Questions tagged [orbitals]

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Why the energy of a state increases with increasing azimuthal quantum number $\ell$?

I am reading Griffiths' introduction to quantum mechanics. But I am confused about the relation between the state energy and azimuthal quantum number $\ell$, which is discussed in Chapter 5.2.2 where ...
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2answers
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Does the intrinsic spin of electrons change when we excite electrons for hybridisation?

Have had been told that electrons can move from one energy level to another by transmitting or taking in energy, and do that profitably in hybridisation. I am interested in knowing how exactly do they ...
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How do electrons move from one energy level to another?

EDIT 1: Many people are recommending that the question Do electrons really perform instantaneous quantum leaps? is very similar to mine. However, that question is very specific to quantum leaps. I am ...
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Conceptual question about the transition dipole moment and its components

I'm looking at the following transition: $1s\to2p$. For this transition, my textbook says: We have to consider three degenerate $m$-components $m=0,\pm1$. We put the quantization axis in the $z$-...
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How do delocalized electrons conduct electricity?

I have learned that for a meterial to be conductive, it must contain free charge carriers, in most cases electrons. Graphite does conduct electricity parellel to its graphene layers, which is due to ...
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How to couple the $^3p_2$ with $d_{5/2}$?

The first two electrons' LS term is $^3p_2$,how can this term coupling with another electron $d_{5/2}$?(this electron in another shell) for $^3p_2$,$L_{12}=1$,$S_{12}=1$,and only the orientation of $...
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Why does exchange energy of electrons lead to stability?

My text book says "electrons of the same spin in degenerate orbitals tend to exchange their positions and this leads to stability". Firstly, why should the electrons exchange their positions?...
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1answer
29 views

Why is there a third extremum radial coordinate for “rosace-like” trajectories in the Schwarzschild geometry?

I drop a test-particle in the Schwarzschild geometry, at an initial radial coordinate $r_0 > a \equiv 2 G M$ ($a$ is the Schwarzschild "radius"), with initial velocity $v_0 < 1$ ...
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114 views

Do electron (or other quantum particles) move in a 4th spatial dimension? [closed]

I was told that an electron can change its position from position A to position B without appearing anywhere between A and B. So i think that it might be possible for an electron to move in 4D or ...
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1answer
28 views

If atomic electron is in $f$-state, what values of the total angular momentum are allowed?

What I know is total angular momentum $\vec{j}= \vec{\ell}+\vec{s}$, here $\ell=3$ for $f$ state, $s=1/2$ for spin, so the total angular momentum should be $7/2$, is this correct? is there any other ...
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Bohr's second postulate

What was Niels Bohr's reasoning behind his second postulate (about integer angular momentum)? How did he come up with it without any knowledge of matter waves? I only have a high school level ...
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How do we know that $^1S$ is the ground state of the helium atom?

Let $\psi=a_1\phi(1s(2) \ ^1S)+a_2\phi(1s(1)2s(1) \ ^1S)+a_3\phi(2s(2) \ ^1S) +... $ be a state of the helium atom. Applying variationally calculus we can found the energy expectation value of this ...
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Do different eigenstates of total angular momentum have necessarily different energies?

Let $H$ be the Hamiltonian of a specific atom (not hydrogen) and $J$ the total angular momentum. Since $H$ and $J$ commute, they have common eigenstate. So we can label the atomic states by their ...
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Is $1s2s$ state an upper bound of Helium excited states? [closed]

Generally people says that the state $1s(1)2s(1)$ $ ^1S$ is an excited state of Helium atom . Variation theorem guaranties that the expectation value of this state is greater than the ground state, ...
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1answer
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Locating a point in circular orbit on the Cartesian plane after some $t$ seconds

The second hand of an analog clock has angular velocity $\omega=\pi/30$ rad.s-1. The blue body in the image below mimics the hand's clockwise motion on the Cartesian plane with the center of ...
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Why do the $d$ orbitals have such strange symbols?

