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Questions tagged [hydrogen]

Could refer to (1) A hydrogen molecule; two hydrogen atoms bonded together or (2) A hydrogen atom; One electron electromagnetically interacting with a nucleus made of a single proton. Hydrogen atoms are the simplest atoms, and they are the only atoms for which we can exactly solve the Schrodinger Equation. Hydrogen atoms are the only atoms which could exist even n a world with fine - structure constant 1.

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32 views

What is the precise internal structure of Jupiter?

I've been trying to find out exactly where the layers of molecular hydrogen, and metallic hydrogen are precisely, inside Jupiter, in kilometres from the centre. Ideally with an error margin of 1-10kms....
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Precise theoretical energy of the dihydrogen molecule as a function of internuclear distance?

I am currently looking for the most state-of-the-art theoretical prevision of the energy of the dihydrogen molecule as a function of internuclear distance as a means of comparison with numerical ...
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51 views

How much energy is stored in the field of a hydrogen atom?

How much energy is in the electric field of a single lone hydrogen atom that has no neutrons and exists at the lowest energy state possible? Well in a universe where nothing else exists.
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Why is Cosmic Microwave Background Radiation thermal? [duplicate]

Cosmic Microwave Background (CMB) Radiation is known to be thermal to very good approximation. This means that when it was created, this radiation has already been thermal. This is because the ...
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Spin of hydrogen orthonormal

In this video lecture, the lecturer wrote spin up is $|\alpha\rangle = [\frac{1}{2}, \frac{1}{2}]$ and spin-down is $|\beta\rangle= [\frac{1}{2}, -\frac{1}{2}]$. He then wrote that $\langle\alpha|\...
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Hydrogen atom orbital projections resemble to some Chladni figures! Mathematical reasoning?

Chladni figures are formed by sprinkling salt on a vertically vibrating membrane, f.e. [. Some of them are purported to be projections of hydrogen atom orbitals f.e. 1s, 2s, 2p, 3d, etc., e.g. . One ...
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Why can't hydrogen and helium fuse?

In the hearts of stars, hydrogen atoms fuse together to make helium. After the hydrogen in the core is depleted, the star changes state and conditions at the heart of the star make it possible for ...
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59 views

It more efficient to generate heat burning electrolyzed hydrogen, or through an electric resistance?

It's convenient and simple to use electricity to generate heat, doubtlessly, say in en electric kettle or boiler or heater, but is it more efficient to generate heat burning electrolyzed hydrogen, or ...
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How to understand the hydrogen energy level and its wave function?

I have difficulty to understand this Hydrogen atom's energy level and its wave function. My difficulty is regarding the hydrogen atom itself, not the energy level and the wave function their selves, ...
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1answer
52 views

Could water be converted into hydrogen and oxygen using very strong magnetic fields?

Had a crazy thought experiment and was wondering if this is possible/feasible. You place water in a electrically neutral container like glass. Then the glass container is placed between two opposing ...
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40 views

Viscosity of liquid hydrogen and its effect

The dynamic viscosity of saturated liquid hydrogen at atmospheric pressure is roughly $\mu_{LH_2} = 1.3\times10^{-5}~Pa.s$. For the same conditions, its density is $\rho_{LH_2}=70.8~kg/m3$, so the ...
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67 views

Dirac equation for hydrogen atom

I went over a calculation of the hydrogen wavefunction using Dirac equation (this one) and I am a bit confused by the angular part. The final result for the wavefunction based on that derivation is ...
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The most precise analytic solution of the hydrogen energy levels [closed]

Consider the problem where we want to calculate the energy levels of an electron in a hydrogen atom and we want to find the most precise analytic (i.e. a closed-form solution) solution that matches ...
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Question about Sakurai's $SO(4)$ symmetry section

In Sakurai's Quantum mechanics book, he says the hydrogen atom has $SO(4)$ symmetry by explicitly exhibiting operators $I_i,K_i$ that satisfy the commutation relation of the Lie algebra $so(4)$. ...
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Do all of the energy levels listed in Hydrogen Spectral Series assumed to be s ('sharp') sublevels?

When reading about the hydrogen spectral series (Lyman, Balmer, etc.) I noticed that nowhere are suborbital or sublevels (azimuthal) mentioned; only principal quantum numbers n .... Are there any p or ...
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Can the amount of heavier elements in the Sun's core be approximated?

