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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Hydrogen Atom in two spatial dimensions with $1/r$ potential [closed]

I am almost new to Quantum Mechanics. Recently I learned about the hydrogen atom in three dimensions. I struggle to answer the following exercise where the hydrogen atom in two dimensions is ...
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Origin of Spin-Orbit Interaction

The spin-orbit interaction in a hydrogen atom is often explained as arising from an interaction energy $U=-\mathbf{m}\cdot\mathbf{B}$ where $\mathbf{m}$ is a magnetic moment due to the electron’s spin ...
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Why ionization is more probable in hydrogen atom than excitation to the $n = 3$ level?

The Wikipedia article about the H$\alpha$ spectral line states "it takes nearly as much energy to excite the hydrogen atom's electron from $n = 1$ to $n = 3$ (12.1 eV, via the Rydberg formula) ...
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Can wavefunctions always be separated into a product of spatial and spin parts? [duplicate]

Firstly, I wanted to check. Can wavefunctions exist that are not in the form $\psi = \psi_{\mbox{spatial}}\times\psi_{\mbox{spin}}$? I am assuming you can have situations that are dependent on spin ...
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Could you survive on hydrox in at 10 atmospheres?

I was told that hydrox is incredibly dangerous, that pure oxygen will combust without any source of ignition at 3 to 4 atmospheres of pressure, and that because humans are hydrocarbons they will act ...
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Hydrogen radial wave function in Feynman

I'm reading the classical Feynman's lectures on hydrogen atom, and I want to calculate the radial component of the wave function with the formula (19.53) $$ F_{n,l}(\rho)=\frac{e^{-\alpha\rho}}{\rho}\...
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About calculating a contribution to Lamb-shift through Uehling's potential

Well, I've been calculating Uelingh potential using the amplitude of the QED vacuum polarization. Now, I'd like to go on and calculate the Lamb-shift. And here is my question: How can I do that? ...
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Good quantum number for the weak field Zeeman effect

To find the fine structure of hydrogen using nondegenerate perturbation theory, we choose the eigenstates of L2, S2, J2, and Jz. As stated in Griffiths Introduction to Quantum Mechanics, the good ...
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Nuclear beta decay to hydrogen

In reading about nuclear beta decay: $$n \longrightarrow p + e^{-} + \bar \nu$$ It occurred to me that two of the particles resulting from this decay are the constituents of the hydrogen atom. So why ...
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Pauli exclusion principle for $H_{2}$

We know that depending on whether their spins are parallel or antiparallel, two electrons (each with spin ½) can combine to give a total spin of $1$ (parallel)or $0$ (antiparallel). But only one of ...
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Is the energy of an orbital dependent on temperature?

In the Schrodinger Equation's solution for electron orbital energy levels of the hydrogen atom there is no temperature dependency. $$ E_n = - \frac{m_{\text{e}} \, e^4}{8 \, \epsilon_0^2 \, h^2 \, n^2}...
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Cross section for Hydrogen molecule formation

I have been searching for theoretical articles that calculate the hydrogen formation cross section $\sigma(H+H \rightarrow H_2)$, but I found nothing. Can anyone suggest me articles or computer ...
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What is the most common method used to cool hydrogen below its boiling point?

I would like to know what methods companies/organizations/scientists use to cool gaseous hydrogen below its boiling point of ~250 degrees Celsius. I am a new student to thermochemistry and am not ...
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Another way for production of positive fusion

I am wondering why energy positive fusion cannot be produced in the following manner. Large tank of hydrogen pressurized to such a high a level it would push the limits of current technology. ...
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Hydrogen gas tube and the spectrum [duplicate]

Generally to detect the hydrogen spectrum people uses the hydrogen gas tube as a light source. My question is, since the gas in the tube is the hydrogen molecule $H_2$ why is the spectrum equal to the ...
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Balmer spectroscopic lines from plasma?

In stars, the Balmer lines are usually seen in absorption, and they are "strongest" in stars with a surface temperature of about 10,000 kelvins (spectral type A). Balmer series|Role in ...
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Can this matrix be evaluated with the help of the Wigner-Eckart theorem?

