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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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Why do electrons tend to be in energy eigenstates?

An oft cited problem with the planetary model of hydrogen is that, if the electron were in fact classically orbiting the proton, then it would radiate away all of its energy and fall into the nucleus. ...
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Electric field due to a hydrogen atom

Electric field due to two opposite charges According to the answers in the previous questions, if you separate the two charges from each other, they will produce a non-zero electric field ...
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Can liquid hydrogen be ionized?

Does stripping the electrons off of hydrogen atoms affect it's boiling point in any way?
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Cold fusion with ionized hydrogen and neutron radiation

Would bombarding ionized hydrogen gas with neutron radiation cause cold fusion as the neutrons have no electrostatic repulsion to overcome therefore making it much easier to get within range of the ...
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Relativistic correction to Hydrogen atom - Perturbation theory

Given the relativistic correction $$ H_1' = - \frac{p^4}{8m^3 c^2} $$ to the Hamiltonian (i.e. a perturbation), what does it mean when $[H_1', \mathbf{L}] = 0$? The book I'm reading says this implies ...
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Does linear momentum of a hydrogen atom-system remain constant during electronic transitions?

When electronic transitions(excited to ground) take place in a hydrogen atom, does the linear momentum of proton-electron system remain constant?
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What happens if the bound electron of hydrogen atom gains kinetic energy exceeds binding energy?

Say a hydrogen atom is accelerated so that both the nucleus and the bound electron gains kinetic energy exceeding it's electron binding energy, yes I know an hydrogen atom with 1 proton, 1 neutron and ...
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How does an electron in the same shell of an atom have same energy despite of having different magnitudes of orbital angular momentum?

For example, consider the $n=2$ shell. This will have $l=0,1$ values, so correspondingly there are 2 angular momentum states having magnitude $0$ and $\sqrt{2}\frac{h}{2\pi}$. So how do these 2 ...
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Compute degeneracy in energy levels of a wavefunction which is a sum of other wavefunctions

Given a hydrogen atom-like wavefunction at time $t=0$, say: $\Psi(r,t=0)=A(2\psi_{100}+\psi_{210}+\sqrt{2}\psi_{211}+\sqrt{3}\psi_{21-1})$ How can I compute the degeneracy of the energy levels for ...
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Bohr Radius of Uniformly Accelerating Hydrogen Atom

Suppose we have a rocket-ship that is uniformly accelerating along its bow-stern axis (connecting line). Also, assume we have a hydrogen atom in the rocket. Mathematically (theoretically), does ...
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How can you use the Delta Function to find the Electric field inside of a Hydrogen Atom?

This is a problem from my homework, but I'm lost conceptually on how to do it. I'm not looking for someone to do the work for me, I'm looking for some guidance on how I can set it up/understand it ...
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How to find the electrostatic potential of a hydrogen-like charge density?

I've been trying to find the scalar potential that would correspond to the charge density of a ground state hydrogen atom. The result is known, and the inverse of my problem can be found e.g. in ...
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Why does the Dirac equation work for the hydrogen atom?

The Dirac equation works well for predicting the spectrum of the hydrogen atom, famously incorporating relativistic effects like fine structure. Yet, there seems to be a sense in which this is ...
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Calculating Darwin Term for Hydrogen

The standard classical approximation of the Darwin term in hydrogen's fine structure goes something like this. We approximate the 'smeared' potential due to the electron's fluctuating position as $V(\...
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Eigenspaces of the hydrogen atom as representations of $SO(3)$

When we computing the discrete spectrum of the hamiltonian of the hydrogen atom $$H=\Big(-\frac{\hbar^2}{2m} \Delta - \frac{e^2}{r} \large),$$ by some explicit computation we get that eigenspace $...
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What is the difference between Lamb shift and the Darwin term?

I am currently learning for an exam and I wonder what the difference between the Lamb shift and the Darwin term is. What I know is that the Darwin term affects only the s-states of the hydrogen atom ...
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Does hydrogen gas laser exist? If not, why?

