Questions tagged [orbitals]

The tag has no usage guidance.

54 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
4
votes
0answers
130 views

Why do electrons abide by Hund's rule?

Is the reason why Hund's rule exists, that when electrons are in different orbitals (such as 2px, 2py, or 2pz), they are most stable (lowest energy)? If the purpose is stability/lowest energy, ...
4
votes
0answers
89 views

How are hybrid orbitals more energetically favorable than their components?

In the orbital hybridization theory, the $s$ and the $p$ orbitals are said to combine to form hybrid orbitals which are degenerate in energy. How does the linear combination of the $s$ and $p$ ...
3
votes
0answers
52 views

How come the xenon $6s$ state is metastable?

I'm having some trouble puzzling out some aspects of the electronic excitation spectrum of xenon, and I'd appreciate some help with it. This classic paper ─ the first one to pioneer the use of laser-...
3
votes
1answer
79 views

In chemical compounds, where does the “magic” come from in atomic “magic numbers”?

It is well known that atoms with a full electron shell are more stable, it is one of the first facts taught in a middle school Chemistry course: "An element whose atoms have no electrons outside ...
2
votes
0answers
34 views

What are the prerequisites for a free electron and an atom/ion to recombine?

I'm mostly interested about recombination not in plasma (e.g., recombination of beta particles with atoms that they pass by), although the rules are probably the same. Say, there's a free electron ...
2
votes
0answers
45 views

A question about almost stationary orbits

For an orbit around the earth with period equal to a sidereal day with eccentricity $e=0$ and inclination $i=0$, the path on earth would be a single point on the equator. I have done some simulations ...
2
votes
1answer
143 views

Physical Intuition for thermodynamic limit of the average occupancy, $\langle N\rangle$, of an orbital

Say your allowed occupancies for an orbital are $0, 1, 2$, and the values of energy associated with these occupancies are $0, \epsilon, 2 \epsilon$. Give an expression for the ensemble average ...
2
votes
0answers
97 views

Gravitational aberration and unstable orbits

From this link http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html it says that Putting a "light travel delay" (technically called "retardation") into newtonian gravity would make ...
2
votes
1answer
66 views

The Existence of the $^1D$ term and the non-existence of the $^3D$ term?

Yesterday I asked this question concerning the existence of terms. This question is on the same topic. I have been looking at some tables (in Yang and Hamilton (2010), pg 199) at the terms that exist ...
2
votes
0answers
56 views

Is it possible to reach orbit without turning the rocket?

A comment to this question sparked my interest. If we start a rocket from the surface at the equator, it has some angular momentum with regard to Earth. This angular momentum is definitely much too ...
2
votes
0answers
203 views

Hund's rules on wikipedia

I'm trying to understand the examples on Hund's rules on Wikipedia, but I have a problem. Wikipedia says that for Silicon the possible combinations of quantum numbers are $1D$, $3P$ and $1S$ (first ...
2
votes
0answers
59 views

A question on energy levels of molecular orbitals

Here is a phenomenon from MO theory for diatomic homonuclear molecules that I could not understand. If $Z \le 7$ then $\sigma_{2pz}$'s energy is higher than $\pi_{2px}$'s energy. I did not get ...
1
vote
0answers
24 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 ...
1
vote
0answers
47 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 ...
1
vote
0answers
15 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 ...
1
vote
0answers
26 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 ...
1
vote
0answers
43 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 ...
1
vote
0answers
36 views

In the pilot-wave theory, is the quantum potential moving electrons randomly inside atoms?

As we know, in the pilot-wave theory (Bohmian mechanics), particles are guided on certain trajectories by the wavefunction. Here (In Bohmian mechanics, do electrons move inside an atom?) I asked about ...
1
vote
0answers
62 views

When will Hund's rules fail?

