Questions tagged [orbitals]

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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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11 views

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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37 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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23 views

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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18 views

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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37 views

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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27 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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31 views

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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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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25 views

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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48 views

Orbital Angular Momnetum Explained as simply as possible

TL;DR Why is $\ell$ defined as the shape of an orbital? And what relation does angular momentum of the electron have with the shape of the orbital? Why is the $z$-component the magnetism (why does ...
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116 views

Why does perturbation theory work for helium atoms?

I saw the following argument for calculating the energy levels of a helium atom. First, ignore the Coulomb interaction term between two electrons. For this simplified model, we have the same solutions ...
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35 views

How do we know that the probability of finding an electron on some specific pattern is high and on other patters are not?

I have watched a video about the positions of electrons inside of an atom and on some specific patterns probability of finding an electron is high for example in- s,n,d why?
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20 views

Does 1 electron in each orbital guarantee maximum multiplicty?

An easy question(which most of the students of my class got correct) asks: Pairing of electrons in the orbitals belonging to the same subshell (p, d or f) does not take place until each orbitals ...
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18 views

What is the continuum function in $R$-matrix basis?

In the book $R$-Matrix Theory of Atomic Collisions it is defined the $R$-matrix basis \begin{aligned} \psi_{k}^{\Gamma}\left(\mathbf{X}_{N+1}\right)=& \mathcal{A} \sum_{i=1}^{n} \sum_{j=1}^{n_{c}}...
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30 views

Why the energy of a state increases with increasing azimuthal quantum number $\ell$?

I am reading Griffiths' introduction to quantum mechanics. But I am confused about the relation between the state energy and azimuthal quantum number $\ell$, which is discussed in Chapter 5.2.2 where ...
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32 views

Does the intrinsic spin of electrons change when we excite electrons for hybridisation?

Have had been told that electrons can move from one energy level to another by transmitting or taking in energy, and do that profitably in hybridisation. I am interested in knowing how exactly do they ...
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39 views

Why does exchange energy of electrons lead to stability?

My text book says "electrons of the same spin in degenerate orbitals tend to exchange their positions and this leads to stability". Firstly, why should the electrons exchange their positions?...
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28 views

If atomic electron is in $f$-state, what values of the total angular momentum are allowed?

What I know is total angular momentum $\vec{j}= \vec{\ell}+\vec{s}$, here $\ell=3$ for $f$ state, $s=1/2$ for spin, so the total angular momentum should be $7/2$, is this correct? is there any other ...
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38 views

How do we know that $^1S$ is the ground state of the helium atom?

Let $\psi=a_1\phi(1s(2) \ ^1S)+a_2\phi(1s(1)2s(1) \ ^1S)+a_3\phi(2s(2) \ ^1S) +... $ be a state of the helium atom. Applying variationally calculus we can found the energy expectation value of this ...
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20 views

What problem excatly did Sommerfield solve in his atomic model and how?

I am curious to know what problem did Sommerfield solve in his atomic model and how does his atomic model solve it? Most books say it solved the problem of splitting of lines but what excatly does it ...
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39 views

Where can I find the energy spectrum of larger atoms (e.g. Nd$^{3+}$)?

I would like to find a ressource where the binding energies of the outer electrons of larger atoms are listed. I'm discussing Neodymium lasers and I think it would be nice to have a graphic with all ...
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1answer
26 views

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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26 views

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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29 views

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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34 views

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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40 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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42 views

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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90 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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113 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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215 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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61 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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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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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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49 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 ...
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45 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) ...
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70 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? ...
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125 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 $^1P_1$ ...
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50 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 ...
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1answer
50 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 ...
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193 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}}...
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37 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 ...
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168 views

Symmetry of a spatial wavefunction independent of $M_L$?

Consider the atomic wavefunction: $$\newcommand{\p}[2]{\frac{\partial #1}{\partial #2}} \newcommand{\f}[2]{\frac{ #1}{ #2}} \newcommand{\l}[0]{\left(} \newcommand{\r}[0]{\right)} \newcommand{\mean}[1]{...
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56 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 ...
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59 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 ...
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45 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, $E$?
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89 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.
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51 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 ...
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22 views

Does the mediation of electric or magnetic force require distinct electron orbitals?

In the case of ordinary photons of light, matter interacts with light via electrons that orbit the nucleus. If the specific energy of a photon E = hv can be found in the atom as the energy difference ...
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1k views

How to get the radius of Bohr from the uncertainty principle?

I would like to know how to get the following result: \begin{eqnarray} a_0=\frac{4\pi\varepsilon_0 \hbar^2}{\mu e^2} \end{eqnarray} from the beginning of the uncertainty of heisenberg. If possible, I ...