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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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69 views

Can Classical Mechanics and/or Quantum Mechanics explain the formation of a single hydrogen atom? [duplicate]

If we have a single electron and a single proton, Can Classical Mechanics and/or Quantum Mechanics explain why the electron revolves around the proton and not the proton around to electron?
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Why can't two hydrogen atoms be slowly “pressed together” (fused to form helium) with some advanced device (not collided at high speed)?

I apologize for my lack of physics knowledge, and I won't be gaining much any time soon, since I'm focusing mostly on work and physical exercise. I can't help but wonder about this: Questions: ...
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Expectation value for $\frac{1}{r}$ in the $|nlm\rangle$ state of hydrogen

I'm trying to derive $\left\langle \frac{1}{r} \right\rangle = \frac{1}{n^2 a_0}$ (where $a_0$ is the Bohr radius) for the $| nlm\rangle$ state of hydrogen. I've separated the radial and angular ...
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271 views

What is the density of molecular hydrogen in the solar system?

Can the density of molecular hydrogen in the solar system be estimated remotely or would a space craft have to be sent up to measure it directly? I understand that there is such a thing as the 21-cm ...
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Is there a “complete” Hydrogen level spectrum diagram out there?

From basic quantum physics we know that the energy levels in Hydrogen are quantized, with the first steps being made with the Bohr model. Then, spin gets introduced, and we get spin-orbit coupling, ...
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Does energy quantisation entail spatial orbit quantisation?

First and foremost, what is meant by 'orbit quantisation'? Is there a relation between the spatial orbits of, say, a bound electron in a Hydrogen atom or in a Landau level, and the fact that its ...
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2answers
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Finding the maximum of the radial probability density in the hydrogen atom

I have a question about a task I am supposed to solve : A hydrogen atom is in the ground state, with the radial part of the wave function equal to $R (r) _{n,l}=2 \space r_{B}^{-3/2}e^{\frac {-r}{...
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1answer
752 views

Most probable radius of an atom

Exactly WHAT is the most probable radius of a hydrogen atom? On what factors does it depend, if at all? Does it perhaps decrease/increase with an decrease/increase in the principal quantum number, n? ...
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Gravitational radiation from hydrogen atom [duplicate]

Background: It is known that orbital motion is accelerated motion under the influence of a central force; and that in a hydrogen atom the electron orbits the proton and is therefore accelerated; and ...
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101 views

What would the shape of a singly excited hydrogen atom be?

Suppose a hydrogen atom is excited up to a $\underset{1s}{[\;]} \underset{2s}{[\uparrow]}$ state which takes about 1000 kJ/mol. Due to electron shielding f orbitals tend to be higher energy than d ...
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How is a neutron produced in a hydrogen fusion?

So during a fusion reaction, a hydrogen atom (which consists of only a electron and proton) fuses with another hydrogen atom to produce deuterium which contains a proton and neutron. My question how ...
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Confusion in a trick in solving an energy eigenfunction

Given a non-relativistic energy eigenfunction for a central potential $\left|\Phi \right>$ In solving relativistic hydrogen atom, one of the terms is $$ \left<\Phi\middle|\frac{e^2}{r}\middle|\...
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Energy Spectrum and Gauge Transformations

There is a question in SE about the fact that the Hamiltonian isn't invariant under the EM gauge transformations. I wanted to ask about its consequences here. I know that in general, the Hamiltonian ...
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1answer
195 views

Corrections to the Bohr energies of Hydrogen [closed]

Among fine structure, Hyperfine splitting and Lamb shift, why Hyperfine splitting is the smallest while Fine structure is the largest?
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477 views

Most probable radius of hydrogen in its ground state [closed]

I'm having trouble understanding how we do this. I know we must find the probability density function and then we can optimise it to find the most probable radius. I thought we would just take the ...
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Darwin term affecting hydrogen s-states

The Darwin term, a correction to the non-relativistic hydrogen Hamiltonian due to the zitterbewegung of the electron, is given by $$H_{Darwin}=\frac{e^2\hbar^2}{8m^2c^2\epsilon_{0}}\delta^3(\...
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Energy term in Wavefunction Normalization

I recently started learning quantum mechanics and when I solved the Schrödinger equation for the Hydrogen atom, in particular the Radial equation, I found that I had normalized it but a term in the ...
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6answers
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Prove that an electron in a hydrogen atom doesn't emit radiation [duplicate]

According to electrodynamics, accelerating charged particles emit electromagnetic radiation. I'm asking myself if the electron in an hydrogen atom emits such radiation. In How can one describe ...
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Why can the 2p0 to 1s transition in hydrogen with dipole interaction not be solved without splitting into x,y,z polarisation?

