Questions tagged [orbitals]

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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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1answer
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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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1answer
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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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2answers
130 views

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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2answers
142 views

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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1answer
88 views

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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0answers
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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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1answer
55 views

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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1answer
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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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2answers
67 views

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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0answers
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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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1answer
36 views

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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37 views

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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2answers
137 views

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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3answers
172 views

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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2answers
1k views

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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2answers
200 views

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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2answers
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How to get effective quantum numbers of a linear combination of $\rm H$-atom wavefunctions?

The convention for the Hydrogen atom's interpretation subject to the laws of quantum mechanics is that you can prove the quantization of $|L|$, $L_z$, and Energy through quantum numbers $\ell$, $m_\...
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2answers
86 views

Orientation of the $2p$ states in a Neon atom

Consider a Neon atom. It has 10 electrons: two in the $1s$ state, two in the $2s$ state and six in the $2p$ state. The six electrons in the $2p$ state have a wave function which is not spherically ...
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2answers
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How do electron wavelengths relate to orbitals and probability density?

I'm doing a physics research project and I am a bit confused. We haven't learnt much of this on our course so I'm sorry if this is a stupid question, I couldn't seem to find an explaination that I ...
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3answers
386 views

Electrons in the quantum mechanical model of the atom [duplicate]

according to bohrs atomic model, the orbits of electrons are quantized and cant have an arbitrary radius, the electron revolving around the nucleus in this orbit, but when I was taught the quantum ...
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6answers
219 views

How exactly does an electron falling back to its original state from an excited state produce electromagnetic waves?

TL;DR Alternating currents create EM waves, that is quite clear. But why do electrons falling back to their original state create EM waves? Is there are clear explanation like alternating currents? ...
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1answer
430 views

How do I calculate the electron density of a gold atom?

I have to calculate the electron density of a gold atom. As far as I know, it is given by $\rho=e|\psi|^2$ if $\psi$ is the wave function of the electrons. The only way I know for calculate the wave ...
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2answers
83 views

Does an electron have a fixed orbit in reality? [duplicate]

The Heisenberg's uncertainty principle prevents us from measuring the position and momentum of an electron accurately at the same time. But that is just our inability, right? In reality, would ...
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1answer
118 views

Is the $1s^22s^22p^6$ atomic configuration lower in energy than the $1s^22s^22p^5$ atomic configuration?

I read that atoms in the first few rows of the periodic table gain or lose electrons to have 8 valence electrons so that they are energetically stable and has minimum energy. This means that an atom ...
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1answer
55 views

Can an electron transit within the same $n$-level?

Under selection rules for multi-electron atoms in LS coupling, its generally written that there is no restriction on the total quantum number $n$. Does it mean that an electron transit within the same ...
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1answer
108 views

What is the justification for $n+\ell$ rule in quantum mechanical model of atom?

So my textbook says Mathematically, the dependence of energies of the orbitals on $n$ and $\ell$ are quite complicated but one simple rule is that, the lower the value of $n+\ell$ for an orbital, ...
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3answers
115 views

What is an electron? Is it an orbital?

Is an orbital a wave or is an electron a wave? Does an electron exists in an orbital or is an orbital a wave cloud of electrons? Is there really particle inside an orbital or is an orbital a particle?
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2answers
61 views

Number of nodes in Hartree-Fock solution

The Hartree-Fock equation for atoms is of the form $\left[\frac{d}{dr^2}+f(r)-\epsilon\right]P(r)=g(r) \tag1$ Usually algorithms to solve this equation assumes that the number of nodes of $P(r)$, ...
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3answers
170 views

Why must energy transitions in hydrogen atom be between stationary states?

In Griffiths QM textbook, he said that a hydrogen atom in the ground state may undergo a transition to some other stationary state by absorbing a photon. Why must this transition be to another ...
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0answers
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Are specific energy levels the same distance away from the nucleus for all elements?

Atomic radius decreases across a period, but does this mean specific energy levels are different distances away from the nucleus for different elements (eg- the 2nd energy level)?
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0answers
28 views

Why does an overlap of atomic orbitals in a solid cause a continuous emission spectrum? [duplicate]

A given explanation for a light bulb's continuous spectrum of emitted light was that energy levels in solids overlap, therefore all energy changes can occur. How can these changes occur? If an ...
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4answers
7k views

Is the probability of an electron being somewhere zero?

