Questions tagged [orbitals]

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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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Why do I see two peaks in the KER spectrum of a Dinitrogen-electron collision?

I am currently reading a paper about an experiment, where they have a Dinitrogen atom and smash a 1000 keV electron into it. This results in a fragmentation where the Dinitrogen atom + the electron ...
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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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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
25 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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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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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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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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1answer
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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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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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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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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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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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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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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
159 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
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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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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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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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Hydrogen bonding under quantum mechanics

I know that Fermi-Dirac statistics can be used to account for covalent bonding, but how does quantum mechanics explain hydrogen bonding?
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What difference does it make if a molecule has odd or even parity?

I've been reading a lot about term symbols and spectroscopic notation, but I must have missed the part about WHY a molecule's evenness or oddness matters, in terms of spectroscopy or whatever...
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Energy levels and bands in solids: What does $^4\text{F}_{3/2}$ and $^4\text{I}_{11/2}$ mean?

I am currently studying Diode Lasers and Photonic Integrated Circuits, second edition, by Coldren, Corzine, and Mashanovitch. In chapter 1.2 ENERGY LEVELS AND BANDS IN SOLIDS, the authors say the ...
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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 this quantum state means? In classical mechanics, this means that the two particles cannot have the ...
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Why do we care about real form spherical harmonics?

I'm studying atomic orbitals and the shape is usually represented with real form spherical harmonics, taken as an appropriate linear combination of the complex ones. If, however, the physical quantity ...
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Do atomic orbitals have a well-defined geometry or concrete spatial dimensions?

Can one atomic orbital be distinguished from another by its size/volume? And does this depend on the kind of atom, I mean does it differ from element to element?
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Can a particle move from one place to another without traversing the space in between? [duplicate]

Say I measure a quantum particle at some place, and then I find it at another place. According to my understanding of wavefunctions the particle can get from one place to another without traversing ...
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Compatibility of spectroscopic term values with Pauli Exclusion Principle

The ground electronic configuration of Carbon is $1s^2$$2s^2$$2p^2$ $l_1=1$ and $l_2=1$ $\implies$ $L=2,1,0$ $s_1 = \frac{1}{2}$ and $s_2=\frac{1}{2}$ $\implies S=1,0$ So the terms are $^{3}D,^{1}D,^...
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Hybrid Orbitals

https://glossary.periodni.com/glossary.php?page=41&en=high+fructose pictures like the ones in this article make no sense to me. I understand that we can take solutions to the Schrödinger equation ...
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Why do elements want to mimic Nobel gasses so much? [duplicate]

Why is the octet rule true? How can electrons even stay around nuclei with lesser number of protons?
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How Hund's rule 1 and rule 2 prevent double occupancy?

According to Hund's rule of filling up the orbitals, the ground state electronic configuration of Nitrogen is $1s^22s^22p_x^12p_y^12p_z^1$. The electrons first singly occupy the orbitals $2p_x, 2p_y$ ...
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Is there a quick yet semi rigorous way to derive the Bohr radius of hydrogen?

I will be taking an oral exam, where I have to do some "airport physics", fast and easy magnitude estimations. Currently I try to come up with a good way to find the Bohr radius of the hydrogen atom ...
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Is orbital and wave function are same thing?

As we know that wave functions are the solution of schrodinger wave equation which contains all the information about an electron. We also tought that these wave functions are the atomic orbitals of ...
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Configuration Interaction for Hydrogen Molecule

Reading a book (introduction to computational chemistry, frank jensen, Chapter 4.4 The UHF Dissociation and the Spin Contamination Problem) on Quantum Chemistry, it introduces Configuration ...
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Localizing position of electron in hydrogen atom

Consider the hydrogen atom, just taking into account the electrostatic force and not magnetism nor spin. Is it possible to take the wave functions of the energy eigenstates of that hydrogen atom, ...
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Orbital angular momentum of a electron

I am a high school student. My query is that I have read somewhere that orbital angular momentum is related to the motion of the electron or any subatomic particle (I know that this is not the same as ...
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Do the hydrogen atom's electron orbitals have Gaussian probability density functions?

In this article they show the following diagram: Are all the diagrams in the little boxes really just Gaussian probability density functions with mean and variance (or covariance)? If not, what kind ...
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Selections rules for spin

what do we mean by the selection rule $\Delta S=0$? Can you give me some example for hydrogen atom? For example if I want to go from $1s$ to $2p$ how can I calculate $S$ for $1s$ or for $2p$?

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