Questions tagged [orbitals]

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Meaning of quantization of energy

I am trying to understand the concept of energy quantization. For example, Sodium. Let's talk about $2p$ and $3s$ for this example. So $2p$ has 6 electrons and and $3s$ has one. So when we say energy ...
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Can Aufbau principle be derived/proved with a definite reason? [duplicate]

How is Aufbau principle derived or proved? on a note, why does the energy of 3d subshell is More than that of 4s subshell, instead as 4s is greater in extent than 3d,4s should have greater energy! ...
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Magnetic quantum number assigning

How do we assign magnetic quantum numbers to orbitals? For example $m = 0$ for $d_{z^2}$, ... And does this numbering affect any character e.g. if I name $m = 1$ as $d_{z^2}$, will it really change ...
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The real amount of energy in $\rm HBr$ greater than the real energy stored in $\rm HCl$

Our teacher told when a system contains more energy its unstable. Bond dissociation enthalpy of $\rm HCl$ is around 430kJ/mol and $\rm HBr$ is around 360kJ/mol. The bond length between $\rm HCl$ is ...
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What's the difference between an orbital and an energy level? Are they the same thing?

In chemistry, you're likely to learn that each atom has a given number of orbitals, or electron shells, where the first orbital contains two electrons, the next contains eight electrons, and so on. In ...
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Why don't electrons in $s$ orbitals scatter off the nucleus?

Electrons in $s$ orbitals statistically spend the better part of their time in the nucleus. What stops them from scattering off the nucleus?
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28 views

Linear combination of atomic orbitals

For example, I have linear combination of states $$|n,l,m\rangle:~| \psi \rangle = c_1 |2,1,0\rangle + c_2 |2,1,-1\rangle +c_3 |2,1,1\rangle $$. Here $n =2$, $l = 1$, so it's three p-orbitals with ...
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1answer
21 views

Rydberg Frequency

Is the frequency of radiation emitted or absorbed = $R_\nu(\dfrac {1}{n_i^2}-\dfrac {1}{n_f^2})$ where $R_\nu$ is the Rydberg Frequency = $3.29 \times 10^{15}$ Hz?
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4answers
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Why 2nd Shell can have 8 electrons?

I recently watched this video:https://youtu.be/INYZy6_HaQE and understood why 1st orbital can have only 2 electrons: According to Pauli's exclusion principle, two electrons cannot have the same ...
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SAM & OAM between different electrons?

when we consider the coupling of angular momentum between different electrons, we tend to only take L_1 & L_2 coupling, L_1 & S_1 coupling, S_1 & S_2 coupling and L_2 & S_2 coupling ...
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1answer
38 views

What is the IRREP of the $p_z$ orbital in a $C_s$ point group?

What is the representation on the $p_z$ orbital in a $C_s$ symmetry group? The $C_s$ symmetric group has two irreducible no. of representations $A^{'}$ ---> $s, x, y, xy$ and $A^{''}$ ---> $...
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137 views

Why don't electrons in an atom stop moving?

I've studied electrostatics and we always use Coulomb's law to calculate the force on a particle due to another particle. In an atom there are many electrons and many protons, and if we "take a ...
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1answer
78 views

Proof that $L=S=0$ for filled electron subshells?

It is commonly stated that if you have a filled subshell, such as $p^6$ or $d^{10}$ that one must have $L=S=0$ implying $J=0$ and $M_J=0$ so that the atom is spherically symmetric. Why is it clear ...
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1answer
50 views

What determines the class of ferromagnet?

I believe that iron, nickel, and cobalt are all 3d ferromagnets. As I understood, those 3 are the only ferromagnetic elements, so why do we specify 3d? Here is an example of a 4f ferromagnet: https://...
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What did Bohr take as the amplitude of the Bohr-atom theory?

I'm trying to model the Bohr atom as discussed in page-431 of this pdf , while trying to make an animation for it, I got confused on what exactly take as the amplitude of the Bohr orbit. Hopefully ...
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2answers
87 views

How should get the expectation value of $1/r$ in the hydrogen atom? [duplicate]

I have a question of quantum mechanics. I want to calculate \begin{align}\left\langle \frac{1}{r} \right\rangle \end{align} in the state $n, l$ of the hydrogen atom. In the textbook I have, the ...
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1answer
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What determines a bonding/antibonding molecular orbital?