The $2p_0$ and $1s$ wavefunctions for hydrogen; $ \psi_{2p_0} = \dfrac{1}{4\sqrt{2\pi}} \left(\dfrac{Z}{a_b}\right)^{\frac{3}{2}} \dfrac{Z r}{a_b} e^{\frac{-Zr}{2a_b}} \cos(\theta) $ $ \psi_{1s} = ...
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Higher order corrections to hydrogen and their consquence

I was wondering if there have to be higher order corrections for the quantum mechanical description of the Hydrogen atom. I'm aware that there are relativistic corrections and also QED corrections. ...
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2answers
510 views

What don't electrolysis produce a vast amount of hydrogen?

In my research and by asking questions on sites like this. I have learned that why using electricity in water can make hydrogen using the process electrolysis, why isn't it the most effective way? To ...
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1answer
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Spectroscopic properties of hydrogen: H vs. H2

One of the basic experiments everybody learns about when it comes to physics is the spectroscopy of hydrogen gas. The typical set-up has a charge discharge lamp containing the hydrogen. The resulting ...
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Why does a “typical” hydrogen atom have no neutron?

There are quite a few sources (mostly high-school physics textbooks) that I've read which don't give the disclaimer that the hydrogen atom they are using in a diagram is an isotope (as in having ...
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553 views

Hydrogen Ground State Energy

Using the non-relativistic Schrodinger equation, the energy levels for hydrogen are found to be $E_{n} = -\frac{1}{2n^2}mc^2\alpha^2$. Using the relativistic Dirac equation, the energy levels for ...
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What is known about the hydrogen atom in $d$ spatial dimensions?

In a first (or second) course on quantum mechanics, everyone learns how to solve the time-independent Schrödinger equation for the energy eigenstates of the hydrogen atom: $$ \left(-\frac{\hbar^2}{2\...
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1answer
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Energy of photon after emission

Exercise: A hydrogen atom is at its first excited state. When it de-excites it emits a photon. What is the energy of the photon and the kinetic energy of the atom? Question: Is it correct to ...
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2answers
643 views

What is the difference between metallic hydrogen and plasma of hydrogen?

As far as I know, metallic hydrogen and plasma seems share some common properties, eg:conduct electricity, nuclei share electrons, high temperatures... So my question is, is metallic hydrogen in fact ...
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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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1answer
668 views

How could we describe the electric bound state like hydrogen by QED? [duplicate]

We can solve the Schrodinger equation for the Hamiltonian operator from the classical Hamiltonian of hydrogen bound state, consisting of proton and electron attracting each other electrodynamically, ...
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Why does parahydrogen have a lower energy than orthohydrogen?

I found this on the wikipedia page on spin isomers of hydrogen: Parahydrogen is in a lower energy state than is orthohydrogen. It seem almost like it is obvious but I am having trouble reasoning ...
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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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2answers
319 views

Why can't space become fuel for spaceships? [closed]

I read somewhere that space is constitued mostly of hydrogen. So why can't space and its constituants (not only hydrogen) serve as fuel for future spaceships? The dreamer I am simply imagine a ...
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In the LHC, how is the proton separated from the electron in the hydrogen? [duplicate]

I know that we use protons in the LHC. So my question is, how is the proton separated from the electron in the hydrogen?
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Rydberg and electrical energy

I am a high school student. This year I learned the Rydberg constant and its use of finding energy of an electron in chemistry, besides in physics I learned to calculate the energies of two loaded ...
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2answers
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Could I create a banana? [closed]