Why are the five d-orbitals denoted by the symbols $d_{z^2}, d_{x^2-y^2}, d_{xy}, d_{yz}$ and $d_{zx}$? Does it have to do with the wavefunctions of d-orbitals? The symbols for the f-orbitals are ...
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1answer
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Interpretation of the azimuthal quantum number [duplicate]

On the German Wikipedia page, we can read: "The higher the azimuthal quantum number $\ell$ for a fixed principal quantum number $n$, the more the average distance of the electron from the nucleus ...
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What problem excatly did Sommerfield solve in his atomic model and how?

I am curious to know what problem did Sommerfield solve in his atomic model and how does his atomic model solve it? Most books say it solved the problem of splitting of lines but what excatly does it ...
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1answer
39 views

Where can I find the energy spectrum of larger atoms (e.g. Nd$^{3+}$)?

I would like to find a ressource where the binding energies of the outer electrons of larger atoms are listed. I'm discussing Neodymium lasers and I think it would be nice to have a graphic with all ...
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3answers
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Quantum model of the atom

please note that I am a high school student trying to understand the quantum model of the atom; I have only the most basic understanding of quantum mechanics. I am trying to comprehend the wave nature ...
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Physically, why is the ground state wavefunction of Neon be spherically symmetric?

For a may electron atom, a closed subshell structure implies $$L=S=0$$ and therefore also, $J=0.$ Therefore, the ground state wavefunction of such an atom is spherically symmetric because the rotation ...
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How is it that for a closed subshell configuration $L=S=0$?

For a closed subshell configuration of a many-electron atom, $M_L=\sum_i m_{\ell_i}=0$ and $M_S=\sum_i m_{s_i}=0$. But I do not understand why does it necessarily mean $L=S=0$. The values $M_L=M_S=0$ ...
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Which atoms are orbited by shared electron?

A covalent bond, also called a molecular bond, is a chemical bond that involves the sharing of electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs, and the ...
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If nitrogen has 7 electrons, how come the ground state is $2s^2 2p^3$?

If nitrogen has 7 electrons, how come the ground state is $2s^2 2p^3$? This would mean that there are only 5 electrons in the nitrogen atom.
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1answer
49 views

Transition between 2 energy levels - wave function picture

Suppose we have a system that has discrete energy levels (e.g. hydrogen atom, potential well) and the stationary solutions for the wave function are $\psi_n$. I would assume that there should be a way ...
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1answer
26 views

The connection between the wavelength and the atom level

In my textbook it said the following: Photons with wavelengths in the spectral range of $[94\mathrm{\ nm},104\mathrm{\ nm}]$, interact the hydrogen atom in the basic state. Photons having those ...
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2answers
166 views

Imagine if the electron had a spin $s=3/2$. Would atoms in their ground state still display the Electron shell structure? [closed]

My answer would be yes, since instead of starting with $2s+1=2$ electrons in the first shell you would have $2s+1=4$ electrons. This is a question my quantum mechanics prof posed in the last lecture, ...
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1answer
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Why an electron does not get stuck to nucleus?

An electron remains in its orbit because of electrostatic and centrifugal force. But when a reaction takes place some electrons are gained or removed. Then how they still are stable?
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1answer
121 views

Can why electrons exist in shells be explained by the Pauli exclusion principle?

Do you know the Pauli exclusion principle?-'No two particles could be in the same quantum state at once'. Well can you use that principle to explain why electrons stay in shells and electrons in ...
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91 views

Element well in periodic table

It may be a very stupid question, but still. Given a periodic table Why there is a well/hole of missing elements in atop of periodic table ? (Pictured as green area). Is this just a side-effect of ...
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51 views

Proof that total orbital angular momentum square can only take integer values of $\hbar^2$ [duplicate]

I am comfortable with the argument that in order for the wavefunction to be single valued/2$\pi$ invariant this means that $L_z$ must be an integer value of $\hbar$. $$U(2\pi e_z)=e^{-(2\pi i/\hbar)\...
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Do orbitals of electrons line up in external magnetic field?

If a current carrying loop is in external magnetic field it feels the force and moves to its equillibrium position. Similarly, in quantum level will electrons revolve nucleus in a lined up manner for ...
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What does $LS$ coupling and $jj$ coupling signify?

