Questions tagged [orbitals]

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3answers
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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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171 views

Why is $m_{\ell}$ called the magnetic quantum number? What is its association with magnets?

I am going over my quantum lecture notes and I can't seem to link the quantum number $m_{\ell}$ with any magnetic property. It just seems to specify the shape of an orbital with a particular principal ...
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0answers
42 views

Question on Kleinman-Bylander pseudopotentials

When Kleinman-Bylander pseudopotentials are used the Hamiltonian operator is given by $$\hat{H} = -\frac{1}{2}\nabla^2+V_{\textrm{local}}+\delta \hat{V}_{\textrm{NL}}$$ where $$\hat{V}_{\textrm{NL}} = ...
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1answer
87 views

Griffiths Quantum Mechanics - How can magnetic quantum number $m$ possibly be negative?

I apologize if this is already somewhere on this site, I searched with relevant keywords but could find nothing. This is from David Griffiths' Introduction to QM. In section 4.1.2 (Angular Equation),...
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1answer
97 views

Labeling the eigenstates of the many electron Hamiltonian

I'm taking a course on atomic and molecular physics and there is a chapter about finding suitable quantum numbers that label the eigenstates of a given Hamiltonian. The lecture notes say that it ...
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2answers
202 views

Why is the energy eigenstate of hydrogen atoms $\lvert n\ell ms \rangle$?

When solving the Hydrogen Atom using the Schrödinger's equation, we find the wave function represented in the position bases, and it turns out that the wave function has parameters $n$, $\ell$, $m$, ...
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1answer
84 views

Electrons can't orbit at any old radius [closed]

Electrons can't orbit at any old radius from the atom's nucleus, but are rather restricted to only specific orbits at a fixed set of distances. This is called orbital quantization. Why this ...
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1answer
156 views

Hydrogen atom from the perspective of the old quantum theory

I am trying to understand the old quantum theory's description of the Hydrogen atom. So far, I have read a physics stack exchange post about Sommerfeld's approach to quantization (Deriving the Old ...
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1answer
49 views

Symmetry on Bohr's Hydrogen Atom

I was studying the applications of the Schröedinger wave function in the Bohr's atom. For what I understood, the $\psi$ should only depend on r and not on $\theta$ and $\phi$. Does that mean that $\...
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0answers
36 views

Visualization of a system of two electron orbitals

There are many clear and beautiful 3D pictures of different orbitals of a single electron: sphere-symmetric s orbitals, p-, d- and so on. But what is about systems of many electron? In this case ...
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1answer
140 views

Feynman-Hellmann theorem problem in Griffiths - somewhat inaccurate?

Problem 6.33 in Griffiths (typing out only the relevant parts) is stated as follows: The Feynman-Hellmann theorem can be used to determine the expectation values of $1/r$ and $1/r^2$ for hydrogen. ...
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1answer
129 views

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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3answers
601 views

Energy levels of hydrogen as $n$ goes to infinity

As you increase the energy level of a hydrogen atom $n \rightarrow \infty$ I have learned that the energy of that energy level changes according to $$ E_n =- \frac{13.6 {\rm eV}}{n^2},$$ and that ...
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1answer
369 views

What is the difference between HOMO-LUMO Energy gap and Forbidden (Energy) gap?

I have found a similar question on a different website upon searching on google but it didn't clear my confusion (which might be because I didn't understand the explanation). (PS: I am a 12th STD ...
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1answer
79 views

What do we see when we observe a molecular orbital?

My understanding is that when two hydrogen atoms bond (for example) the wavefunctions describing each atom combine into a single molecular wavefunction. Assuming the Copenhagen interpretation, does ...
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1answer
62 views

Why are $p$ orbitals independent from this symmetry rule?

I am very new to quantum mechanics and I have a question about $p$ orbitals. I am studying Beiser's Modern Physics and according to that in the Bohr Model the wave the probability density of ...
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0answers
41 views

Ground state term symbol, why is $L = |M_L|$, if $L$ must be a maximum?