As I understand it, until such time as stars were formed and heavier elements could be created, there was just hydrogen and helium, plus trace amounts of lithium an beryllium. Question: if everything ...
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1answer
756 views

$SO(4,2)$ symmetry of the hydrogen atom

The hydrogen atom with Hamiltonian obviously has $SO(3)$ symmetry since it just depends on the radius. $$ H = \frac{\mathbf{p}^2}{2m} - \frac{k}{r}$$ This is generated by angular momentum $\mathbf{L}...
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1answer
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Will hydrogen die out? [duplicate]

Stars create heavy elements up to iron during their lifetimes, and heavier elements beyond iron during supernova events. Are there any processes which create new hydrogen? If not, will all (or most) ...
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1answer
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Do plasmas have their own magnetic fields?

Do Plasma generate a magnetic field of their own ? Can they cause electromagnetic induction?? For example if a hydrogen plasma is ionized and its electrons removed.. And the protons accelerated ...
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0answers
322 views

Expectation value of the Hamiltonian [closed]

How to calculate expectation value of the Hamiltonian for hydrogen atom? $$\langle H \rangle_{\alpha l} \equiv \frac{\langle \psi_{\alpha l m}|H(r)| \psi_{\alpha l m}\rangle} {\langle \psi_{\alpha l ...
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Z coordinate expectation value of the Hydrogen atom

I want to find $z-coordinate$ expectation value $\textbf{<z>}$ of the Hydrogen atom wave function $\psi_{1,0,0} = (\pi a^3_0)^{-1/2}e^{-r/a_0}$ in its ground state. I read in some text that $&...
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1answer
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Water + RF + Spark = Continuous Fire

Can anyone explain the physics of what is happening in the following video? https://youtu.be/p8xYUDiSGDk?t=37 Is this process Radiolysis? At what radio frequency & power level is h20 ...
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1answer
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Deriving the Bohr radius of a hydrogen atom using Schrödinger's equation

I'm trying to follow the book for the introduction to quantum mechanics by Griffiths. I'm following the part where he is solving Schrödinger's equation for the hydrogen atom. There, he found the Bohr ...
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3answers
356 views

Complex conjugate of hydrogen ground state wave function [closed]

For hydrogen atom ground state we know . I want to know the complex conjugate of .
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Temperature of fusion in the Sun vs. fusion in controlled experiments on Earth

I recently learned that hydrogen fusion (i.e., hydrogen to helium) experiments on Earth have been successful at temperatures in excess of 100,000,000 degrees Celsius. However, I also learned that ...
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1answer
661 views

How does speed of gas molecules change with pressure? [closed]

A thought experiment. I have a box of fixed dimensions, inside this box I have molecules of $H_2$ at constant temperature. I'll be gradually increasing pressure inside the box and the temperature ...
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1answer
311 views

Does the proton wobble due to the electron's orbit in a Hydrogen atom?

In a hydrogen atom the nucleus only has one proton and no neutrons so the electron to nucleus radio is higher for hydrogen than that for any other atom. Does the orbiting electron induce a wobble on ...
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138 views

Transform QM radial equation to spherical Bessel equation

I'm currently learning about spherical potentials (ex. hydrogen and hydrogen-like systems) and am trying to work through the problem of a generic spherical potential well such as: $$V(r) = \left\{\...
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1answer
184 views

The point of charge neutrality in the Hydrogen Atom

If we treat the Hydrogen Atom like the Bohr model then we have a proton in the center with an electron orbiting at some radius (the Bohr radius). In this picture you can imagine the electric field ...
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In the hydrogen atom, why is the electron orbital spherical rather than flat like a 2D orbit plane?

In a hydrogen atom an electron is orbiting around a proton, similarly to a moon around a planet. The orbit of a moon around a planet is flat (2D) whereas the orbit of an electron around a proton is ...
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2answers
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Why is the blue line in the Balmer series sometimes not visible?

So I've conducted an experiment to find the four visible hydrogen emission spectrum lines in the Balmer series in a laboratory. I don't have any background in quantum physics. When I looked through ...