I heard someone mentioned that Hund's rules do not always work. Looking at atomic spectrum: (https://qudev.phys.ethz.ch/phys4/PHYS4_lecture10v1_2page.pdf page 10 Hg spectrum) How could singlet (with ...
1
vote
2answers
73 views

What is the energy of an atomic orbital?

When we refer to energy of an atomic orbital what is this energy ? is potential energy ? but if is potential energy then shouldn't be considered the whole potential energy of the atom ( potential ...
1
vote
1answer
50 views

A dreidel on a spinning table

In the spirit of the holidays. Let's assume that a dreidel is spinning counter-clockwise at frequency $f$ on a table. From external point of view, what will I see if I rotate the table clockwise at ...
1
vote
0answers
87 views

How to use Hund's third rule for excited electronic configurations?

Hund third rule states: For a given term, in an atom with outermost subshell half-filled or less, the level with the lowest value of the total angular momentum quantum number ${\displaystyle J\...
1
vote
0answers
29 views

Orbitals and configurations with degenerated energy

When we have to choose, given $n$, $\ell$, where to put an electron, when there are several $m$ orbitals, with the same energy, is there a concrete quantum mechanic rule or some superselection rule to ...
1
vote
0answers
25 views

Spin in 3d orbitals of 2 irons

Which technique/method/theory must I use in order to calculate/see what happens at the spin of 3d orbitals when two atoms of Iron come close?
1
vote
2answers
101 views

Can atomic orbitals of an isolated atom rotate relative to the nucleus?

I am a beginner at orbitals. It seemed interesting to me while studying p orbitals that the texts don't suggest that the orbitals are rigid relative to the nucleus. But I thought mathematically these ...
1
vote
0answers
640 views

Electron Levels of Atomic Nitrogen Vs. Molecular Nitrogen

So I have a question about the the affect of the electron energy levels of Nitrogen when it becomes diatomic. In Figure 1 below you see the electron energy levels of atomic Nitrogen, and it shows that ...
1
vote
0answers
55 views

How does the filling of the 2p orbitals occur?

When electrons enter the 2p orbitals, electrons of the same spin occupy the 2p orbitals first and then electrons of the opposite spin fill up the orbitals. Why is that? My professor told me that there ...
1
vote
0answers
31 views

Surface potential and symmetry breaking

I am studying surface states currently and am a little confused about something. If I consider p-orbits on a surface state that is the top layer of an HCP structure -- I understand the hopping terms ...
1
vote
0answers
949 views

How do the Fermi level, HOMO and LUMO change with doping?

I am a bit confused about solid state physics of organic materials because as I know the workfunction changes with the doping of a material but the Fermi level is constant with doping. So depend on ...
0
votes
0answers
11 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 ...
0
votes
1answer
52 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)?
0
votes
0answers
50 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 ...
0
votes
0answers
8 views

How to deduce the SK (Slater-Koster model) integral for two-center with px, py orbital?

I would like to get the Slater-Koster integrals from formula: $$ \sum{R_j}expi\textbf{k}\cdot(R_j-R_i)\int\psi^*_n(\textbf{r}-\textbf{R}_i)H\psi_m({r}-\textbf{R}_j)d\nu, $$ (1) where the sum is ...
0
votes
0answers
20 views

Band formation in diamond

Why is it that in the band diagram of diamond does the sp3 hybridised orbital split into two forming valence band and conduction band? I thought that these sp3 hybridised orbital forms 4n bonding and ...
0
votes
2answers
32 views

How many pions can be accomodated in an orbital?

electrons have a spin of 1/2 and 2 electrons are accomodated in an orbital pions have a spin of 0 so how many pions can be accomodated in an orbital? i thought that since no two electrons (or pions) ...
0
votes
0answers
20 views

How to use Dyall basis sets for radial wave functions?