I'm trying to understand how to predict ground state term symbol of atoms. After finding the biggest S, why the biggest $L$ will be $L = |M_L|$, where $M_L = \sum m_l$? I know this rule works to ...
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1answer
73 views

Formula for the sequence of hydrogen orbital quantum numbers [closed]

My previous question had a poor reception because somebody thought my question was not about physics. Therefore, I repost the question in a less mathematically precise way, such that it is about ...
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1answer
50 views

Why does heating an atom make it emit certain wavelengths?

We're going over quantum basics in chemistry right now and I'm very confused. Electrons can only accept in discreet quanta to move up an energy level, right? And they reflect other forms of light ...
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2answers
369 views

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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2answers
52 views

Higher energy of outer orbitals around nucleus [duplicate]

I remember reading that the outer orbitals of atom have higher energy. If an electron is given enough energy it goes to higher energy orbitals from $n=1$ to $n=2,3,4...$ My question is that why do ...
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1answer
58 views

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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1answer
150 views

Relation between magnetic quantum number and angular momentum quantum number

The energy levels of a quantum rigid rotator are given by $$ E_{\ell}=\frac{\hbar^{2}}{2 I} \ell(\ell+1), \quad \text { for } \ell=0,1,2,3, \dots $$ It is also stated that the degeneracy of each level ...
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0answers
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Why do all atoms follow the same $n$ and $\ell$ quantization conditions as hydrogen? [duplicate]

The quantum state of an electron in a hydrogen atom is specified by 4 quantum numbers: $n$ , $\ell$, $m_\ell$, $m_s$ which can take the following values: $$n = 1, 2, 3, ... $$ $$\ell = 0, 1, 2, 3, ......
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1answer
58 views

Query about Heisenberg uncertainty principle

acoording to heisenbergy uncertainty principle if the electrons change the radius of their orbit, then it is like making transition even though the change in radius is small and they should emit ...
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3answers
2k views

Why does transition from one electron shell to another shell always produce massless photon?

When electrons transition from a higher energy state to a lower energy state (energy difference $E$), they produce massless photon with frequency $\nu$ where $ \Delta E= h \nu$ (h is Planck ...
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3answers
426 views

Do electrons in the same orbital but different spin feel each other's Coulomb repulsion?

Or is it irrelevant, as orbitals are QM while Coulomb interactions are classical physics? What I think I understood of orbitals is that particles with the same quantum numbers cannot occupy the same ...
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1answer
127 views

In De Broglie's Explanation for Bohr's Quantization Condition, why do we not use 2πr = n λ/2, why do we use 2πr = n λ?

In de Broglie's explanation for Bohr's quantization condition, why do we not use $2\pi r = n\lambda/2$, why do we use $2\pi r = n\lambda$? We know that in waves on strings, for standing waves ...
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0answers
36 views

What exactly does it mean for an element to experimentally violate the Madelung ordering rule?

The Madelung ordering rule says that as you increase the atomic number of a neutral atom, the electron orbitals fill up in order of increasing value of $n+l$, and in increasing order of $n$ within a ...
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0answers
49 views

Naive question on the development of quantum numbers

In my freshman Chem 101 course, we are going over the development of the atomic model upto the basic modern quantum model. I learned that the azimuthal and magnetic quantum numbers were introduced to ...
2
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1answer
491 views

Difference between $nh/2π$ and $\sqrt{\ell(\ell+1)}h/2π$

My textbook mentions that the orbital angular momentum is the second formula and the angular momentum of an electron is given by $nh/2π$ in Bohr model. Please help me realise the link between these ...
2
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1answer
304 views

Can an electron be inside a proton?

This article has an image showing the 2S and 2P states of a hydrogen atom. The caption makes the following claim: The 2S and 2P states of hydrogen show where the electron could be found at any ...
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1answer
39 views

Interaction between electrons in which the magnetic dipole moments interact more strongly than their electric fields

Asking a question Has anyone tried to incorporate the electrons magnetic dipole moment into the atomic orbital theory?, I was curious whether anyone has attempted to relate the intrinsic property of ...
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0answers
27 views

Determining the binding energy in the L-shell in copper

Im having trouble grasping the following problem: Calculate the binding energy in the L-shell for copper, if the binding energy for the K-shell is $ \ 1,439*10^{-15} J\ $. I know that you find the ...
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3answers
678 views

Are the electrons' orbitals the same for all atoms?