I wonder if the problem in the image can be solved with the Wigner-Eckart (W-E) theorem. These elements have to vanish. I tried introducing the identity operator in between $r$ and $p$ to then use the ...
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1answer
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Franck and Hertz's experiment

The Bohr's model of the atom was defined only for hydrogen and hydrogen-like species. Yet, the Franck-Hertz experiment was performed with Mercury vapour- which, obviously, isn't hydrogen-like. What's ...
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Hydrogen-One (HI) Image and R-band

In the paper below, on page 3, it says "In the lack of HI image, we use the r-band b/a ratio to correct for the inclination". Am I correct in thinking that what this means is that if we ...
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What would happen if you tried to use oil as fuel in a fusion reactor? [closed]

At first, this question seemed silly, but there might be some sense to it. OpenAI's GPT algorithm suggested to me that using oil in fusion technology could be a breakthrough. I thought about it for ...
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Why do molecules form band spectrum?

If we observe any textbook they say that molecules form band spectrum. But a H2 molecule is just 2 H atoms and both form line spectra but somehow combination of 2 H atoms formed band spectrum. Because ...
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Why do the $d$ orbitals have such strange symbols?

Why are the five d-orbitals denoted by the symbols $d_{z^2}, d_{x^2-y^2}, d_{xy}, d_{yz}$ and $d_{zx}$? Does it have to do with the wavefunctions of d-orbitals? The symbols for the f-orbitals are ...
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Is there an entangled ground state solution to the hydrogen atom? (spin neglected)

When solving the hydrogen atom, to separate the two-particle Time-Independent Schrödinger Equation (TISE) into two separate equations, we make the change of variables: $$\vec{r}_{CM} = \frac{m_e}{m_e+...
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Hydrogen atom in quantum field theory

In principle, how would we demonstrate the existence of the hydrogen atom in quantum field theory and the standard model? Has it been done in practice? Some naive ideas: Demonstrate that the familiar ...
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Interpretation of the azimuthal quantum number [duplicate]

On the German Wikipedia page, we can read: "The higher the azimuthal quantum number $\ell$ for a fixed principal quantum number $n$, the more the average distance of the electron from the nucleus ...
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How can we detect antihydrogen?

From a mathematical standpoint (CPT symmetry) it is most probable that antihydrogen has the same spectra (absorption and emission) as hydrogen. The CERN confirmed this hypothesis to a high accuracy ...
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Analytical Solution for a second order elliptic PDE with variable coefficients

It has been a while i'm struggling with the following elliptic PDE: $$ \left(\frac{\partial^2}{\partial r_a^2} + \frac{\partial^2}{\partial r_b^2}\right) f(r_a, r_b) + 2\left( \frac{1}{r_a} -\frac{1}{...
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Producing Pressurized Hydrogen Underwater Then Using it To Do Work

This is a bit of a weird one but I didn't know where else to ask this. I was recently talking to my brother and he told me about an idea he had talked with his boss about how to create compressed ...
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Energy eigenvalue in 2D hydrogen atom [closed]

I encountered the following issue. Consider a 2-dimensional Coulomb potential $$\Phi(x,y) = \frac{1}{\sqrt{x^2 + y^2}}.$$ It is important to know that all the analytical results in this question were ...
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Can hydrogen atom exchange induce attractional forces between $e^-e^-$?

G. Feinberg and J. Sucher showed that neutrino-pair exchange can induce long-range repulsive forces between electrons that is proportional to $r^{-6}$. In the paper, they also stated that changing a ...
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How is the size calculated of the area near a hydrogen atom that a photon must hit to ionize the atom?

I do not know of any specific other information needed to answer the question.
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Solving Schrodinger equation for the hydrogen atom

In University Physics with Modern Physics by Hugh Freedman in Chapter 41.3 they go about solving the Schrodinger equation for the hydrogen atom. At one step they say to substitute the following ...
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E-k diagram of hydrogen atom

The energy of a free (nearly free) electron in a solid (say, metals) is given by $E=h^2k^2/2m$ where k is the momentum vector, h is Planck's constant and m is the mass of the electron. This ...
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What happens to a hydrogen atom under an intense gravitational field (or intense acceleration)?

