# 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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1 vote
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### 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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### 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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### 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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### 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 ...
1 vote
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### Transparency of hydrogen to different electromagnetic wavelengths in the early universe

I can somehow grasp the early universe being compared as a sphere surface filled densly with plasma like a spherical chessboard all filled with chess pieces.So as that surface streched the distances ...
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### Creation and annihilation operators in the hydrogen atom

In my quantum chemistry course, we have been discussing the wavefunctions of the hydrogen atom, further, I am familiar with the idea of ladder operators from the quantum harmonic oscillator. Can we ...
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### Hydrogen atom: Estimation of binding energy from each force

I've been asked to give an estimation on the binding energy related to each fundamental force (gravitational, electromagnetic, weak and strong) for the Hydrogen atom (you know, the one with a single ...
1 vote