Citing from this site: Bonding molecular orbitals are formed by in-phase combinations of atomic wave functions, and electrons in these orbitals stabilize a molecule. Antibonding molecular orbitals ...
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2answers
102 views

Why are atoms stable? [closed]

I will ask my question in a way that's all handwaving and no math, and I will welcome handwaving answers. I'm interested in visualizing the concepts. A long time ago we had an idea about the atom as a ...
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45 views

Physics history — the Ultraviolet Catastrophe [duplicate]

I will ask my question in a way that's all handwaving and no math, and I will welcome handwaving answers. I'm interested in visualizing the concepts. We had an idea about the atom as a massive nucleus ...
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1answer
32 views

Hybridisation of orbitals

When we talk about the electronic configuration of boron , sulphur , nitrogen. What I got to learn new was about their hybridisation. For example , boron has electronic configuration as $1s^2 2s^2 2p^...
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1answer
74 views

Can you recover the quantum numbers from just the shape of the spherical harmonic?

So I was wondering, in quantum physics beautiful graphs are introduced displaying spherical harmonics relying on the quantum numbers of $m$ and $l$. But is it possible to recover these quantum numbers ...
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2answers
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Don't the four quantum numbers make two electrons distinguishable?

From the Pauli's Exclusion Principle no two electrons in a bound system have all same quantum numbers. This means that an electron can be uniquely specified by the four quantum numbers and hence can ...
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What are the possible orbital occupation for a triplet state?

I am trying to run some Hartree fock calculation for interaction between an atom and a molecule. The molecule is in its triplet state and i have to indicate the orbitals that these unpaired electrons ...
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1answer
45 views

How does an atom for non-metals look like?

Here, I have drawn a 4 orbits . Now, what I have studied in this atomic structure for non metals is that electron are present in orbits all according to Niels Bohr. So, I have drawn them with yellow ...
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1answer
51 views

Bohr's model of atom

In our textbook, under developments that lead to Bohr's atomic model, it is stated Dual nature of electromagnetic radiation. atomic spectra which could be explained only by assuming quantized ...
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4answers
96 views

Bohr's quantization of angular momentum

I cannot seem to find a derivation for $L=\frac{nh}{2\pi}$ I do not understand what led Bohr to quantize angular momentum in units of Planck's constant and how he was sure it works. I understand that ...
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0answers
36 views

Calculating the electron orbital for the following (4, 1, -1, -1/2) [closed]

I'm fairly new to applications in physics, so would really appreciate your support on whether I performed the following calculation for this orbital correctly. Also, what does it mean when $\pm\frac{1}...
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1answer
60 views

About the calculation of the Spin-orbit correction for the Hydrogen atom

I'm using first order perturbation theory to calculate the energy corrections due to the fine structure of the Hydrogen atom. I'm having some doubts about the calculation of the spin-orbit term. Some ...
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2answers
61 views

How do I find expectation value of $1/r$?

I know that the expectation value of $x$ is $\left\langle \psi \middle| x \middle| \psi \right\rangle=\int_{-\infty}^{+\infty} \psi(x)^2x \,dx$. But what if I need to calculate $\frac{1}{r}$? Do I ...
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1answer
41 views

What does closed orbits mean in Quantum Mechanics?

In classical mechanics, The inverse potential $$\phi=-\frac{C}{r}$$ leads to closed orbits. The planetary motion is one example. The the conservation of the $$\mathbf{n}=\frac{\mathbf{p}\times\mathbf{...
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4answers
80 views

Why aren't protons constrained in the same way electrons are?

I am fairly new to quantum physics, and I have been told that electrons, when inside an atom, only fit in discrete orbitals/wavelengths. I understand why this happens. My question is, protons also ...
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On orbiting electrons losing energy in radiation

I know questions about this have been asked before, but I want to know something specific I haven't seen in the answers for those. Apparently, an accelerating charged particle loses energy, due to ...
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28 views

Physical interpreation of coulomb and exchange integral

When trying to solve the Schrodinger equation for the electronic hamiltonian: $$H_{el} = \sum_{i=1}^{N} \bigg( - \frac{1}{2}\nabla_i^2 - \sum_A \frac{Z}{r_{i_A}} \bigg) + \sum_{i>j=1}^{N}\frac{1}{...
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1answer
42 views

What is the difference between angular momentum of electron by Bohr and orbital angular momentum?