When we consider $1s2p$ electrons in $LS$ coupling we get one singlet and one triplet but in $jj$ coupling, we get $2$ doublets. I know the mathematical (quantum number) work behind it. But what I don'...
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Why is a $3d$ orbital in transition metal higher in energy than a $4s$ orbital? [duplicate]

I was studying this chapter lately, and this part of chapter always confuse me. I often think why $3d$ orbital in transition metal is higher in energy than 4s orbital? (the whole question will refer ...
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Do the electron pair in an orbital, have a net orbital magnetic moment?

It has been made clear to me that 2 electrons in an orbital have opposite spins, and hence their spin magnetic moment nullify each other. But does the same happen with the Orbital magnetic dipole ...
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1answer
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Does an electron in an orbital have exactly the same energy as the orbital's shell?

Solving the Schrödinger equation gives a wave function for each electron in an atom of any element. The wave functions under the atom can be squared to yield probability distribution maps, or orbitals,...
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Does electron orbital theory contradict the Heisenberg uncertainty principle?

The quantum-mechanical model of atoms was derived from Heisenberg's uncertainty principle, which states that the position and momentum of a particle cannot both be determined to an arbitrary degree of ...
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Are there energy levels when $V(r)\not\propto{r^{-1}}$?

For something like the hydrogen atom $V(r)\propto{r^{-1}}$. And there are energy levels described by the equation $$E_n=-\frac{m_ee^4}{8\epsilon_0^2h^2n^2}$$ that indicate where orbitals are allowed. ...
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3answers
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How does an electron move around as a wave in orbitals?

This question arose when I was told that there were positive and negative lobes in an orbital. I wanted to know on what basis this was proposed and hence I searched it on web and found out that it ...
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115 views

How to distinguish the $p_x$, $p_y$, $p_z$ orbitals when one can choose the $x-$, $y-$, and $z-$ axes arbitrary?

How to distinguish the $p_x$, $p_y$, $p_z$ orbitals since one could choose the $x-$, $y-$ and $z-$axes arbitrary? How could the can the wavefunctions that describe the probability of the presence of ...
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1answer
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Origin of $\ell \leq n-1$ orbital rule

I am wondering about the origin of the $\ell \leq n-1$ orbital filling rule. For the hydrogen atom, I believe the reason is because in the spatial wave function there is the term $$\psi \propto \sqrt{(...
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1answer
185 views

Why can only orbitals of similar energy interact significantly?

In molecular orbital theory, it is often said that only orbitals with a) the same symmetry and b) similar energy can interact to a significant degree. I understand the necessity for the same symmetry, ...
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1answer
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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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Relation between velocity of a electron (In the Bohr model of the atom) and the radius

So we can derive this expression by equating force of attraction on the electron by the nucleus to the centripetal force acting on the electron, i.e: $$ \frac{KZe^2}{r^2}= \frac{mv^2}{r},$$ where $m$ ...
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What if we know exact position of electron?

I know many scientist gives many theory to explain structure of atom and that's Quantum mechanics explained very well. Even Schrondiger eq. to get idea where electron more probable is around a nucleus ...
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1answer
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Centre of Mass of Electrons in an Orbital [duplicate]

Without going deep into mathematics and simply using symmetry arguments I made the following observations- An electron has a probability of being at a particular position Let's take the 1s orbital of ...
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3answers
234 views

Why do electrons have fixed energy levels? [closed]

I understand that electrons do not orbit the nucleus, instead they have a higher probability to be found at some specific regions. But what makes they appear more frequently in the orbital regions? ...
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1answer
25 views

Can electrons, upon interaction, change each other's phase?

Imagine two hydrogen atoms which are close together, but not yet bonded. According to molecular orbital theory, the wavefunctions of their 1s electrons have to be in phase for them to interfere ...
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1answer
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Band Theory - which orbitals overlap?

I have another question relating to band theory, wonder if anyone can help? If I am correct, in band theory we have this idea of creating N different energy states for N atoms that are in a system (...
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1answer
35 views

Binding energy for electrons

When protons and neutrons interact attractively and coalesce to form an atomic nucleus, their energy in this state must be less than what it was when they are separated, so they lose mass which is ...

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