Can the amount of heavy and other types of elements as impurities inside the Sun's core be approximated? If these elements are present, do they disturb the process of hydrogen fusion, since they ...
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Is the atomic shell model valid considering electron-electron interaction?

In atomic physics the shell model is motivated by starting looking at the H-atom. Solving Schrödinger's equation leads to atom orbitals labled by quantum numbers n,l,m. Taking Pauli's principle into ...
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Proton Electron Merger

Can somebody explain what would happen if an electron & a proton, very close to each other are left to "fall" to each other in a straight line?
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How to compute the Clebsch Gordan-coefficients for spin-angular momentum coupling of Hydrogen?

Consider a hydrogen atom with Hamiltonian $H$, angular momentum $L$ and spin operator $S$ and total angular momentum $J:= L+S$. Since $H,L^2, J^2$ and $J_z$ all commute with each other, we can find a ...
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Doubt in energy of electron in first shell of hydrogen atom [closed]

Let us calculate the energy of the electron in the first shell of the hydrogen atom. Since hydrogen is a single electron species we can use Bohr's postulates. The kinetic energy (KE) of an electron in ...
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Find the expectation value of angular momentum $L_z$ of a wave function in energy eigenstates

$ψ_{nlm} (r,θ,ϕ,t)$ as expansion in energy eigenstates: $$ψ(r,θ,ϕ,t) =\sum_{n=1}^{∞}\sum_{l=0}^{n-1}\sum_{m=-1}^{l}c_{nlm}ψ_{nlm} (r,θ,ϕ) exp⁡(-\frac{iE_n t}{ℏ})$$ Here: $c_{nlm}$ are complex constant ...
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Formula for wavelength emitted taking into account the quantum orbital number $l$

Rydberg's formula can be used to find the wavelength emitted due to an electron moving from one energy level $n_i$ to another one $n_f$. But when the Schrödinger's model of the atom is introduced we ...
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Question on lamb-shift calculation in Weinberg's QFT book

In short, how does one reproduce the derivation in the footnote on page 588 of Weinberg's QFT book? The derivation there are necessary for lamb-shift calculation. Complete version of my question: ...
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1answer
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Does measuring an observable $\hat{\theta}$ for a QM system in a state $|\psi\rangle$ preserve the expansion coefficients of $|\psi\rangle$?

Consider an idealised hydrogen atom in the state $|\psi\rangle=\frac{1}{\sqrt{6}}(2|1,0,0\rangle-|2,1,0\rangle+|2,1,1\rangle)$ where $|n,l,m\rangle$ are the normalised eigenstates of the Hamiltonian $\...
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Elements Below Ground Energy State

I have been hearing things about people getting elements like hydrogen below the ground energy state. I don't understand how that is even possible. The more interesting thing is how this actually ...
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90 views

How do I normalise the wavefunction of a hydrogen 1s orbital to obtain the normalisation constant?

The wavefunction I've been given for a 1s hydrogen orbital is: $$ \Psi = A e^{-r} $$ And I need to normalize this to find the value of A. I understand to normalise this I would inset this wave ...
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1answer
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Does the $H_2$ in cosmic clouds virtually not radiate?

I am reading the lecture notes of a friend. He has written about the cold (3-20 K) molecular $H_2$ cosmic gas, that "practically doesn't radiate, due to symmetry". Can someone confirm that $...
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33 views

Heating Hydrogen to produce Microwave EMF?

I was reading that exciting a hydrogen atom to a certain point will force lower energy electrons to jump temporarily to high-energy/valence states. These electrons immediately return to the lower ...
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1answer
59 views

Underlying principle of hydrogen lamp

I learned that a hydrogen lamp emits photons at specific spectral lines because of electrons falling from a higher energy level to a lower energy level.I think I understand this. However, nowhere can ...
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Are the properties of anti-hydrogen opposite to those of hydrogen?

In the series Crisis of Infinite Earths, the whole story is that there is a wave of antimatter rampaging through the multiverse. So I got interested and googled "how to create antimatter", ...
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Ratio of atomic and molecular hydrogen depending on temperature and pressure

I am interested in all kinds of theoretical/experimental results about the ratio of atomic and molecular hydrogen, in particlular in the high pressure (>10 GPa) and high temperature (~5000 K) ...
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64 views

Physical meaning of $\langle nlm|\hat{z}|n'l'm'\rangle$

I'm working on a quantum mechanics problem with some friends and we're trying to make an argument using symmetry rather than maths. What would the physical interpretation of $\langle nlm|\hat{z}|n'l'm'...
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I am having a doubt in graphs of $4πr^2|\psi|^2$ vs $r$ and $4πr^2|R(r)|^2$ vs $r$