Orbital angular momentum of an electron is $\hbar \sqrt{\ell(\ell+1)}$ where $\ell$ is angular quantum number. Angular momentum of an electron by Bohr is given by $mvr$ or $\frac{nh}{2\pi}$ (where $v$ ...
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Are angles ($\theta$ and $\phi$) in spherical coordinates treated as operators in quantum mechanics?

Position is specifically considered as an operator in quantum mechanics. I want to know if $\theta$ and $\phi$ are explicitly considered as operators in quantum mechanics for solutions to 3D ...
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4answers
158 views

Why does the antibonding orbital has higher energy (than the bonding orbital) if the Coulomb repulsion is lesser?

Depending on its strength, the attractive double dirac delta potential shown below can support two bound states. They are called the bonding and the antibonding orbitals as shown in the figure below ...
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1answer
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How can real $d$ orbitals be computed from complex orbitals?

I recently completed MIT's 8.04 quantum mechanics course on edX and have been writing python code to compute hydrogen-like electron orbitals, basically just for fun. My program computes the ...
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1answer
64 views

When is the principal quantum number $n$ a good quantum number?

Since I don't know an associated operator to the principal quantum number $n$, I don't know when it is a good quantum number. By 'good quantum number' I mean a quantum number that is conserved over ...
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1answer
114 views

Why does exchange occur between electrons having same spin in “degenerate orbitals”?

I am a high schooler and I read in my chemistry book that half filled degenerate orbitals are stable because electrons with the same spin in those degenerate orbitals exchange their positions and this ...
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3answers
54 views

Can protons have orbital if they gain more energy? [closed]

I read that because a proton is much more massive than electron but an electron has slightly more energy so it doesn't fall into the nucleus and orbital is due to the constructive interference of ...
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1answer
73 views

How to “restrict to a subgroup” to explain representation structure?

I am reading from Quantum Theory, Groups and Representations - Woit. In Chapter 21, on page 237 in discussion of the energy eigenstates of the Coulomb potential, the following figure is presented: ...
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264 views

What actually makes a Bohr's radius stable?

I was told that Bohr introduced the concept of Stationary orbits in which electrons were stable in my school but I never got the reason behind this stability. So can someone explain why is Bohr's ...
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4answers
46 views

How charge is explained, in context of bonding?

In ionic compounds, like NaCl, Cl gains negative charge due to addition of electrons. In covalent compounds, like Cl2, sharing of electrons occurs. Here too, Cl atom has got an extra electron in its ...
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1answer
39 views

How to calculate the sphere of influence of a planet?

I'm making an orbit simulator, and to make it simpler, I'm only simulating one celestial object(planet, moon, sun) acting on each object(sattelite). So that the sattelites and rockets can switch ...
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1answer
42 views

Why do relativistic effects that cause contraction of the $s$ and $p$ orbitals impact the $s$ and $o$ orbitals further away from the nucleus?

I was reading quite a well-known paper titled 'Relativistic Effects in Structural Chemistry' by PEKKA PYYKKO. In the paper, he describes how the electrons occupying $s$ and $p$ orbitals move at ...
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Fermi Energy and single particle state

I have a question about Fermi energy and the single particle state. I have it a bit hard, on how to formulate my question, for the below text, because I don't fully understand the concepts so well. ...
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3answers
82 views

Do actually sharing of electrons make bond?

My book says, "When we bring two atoms close, respective repulsion and attraction happens between the two's electrons and protons. Experimentally it is found that the attraction force is greater ...
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4answers
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Are all atoms spherically symmetric? If so, why are atoms with half-filled/filled sub-shells often quoted as 'especially' spherically symmetric?

In my atomic physics notes they say In general, filled sub-shells are spherically symmetric and set up, to a good approximation, a central field. However sources such as here say that, even for the ...
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Is it better to think of electron shells as depending on the value of $n$, or depending on the energy difference between sub-shells?

Often electron shells are defined as 'states with the same principal quantum number $n$' which would suggest that $3s$, $3p$, $3d$ sub-shells are all in the same shell. Conversely, it is also often ...
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4answers
117 views

What significance can we assign to 'breathing' of $s$-shell orbitals?

In my atomic lecture notes it says We can visualise an $l=0$ $s$-state as a spherical cloud expanding and contracting - breathing, as the the electron moves in space. Similarly in the video enter ...

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