Are the electronic orbitals of an atom always quantified in the same way (i.e. the same energy required to reach the next level), or does each atom have its own values for each level? If the ...
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1answer
97 views

Why is order of electron orbital filling not completely sequential? [duplicate]

Orbitals fill in the following order, 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, etc. Its a nice pattern that many elements follow, but there are exceptions to. For example: V: 1s2 ... 4s2 ...
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0answers
35 views

What is a pseudo wave and how to calculate it?

In a description of the density of states in https://wiki.fysik.dtu.dk/gpaw/documentation/pdos/pdos.html I find the term pseudo (partial) wave (in the section Molecular Orbital PDOS). What is it and ...
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1answer
217 views

Has anyone tried to incorporate the electrons magnetic dipole moment into the atomic orbital theory?

The Pauli exclusion principle is related to the electrons spin. The quantum numbers are complete only with the spin quantum number. I am curious whether anyone has attempted to relate the intrinsic ...
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2answers
327 views

Path of an electron around a nucleus [duplicate]

I have just started reading about quantum mechanics and i stumbled upon this silly question - Quantum mechanical model of an atom says that path of an electron around the nucleus is uncertain. Then ...
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1answer
212 views

What was the origin of Bohr-Sommerfeld's quantization rules?

What made Bohr and Sommerfeld think momentum and angular momentum is quantized? What is the meaning of momentum quantization in harmonic oscillator? Can we imagine it (by some classical example)?
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1answer
94 views

Can the spectra of helium atom be solved by Schrodinger equation?

Can the Schrodinger equation work out the spectra of helium atom, not all, but part of them?
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0answers
52 views

Has man ever observed the spectrum of a single hydrogen atom?

Were there this kind of experiment done before? The spectrum we observed is radiated by huge number of hydrogen atoms in the gas, not by single hydrogen atom. I know it's very hard to test a single ...
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2answers
589 views

Why Bohr atom model is still being tought in high school? [duplicate]

Bohr atom model is still the textbook content of today's high school physics. We all know that the Bohr model is only suitable for single electron hydrogen atom, not suitable for other atoms. For ...
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3answers
4k views

Do electrons really perform instantaneous quantum leaps?

This is not a duplicate, non of the answers gives a clear answer and most of the answers contradict. There are so many questions about this and so many answers, but none of them says clearly if the ...
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0answers
23 views

Crystal Field Theory (CFT) in $s$-$p$ orbitals system

Crystal Field Theory (CFT) is a model that describes the breaking of degeneracies of electron orbital states, usually d or f orbitals (Source: wiki). My doubts: Is it possible to have CFT effect in ...
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1answer
2k views

Why don't all electrons contribute to total orbital angular momentum of an atom?

There are 47 electrons in a Silver atom, but talking about its orbital angular momentum we only take the outermost valence electron which occupies the 5s orbital. Why don't the remaining inner 46 ...
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0answers
35 views

How to calculate orbital densities/shapes of atoms in 3D?

When we read about orbitals, I'm sure we are all used to seeing illustrations of them by drawing some contour "along" the probability density function so that the electron's position is equiprobable ...
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0answers
63 views

Spacial Wavefunction Symmetries and Identical particles

I was reading this and it mentions in the 3-electron section, that for a spacial wave function to be symmetric under fermion swapping, it must be a function of even parity. Similarly for anti-symmetry ...
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0answers
72 views

How can I calculate the hyperfine structure of a $p$-orbital?

I have a little problem with the calculation of the hyperfine structure of the 3p orbital in the hydrogen atom. The Hamiltonian is: Were represents the magnetic moment of the proton and the ...
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1answer
1k views

Role of d-band in metals

I have seen that in many publications authors discuss the metals in the d-block of the periodic table (often called 'transition metals') separately from other metals (e.g. alkali metals and aluminum). ...

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