I'm curious how the observed quantum-mechanical properties of a hydrogen atom would change under very high gravitational fields. Do the energy levels change? Do the chemical bonding properties ...
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Why is hydrogen-boron called a fusion reaction?

As we know, we usually call fusion such a reaction in which two light nuclei make a heavier one and release energy. For fission, a heavy nucleus breaks into light ones. My question is, in proton-boron ...
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How to get Bohr model from Schroedinger equation? [duplicate]

New theories must in some approximation must reduce to older approximately correct theories. In what approximation exactly does the angular momentum quantization condition from Schroedinger's equation ...
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Is the radiation problem actually solved in the classical quantum model of hydrogen?

It's often said that in classical physics a electron-proton system is not stable due to "Bremsstrahlung" and that one instead has to look at it quantum mechanically. This doesn't make sense ...
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1answer
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What do maufacturers do to ensure that a valve is capable of containing hydrogen gas? [closed]

I am a researcher working to develop a hydrogen fuel system for use in a specialized internal combustion engine. The biggest challenge from an engineering standpoint with a project such as this is the ...
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Forces during the formation of hydrogen molecules

In my book it is given that for the formation of hydrogen molecules, hydrogen atoms come closer due to net attractive forces. It is written that initially when the atoms were approaching towards each ...
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Hydrogen Atom in Second Quantization and Two-Particle Bases

Context: In non-relativistic QM and many-body theory, the second quantization formalism allows us to write a Hamiltonian for a many-body system with up to two-body terms as (up to a re-ordering ...
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Is $e^-$ in 1st excited state in the $\rm H$-atom in superposition of possible ($l,m,s$ for $n=2$) substates/in superposition of all possible states?

I want to know how we can determine the probability of various states of hydrogen as there are infinite of them, or electron in a hydrogen atom is in the superposition of which states, maybe it is in ...
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Question about the radial hydrogen eigenfunctions

When calculating the selection rules for electronic transition in the hydrogen atom in dipole approximation, we always focus on the angular integrals. But why the integral $$ \int_{0}^{\infty}[rR_{nl}(...
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Origin of $\ell \leq n-1$ orbital rule

I am wondering about the origin of the $\ell \leq n-1$ orbital filling rule. For the hydrogen atom, I believe the reason is because in the spatial wave function there is the term $$\psi \propto \sqrt{(...
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1answer
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Hydrogen Emission vs Absorption Wavenumbers

I am used to using the formula $ R_H (\frac{1}{n^2_{final}}-\frac{1}{n^2_{initial}}) $ to calculate the transition wavenumbers when an electron in a Hydrogen atom emits a photon. Can you use the same ...
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Schrödinger's equation for hydrogen atom (azimuthal part) [duplicate]

Now, The azimuthal part of the Schrödinger's equation for a hydrogen atom (after separating variables) is: $$ \frac{d^2 \Phi}{d \phi^2} + m^2 \Phi = 0$$ Which has solution $A e^{im\phi} + B e^{-im\phi}...
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How to calculate radius of the $n$th Bohr orbit if the nucleus is not at rest relative to the center of mass?

I've been dealing with a couple of questions regarding Bohr's model except where the mass of the nucleus is not negligible compared to the mass of the (revolving) electron. According to my book (...
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1answer
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Transition $2p \rightarrow 1s$ of Hydrogen Atom

I am reading Mukhanov and Winitzki's book Introduction to Quantum Effects in Gravity and in second paragraph of Sec. 1.4.2 they say that : The spontaneous emission by a hydrogen atom is the transition ...
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Nodes in Spherical Harmonics

In Rydberg Atoms book by Thomas F. Gallagher, Page 14, the author provides the general equation of spherical harmonics which is well-known. He states that there exist $l-m$ nodes in the $\theta$ ...
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Schrodinger Equation of a Hydrogen Atom in a Rydberg State

I am not a mathematician, so I really appreciate it if someone could explain it in a simple way. In Rydberg Atoms book by Thomas F. Gallagher, the Schroedinger equation for the H atom in atomic units ...
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Are there any special websites or data files for materials like tritium?

I was looking for tritium cost per gram online, but i didn't find anything that can be taken as a reference for a scientific article. Wikipedia mentioned its costing of 2000, but i need more recent ...

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