I have searched the internet, and this forum, but can't find a mention of hydrogen gas laser. There does, however, exist the hydrogen maser that used the 21cm radiation. Also there exist Nitrogen gas ...
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virial theorem hydrogen atom

I calculated $\langle T \rangle$ and $\langle V \rangle$ as a function of time of a given state of the hydrogen atom $|\psi\rangle=a|1,0,0\rangle+b|2,0,0\rangle$ and I found that $$\langle V \rangle ...
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Questions on Stark Effect on Hydrogen

Suppose that a hydrogen atom is subject to a weak uniform electric field $\vec{E}=\epsilon \hat{z}$. Let's neglect the effect of electron spin. The perturbation added to the original hamiltonian $H_0$ ...
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why ammonia is not a competitive energy carrier?

reading this article about Germany planning to store renewable energy as hydrogen gas, i'm left wondering why they deem so great this plan, compared with other alternatives like ammonia as a energy ...
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Reasons for problematic behaviour of hydrogen atom states with azimuthal quantum number $\ell=0$

I have been reading "Introduction to Quantum Mechanics by David J. Griffiths" and in the chapter 6- Time-Independent Perturbation theory, when we are explaining the fine structure via relativistic ...
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Black hole nucleus in hydrogen

The hydrogen atom gets the spectrum it has because you analyze the Schrodinger equation in spherical symmetry with the potential given by $V=-\frac{1}{4\pi\epsilon_0}\frac{e^2}{r}$. Yet the same ...
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Fine Structure Correction

The fine structure correction is composed of the relativistic correction and spin-orbit coupling. The lowest-order relativistic correction to the Hamiltonian is $$ H_r' = -\frac{p^4}{8m^3c^2}$$ ...
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Why does hydrogen give up its electron to a platinum catalyst?

All descriptions of a Hydrogen fueled fuel cell (such as this one) Start with $H_2$ giving up its electrons to a platinum coated anode. Then the $H^+$ ions (protons really) travel through the ...
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How can i obtain the correction to the eigenvalues as a result of adding the gravitational potential to the hydrogenlike atom?

In treating the hydrogen-like atoms, we normally neglect the gravitational potential for the system. I am able to justify the above statement by comparing the gravitational potential to the ...
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Is it possible for liquid metallic hydrogen to be present in a star

Liquid metallic hydrogen can form at extreme temperatures and pressures like that in the center of Jupiter and Saturn. I was just curious since some of the conditions can occur on stars is it ...
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How can we deduce that a hydrogen atom is stable in relativistic QED?

Consider relativistic quantum electrodynamics (QED) with three quantum fields: the electromagnetic field $A_\mu$, one fermion field $\psi$ for electrons/positrons, and one fermion field $\psi'$ for ...
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Interpretation of 21 cm intensity mapping

I'm currently trying to understand the following plot from Astrophysics for physicists by A.R. Choudhuri. I think I understand the basic concept of measuring the line-of-sight velocities with the ...
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260 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}\...
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What are estimated magnetic properties of liquid metallic hydrogen?

I understand that liquid metallic hydrogen isn't easy to produce, or keep it stable on Earth, but can be liquid metallic hydrogen magnetised? Does it have magnetic properties at all?
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Hydrogen in an electromagnetic field bound states for full quantum electrodynamics

I am looking for a reference or derivation of the non-relativistic bound states of hydrogen in an electromagnetic field that include Zeeman effect, Stark shift, and Lamb shift. I am looking for a ...
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354 views

Using the Heisenberg Uncertainty Relation to Estimate Ground State Energies

In Shankar's Principles of Quantum Mechanics, he applies the HUP to estimate the ground state energy of the Hydrogen atom. In the proof, it is said that the first step to minimizing the expectation ...
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What will happen if a ground state hydrogen atom is placed in a low frequency, but high intensity laser field?