I have found the dyall basis set coefficients on the homepage http://dirac.chem.sdu.dk/basisarchives/dyall/ Does anyone in the forum has experience for using for example the "5p" basis set? I only ...
0
votes
0answers
13 views

Spectroscopic notation for $As$

I’m wondering if I’m approaching hund’s Rules for Arsenic correctly (Ar): (Ar)$(3d)^{10}(4s)^{2}(4p)^{3}$ I started with HR1: Maximize the spin. I have 6 orbitals so I can put one electron in the ...
0
votes
0answers
56 views

What is the point of talking about three axes for hydrogen orbitals?

The hydrogen orbitals are usually described using polar coordinates ($\Psi(r, \theta, \varphi)$). I understand that $r$ is the distance from the center of the atom, but how are the angles defined? ...
0
votes
1answer
54 views

State with highest energy of Carbon atom

A possible excited state of the $C$-Atom is one with a $3s$ electron: $(1s)^2(2s)^2(2p)^1(3s)^1$. One can find out that there are the 4 possibilities $^1P_1, ^3P_2,^3P_1,^3P_0$. Why is the $^1P_1$ ...
0
votes
0answers
47 views

atomic orbitals calculation in Heisenberg picture

It sounds like this question was answered at the beginning of the last century. Nevertheless, going through some notes on basic quantum mechanics I noticed that Schordinger picture enables one to ...
0
votes
1answer
42 views

How do I obtain the orbital shapes for an electron moving in a uniform magnetic field?

I'm quite familiar with orbital shapes for a hydrogen atom (where a potential field due to a point charge, i.e nucleus exists). I've been interested in trying to figure out the orbital shapes for an ...
0
votes
0answers
125 views

Orbitals of hydrogen, superposition

I'm trying to find the time evolution of the following superposition states in the hydrogen atom: $$\psi_- = \frac{1}{\sqrt{2}}\left(\psi_{1,0,0}+\psi_{2,1,-1}\right) \\\psi_0 = \frac{1}{\sqrt{2}}...
0
votes
1answer
202 views

How to calculate expected angular momentum for $d_{x^2 - y^2}$ orbital

I know that the expectation values of $L_x, L_y, L_z$ are $0$ for a $d_{x^2 - y^2}$ orbital, but how is this done using algebra? In other words, can someone show me how $<d_{x^2 - y^2}|\hat{L_z}| ...
0
votes
1answer
32 views

How does geometry affects the energy content of an Orbital?

My chemistry books state without giving any reason that due to its' Bell shaped(2d:planar*) structure p_orbital possess more energy than s -orbital?(speherical/ 2d:circle) So how does geometry ...
0
votes
0answers
55 views

How can an orbital be recognised from the wavefunction notation?

I am a student and was working up the exercises in my book when I came across a problem that required me to identify the orbital given by $ \psi_{3,2,1}\,.$ What I can work out is that the sub-shell ...
0
votes
1answer
55 views

What factors relate the number of protons in the nucleons with the number of electrons in the orbitals?

Atoms always want to have a closed shell, because it requires low energy compared to the lattice enthalpy. How does this always match throughout the periodic table between the number of protons and ...
0
votes
0answers
40 views

Higher $L$ lower energy?

For multi-electron atoms, what is the physical reason behind the fact that a higher total orbital angular momentum, $L$ gives a smaller total energy, $E$?
0
votes
1answer
242 views

Rydberg formula for hydrogen

I've been told that if a hydrogen atom is exposed to electromagnetic radiation of wavelength $\lambda$ such that Rydberg's formula $$\frac{1}{\lambda}=R\left(\frac{1}{n_{1}^2}-\frac{1}{n_{2}^2}\...
0
votes
0answers
68 views

Slope of p-orbitals at the nucleus

Is there any analytic expression describing the slope of the p-orbital at the nucleus, for example for hydrogen.
0
votes
1answer
46 views

Find out the expression for angular speed in terms of time

Here is the equation that describes the motion of a planet under the gravitational field generated by a fixed star: $$u=\frac el\cos\theta+\frac 1l$$ where $u$ is the reciprocal of the radial ...