ...
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Different versions for the Radial Solution of the Hydrogen Atom [closed]
Initially, I'm trying to prove if the following is true
$$|\psi_{n00}(r=0)|^2 =\dfrac{1}{\pi n^3a_0^3}$$
I'm looking to solve some calculations made in
Introductory Quantum Optics
Christopher Gerry ...
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How did the Aufbau principle come to be? [duplicate]
How did the Aufbau principle come to be? Being that my education on chemistry doesn't go past highschool, i was never sure how the following diagram was conceived:
I would like to understand how the ...
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Which element has the bigger atomic radius Cr or Mn?
In ncert Mn is bigger. In periodic table app, Cr is bigger.
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Tight-binding: aren't the electronic bands just the eigenvalues of the Hamiltonian?
In the tight-binding model we choose a set of atomic orbitals $\{\phi_1(\textbf{r}), ..., \phi_N(\textbf{r})\}$ and estimate a transfer matrix and hopping matrix
$$
\begin{cases}
S_{ij}(\textbf{k}) = \...
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„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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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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