So recently I've been reading "How to teach Quantum Mechanics to your Dog" by Chad Orzel. In chapter 3, he says, if I understood this right, that electrons can only exist in specific quanta - that is ...
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1answer
102 views

Benzene ground state

I’m currently studying my first course on Quantum Physics. Regarding the topic of Sommerfeld’s quantization rules, I’ve come across a problem where I was asked whether a benzene molecule would require ...
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1answer
85 views

Why does the Bohr model give the correct energy levels for hydrogen even though it assumes a circular orbit?

I've been reading the answers for this question: Why did the Bohr Model Successfully calculate some of the energy levels in hydrogen? but it hasn't really satisfied my curiosity. Some answers suggest ...
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1answer
87 views

Why we use $p_x$ and $p_y$ orbitals?

The wavefunction of $2p$ orbitals with $m_l=\pm1$ have the form: $$\Psi_{p_{\pm1}}=\pm \frac{1}{\sqrt{2}}r\sin\theta\cdot e^{\pm i\phi}f(r)$$ We can make linear combinations and get the $p_x$ and $p_y$...
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1answer
105 views

Local and non-local interactions

When I look for the van der Waals interactions, they are defined as they are non-local interactions but no explanation for what they mean by non-locality. What would be the best way to understand this ...
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3answers
225 views

What are the $sp^3$ orbital bond directions relative to a Cartesian reference frame?

When I try to search for this, I find images like below, but it is not clear to me what the actual bond directions are, i.e. the first one appears to be (0, 0, 1) but then I am not sure of the others.
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1answer
111 views

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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2answers
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Bohr's hydrogen model confusion

As per Bohr model for hydrogen atom,energy of $n^{th}$ electron orbital is given by $\dfrac{-13.6}{n^2}$ eV. Energy of electron in the first orbit will be $-13.6$ eV and in second orbit will be $-3.4$...
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1answer
57 views

Quantitative contribution of kinetic and potential energies to the binding energy of the $\sigma$ orbital in $\text{H}_2$ or $\text{H}_2^+$

When a hydrogen molecule forms, 4.52 eV of energy is released, while for $\text{H}_2^+$ the binding energy is 2.77 eV. Such a binding energy is the difference of energies that have four terms in them: ...
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4answers
310 views

Why does orbital overlap cause attraction?

I have been taught that when orbitals overlap as in $\sigma$ and $π$ bonds, the formation of a bond (which is basically an attraction) takes place. Why does this cause attraction, shouldn't they repel?...
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Double zeta polarised, triple zeta double polarized. What is the definition?

I understand that a single zeta basis contains the hydrogen stationary states $\psi_{nlm_l}$ for a particular selection of quantum numbers $(n,l,m_l)$. You can decide the quantum numbers that will be ...
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1answer
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Which energy levels are assigned to the different orbitals? [closed]

My assumption is that the further you move from the nucleus, the higher the energy level. But does the type of the orbital (s,p etc) also play a role in it't energy level?
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5answers
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Can you please show me a final atomic model which demonstrates movement of electrons inside it? [closed]

Is there any final model of an atom, of which we can say, “This is it”! Or is it still improving and physicists are not completely sure about it? I am particularly interested to know how exactly ...
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1answer
53 views

Why all atoms in an element $\rm Pt$ have different shapes and size?

When we imagine about an atom, the very first image comes in our mind is a sphere. But after watching the video below, that seems not true. https://www.youtube.com/watch?v=yqLlgIaz1L0 So my question ...
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1answer
134 views

Hydrogen atom ionization energy and infinity

We know that the ionization energy of hydrogen atom is 13.6 eV. What bothers is this energy corresponds to infinite seperation between the electron and proton. If we assume that this is true then in ...
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2answers
1k views

Measuring the size of the proton from the hydrogen atom spectrum?

I was reading that besides measuring the angle of ricocheted electrons bouncing off the proton to pin down its size, it is also possible to excite the electron and then measure the frequency of the ...

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