Similar questions have been asked before, but this one extends the scope of interpretation and applications. Let us ask the question: What will happen if we have a laser gun that produces a high ...
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Could hydrogen liberated from water provide lifting energy which exceeds the energy it took to liberate it from water

I was thinking about Hydrogen balloons and that large ones which are used for weather balloons which sometimes go up to 100,000 ft (approx 30km). Then I was wondering, how much potential energy has ...
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How does the electron jump across “gaps” in its orbital?

I saw on perhaps COSMOS, and have heard mention from other professors, that electrons sort of "teleport" or something, in their orbital and the quantum level. So looking at the orbitals for a lone ...
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Decay of hydrogen nucleus?

Very naive question. Nuclear decay is associated to more complex nuclei and explained through radiation. What about hydrogen and less complex nuclei? Will these nuclei eventually break apart? Or is it ...
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A question about Helium spectrum

I'm starting to read about two-electron atoms from physics of atoms and molecules by Bransden. Analyzing Helium spectrum I noticed that the energy of $He^+(1s)+e^-$ is greater than the energy of He, ...
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Can a hydrogen atom temporarily attract an additional electron to form a negative ion?

Negative ions should be a kind of temporary substance form that exists widely. Can a hydrogen atom temporarily attract an additional electron to form a negative ion? Other elements or molecules can. I ...
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How is hydrogen able to emit a light spectrum with only one electron?

When light is shined through hydrogen gas, three colors of light appear. The issue I have with this is that hydrogen has one electron, meaning somehow the electron has to be emitting all three of ...
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Hydrogen in a box

I would like to approximate the 1S wave function of a system constrained to a box $\{(x,y,z)|x\in[0,a],y\in[0,b],z\in[0,c]\}$, subject to the potential of the hydrogen atom. I have proposed the ...
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Why can't we harness the energy from neutron + protium = deuteron reaction?

The answer to this physics se question, established that 2.2Mev (Mega electron volts) of energy is emitted as a gamma ray photon when the hydrogen atom nucleus oka protium absorbs a slow moving free ...
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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 ...
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Are parahydrogen and orthohydrogen identical particles?

I have no formal physics background, just aerospace engineering, and I'm working on a DSMC project simulating relaxation of hydrogen in non-equilibrium, rarefied, 1D flow via translational and ...
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Dependence of radial probability function on quantum numbers

I was reading the book "Quantum Physics" from Eisberg & Resnick about the expected value of the electron radial coordinate, which it defines as \begin{align} \overline{r_{nl}} = \int_{0}^{\infty}...
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Relation of potential energy and total energy in Bohr Model of the hydrogen atom

I am currently in the 11th grade. In the Bohr Model of the hydrogen atom, potential energy is two times that of total energy. It means that magnitude of potential energy is two times that of magnitude ...
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Recombination of hydrogen

Suppose a slow-moving electron and a slow-moving proton are injected into a chamber, such that the two approach each other and are likely to combine to form an atom of hydrogen. How would one ...
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Where can I find relativistic corrections to 2s and 2p levels of Hydrogen Atoms?

I am currently studying for a Quantum Mechanics test, and I want to calculate the 2p and 2s hydrogen atom corrections for the relativistic, spin-orbit and darwin corrections, using perturbation theory....
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Trying to solve TDSE for Hydrogen atom, but I cant determine initial condition

I am trying to solve TDSE for a hydrogen atom in the b-spline basis set. $$i\dfrac{\partial}{\partial t}\Psi(t)=[H_{0}+D(t)]\Psi(t)$$ with initial condition $\Psi(t=-\infty)=\Psi_{g}$, where $\Psi_{g}$...
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More than two linearly independent solutions to the (linear second order) radial wave equation?

I'm puzzled by the following radial wave equation: $$ \left(\frac{\hbar^2}{2m_r}\left(-\frac{d^2}{dr^2} -\frac{2}{r}\frac{d}{dr} + \frac{l(l+1)}{r^2}\right) + V(r)\right)R_{nl}(r) = ER_{nl}(r)$$ ...
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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 ...