To show radial probability, in some sources they used the graph $4πr^2|\psi|^2$ vs $r$ In some other sources, they used the graph $4πr^2|R(r)|^2$ vs $r$ However, $\psi(r,\theta,\phi)=R(r)Y(\theta,\phi)...
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Maximizing probability or probability density

We are given the relation $dP=r^2|R(r)|^2dr$. Also, we are given $R(r)$ for the 1s orbital, and we are required to find the most probable radius of the electron in the 1s orbital of a hydrogen atom. ...
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85 views

Does the principal quantum number, $n$, have an operator?

The hydrogen energy eigenstates are labelled with well-defined $n$, the principal quantum number. Is there an associated operator than one can apply to these wavefunctions which would result in an ...
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How does Hydrogen temperature change in a typical Gaseous Hydrogen Refueling Network?

In a typical Hydrogen Refueling network (Example); Hydrogen is Produced via electrolysis at 20-30 bar Compressed to 150 - 250 bar and stored in Low Pressure (LP) Storage loaded onto a hydrogen tube ...
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Principles and methods of measuring the orbital angular momentum of $\rm H$-atom

When we talk about the orbital angular momentum (OAM) of the $\rm H$-atom, we mean the eigenvalues $l(l+1)\hbar^2$ of the OAM operator of the electron $\hat{L}^2$ defined from its classical ...
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231 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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30 views

How do we recognize 21cm emission line during Dark Ages

I was reading about the 21cm emission line of Hydrogen and its use to probe very different scale of redshifts, but something bothers me a little. How do you recognize an emission or absorption line ...
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1answer
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Hydrogen Transitions in Foot

I was reading through Foot's Atomic Physics, and saw this depiction of the transitions of the hydrogen atom. My understanding is that here we must require $\ell - \ell' = \pm 1$. Indeed, this is what ...
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1answer
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Could liquid hydrogen tank be any shape we want? [closed]

I am doing the initial design of an aircraft for my Aerospace Engineering project. I want to use liquid hydrogen as the fuel of my aircraft. However, a cylindrical fuel tank or spherical fuel tank ...
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Can water thermolyse in significant amounts?

According to Wikipedia water can thermolyse starting at around 1200 celcius, though the auto-ignition point of hydrogen is at around 535 celcius. I'm wondering in what sense water actually even ...
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439 views

How (if) are the hydrogen's "external" and "internal" wavefunction connected?

We can assign to a hydrogen atom an "internal" wavefunction: $$\psi(r,\theta,\varphi)=R(r)Y(\theta,\varphi)$$ We also assign an "external" wavefunction, describing the behavior of ...
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207 views

Quantum Central Force Problem and Angular Momentum

I am currently studying the quantum mechanics of the hydrogen atom. We have a proton and an electron orbiting around, so the Hamiltonian is: $$H=\frac{p_1^2}{2m_1}+\frac{p_2^2}{2m_2}+U(|\vec{r}_2-\vec{...
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27 views

Selection rules for electronic transitions in dipole approximation

I saw this video which provides a clear, though simple, introduction to the argument. I think the main thing missing is a proof for: $\Delta \ell = \pm 1 $ $\Delta m_\ell = 0, \pm 1$ $\Delta m_s = 0$...
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Why is the separation constant (used in obtaining the electron's wave function in hydrogen) a constant and not a function of position (and time)?

The Schrödinger equation for the hydrogen atom in polar coordinates is: $$ -\frac{\hbar^2}{2\mu}\left[\frac{1}{r^2}\frac{\partial}{\partial r}\left(r^2\frac{\partial \psi}{\partial r}\right) + \frac{1}...
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67 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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1answer
80 views

What is the experimental evidence for the hydrogen atom having a Coulomb potential?

It is famously impossible to deduce the shape of a drum from its spectrum, in general. In the case of the hydrogen atom, there are non-Coulomb potentials that produce the same spectral series! (See ...
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33 views

Magnetic field perceived by the electron

This section presents a relatively simple and quantitative description of the spin-orbit interaction for an electron bound to a hydrogen-like atom, up to first order in perturbation theory, using some ...
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428 views

How does protium-protium fusion work?

How does protium-protium fusion work? As far as I know, a proton turns into a neutron by emitting a positron. How does that work? Shouldn't a proton be slightly lighter than a neutron? This seems to ...

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