Questions tagged [orbitals]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
9
votes
3answers
1k views

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 ...
1
vote
1answer
28 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 ...
0
votes
0answers
22 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 ...
-1
votes
0answers
46 views

Find out the order of excited state of the electron in that state [closed]

The energy of an electron constrained to move in a one-dimensional box of length 0.4nm is 603.178eV. Find out the order of excited state of the electron in that state.
1
vote
2answers
99 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, ...
1
vote
3answers
90 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 ...
4
votes
2answers
743 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 ...
0
votes
2answers
43 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 $2p$?
0
votes
2answers
45 views

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_\...
2
votes
2answers
65 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 ...
1
vote
2answers
29 views

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 ...
0
votes
1answer
38 views

Electrons in the quantum mechanical model of the atom

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 ...
4
votes
6answers
101 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? ...
5
votes
1answer
79 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 ...
-1
votes
2answers
69 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 ...
0
votes
1answer
39 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 ...
2
votes
1answer
35 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 ...
3
votes
1answer
80 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, ...
2
votes
3answers
95 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?
2
votes
2answers
57 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 $P(r)$, ...
4
votes
3answers
124 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 ...
0
votes
0answers
36 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)?
0
votes
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 ...
22
votes
4answers
6k 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 ...
0
votes
1answer
69 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 ...
0
votes
0answers
14 views

Is it true that overlap matrix is always diagonal or block diagonal in canonical molecular orbital basis? How about orbital degeneracy cases?

I think it should be true since the basis are orthonormal. But is this generally true for all cases? how about orbital degeneracy case?
2
votes
1answer
69 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 ...
0
votes
1answer
67 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 $p_y$...
1
vote
1answer
47 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 ...
2
votes
3answers
118 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.
0
votes
1answer
48 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 ...
0
votes
2answers
73 views

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 $-3.4$...
2
votes
1answer
39 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: ...
4
votes
4answers
172 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?...
0
votes
0answers
24 views

What are the meaning of the $s$, $p$, $d$ orbital contributions in partial density of states?

Lets say I have pDOS of Na, K or Al. Integrating total DOS for the last energy interval until Fermi level gives number of valence electrons for corresponding metal. That's also okay. My question is, ...
1
vote
0answers
31 views

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 ...
-3
votes
1answer
88 views

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?
21
votes
5answers
6k views

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 ...
0
votes
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 ...
0
votes
1answer
56 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 ...
16
votes
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 ...
6
votes
2answers
1k views

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 ...
1
vote
3answers
65 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 ...
2
votes
0answers
39 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}} = ...
0
votes
1answer
64 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),...
2
votes
1answer
43 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 ...
0
votes
2answers
86 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 $n$, $\ell$, $m$, ...
-2
votes
1answer
73 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 ...
3
votes
1answer
104 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 ...
0
votes
1answer
42 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 $\...

1
2 3 4 5
8