Episode #125 of the Stack Overflow podcast is here. We talk Tilde Club and mechanical keyboards. Listen now

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.

Filter by
Sorted by
Tagged with
51
votes
3answers
7k views

Why is hydrogen the most abundant element in the Universe?

Hydrogen is the most abundant element in nature. Does cosmological nucleosynthesis provide an explanation for why is this the case? Is the explanation quantitatively precise?
27
votes
3answers
2k views

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 ...
18
votes
1answer
1k views

How would one detect antihydrogen in the universe?

Since the spectra of hydrogen and antihydrogen are the same, how do astronomers know which one they're detecting? Is, perhaps, the Lamb shift in antihydrogen different?
18
votes
4answers
4k views

How long will the Universe's hydrogen reserves last for?

I recently became really interested in learning about physics and cosmology, but I still know very little. Hopefully someone with more knowledge will be able to shed some light on my questions. Here ...
17
votes
4answers
2k views

Anti-Hydrogen Spectrum

My question is: What is the spectrum of anti-hydrogen? Could it be the same as regular hydrogen? They both have a core (a proton or an anti-proton) and an electron or a positron so they should have ...
16
votes
1answer
657 views

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\...
14
votes
3answers
4k views

How can one see that the Hydrogen atom has $SO(4)$ symmetry?

For solving hydrogen atom energy level by $SO(4)$ symmetry, where does the symmetry come from? How can one see it directly from the Hamiltonian?
13
votes
3answers
2k views

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. ...
13
votes
3answers
4k views

Why are hydrogen energy levels degenerate in $\ell$ and $m$?

Is there a good physical picture of why the energy levels in a hydrogen atom are independent of the angular momentum quantum number $\ell$ and $m$?
13
votes
3answers
15k views

What made Bohr quantise angular momentum and not some other quantity?

Bohr's second postulate in Bohr model of hydrogen atom deals with quantisation of angular momentum. I was wondering, though: why did he quantise angular momentum instead of some other quantity?
13
votes
3answers
3k views

Why is it so hard to separate isotopes?

I was reading on Wikipedia that heavy water in large amounts is toxic to eukaryotic cells because certain physical properties of deuterium are different enough from those of common protium to disrupt ...
13
votes
2answers
2k views

Why are the higher angular momentum states of a hydrogen atom closer to the nucleus?

I was looking at a plot of hydrogen radial wave functions $r^2|R_{nl}(r)|^2$, and I noticed that for fixed $n$, the states with smaller $l$ were "further out" from the nucleus. This conflicted with ...
13
votes
2answers
547 views

Are there published predictions that hydrogen could remain metallic at ambient pressure?

Below the question For the recently reported production (January 2017) of metallic hydrogen in the laboratory - what is the evidence exactly? there is a comment that directed me to the BBC News ...
12
votes
5answers
2k views

How does the hydrogen atom know which frequencies it can emit photons at?

At university, I was shown the Schrodinger Equation, and how to solve it, including in the $1/r$ potential, modelling the hydrogen atom. And it was then asserted that the differences between the ...
11
votes
3answers
2k views

Proton - neutron fusion?

In reviewing some problems in an elementary book, I ran across a reference to the reaction $p+n\rightarrow d$ + "energy". Is that possible? I don't see any reason why not, but I don't find any ...
11
votes
3answers
1k views

Hydrogen atom, what's the wave equation for the atom's nucleus?

I learned from the class about the equation for hydrogen atom's electron where textbook assumed that the center/nuclei of hydrogen atom was fixed at origin. However, since every particle was a wave, ...
11
votes
2answers
1k views

Scattering states of Hydrogen atom in non-relativistic perturbation theory

In doing second order time-independent perturbation theory in non-relativistic quantum mechanics one has to calculate the overlap between states $$E^{(2)}_n ~=~ \sum_{m \neq n}\frac{|\langle m | H' |...
10
votes
3answers
11k views

Can open, unsafe nuclear fusion reaction burn the atmosphere?

I happened to hear people saying that the nuclear fusion bomb tests could set the atmosphere on fire. I have some serious doubts about that - but I have no facts. Nuclear fusion reaction requires $15*...
10
votes
1answer
757 views

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|\...
9
votes
3answers
2k views

Why is a proton assumed to be always at the center while applying the Schrödinger equation?

Why is a proton assumed to be always at the center while applying the Schrödinger equation? Isn't it a quantum particle?
8
votes
1answer
868 views

Can a quasiclassical electron wave packet in elliptic orbit be formed from bound hydrogen-like eigenstates?

Position probability densities of eigenstates of hydrogen-like systems have axial symmetry, so that the wavefunction too much resembles the circular orbits in Bohr's model. I'd like to have a ...
8
votes
4answers
3k views

What does ionization of neutral Hydrogen have to do with “transparency”?

Most accounts of the early history of the Universe make some reference to (re)ionization as being the reason that the Universe becomes transparent after a period of opacity caused by the absence of ...
8
votes
4answers
2k views

Is there only radial motion in the Hydrogen ground state?

The ground state of the Hydrogen atom is spherically symmetric. In other words, the wave function Psi depends only on the distance r of the electron from the nucleus. As a consequence all ...
8
votes
2answers
1k views

How does one calculate where the “surface” of a gas-giant would be?

Okay, so Jupiter, Saturn, et. al are gas giants. I understand that they have large gassy atmospheres, which, due to the pressure would eventually become more and more dense as one approaches the ...
7
votes
2answers
1k views

Why doesn't the ${\rm H}_2$ molecule have a permanent dipole while the neutral ${\rm H}\,{\rm\small I}$ has one?

According to the National Radio Astronomy Observatory, the $21\,{\rm cm}$ line of hydrogen can be emitted by the neutral hydrogen atom due to the magnetic interaction between the spins of the proton ...
7
votes
1answer
814 views

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 ...
7
votes
3answers
7k views

What is the unit of time on the Voyager Golden Record?

What is the unit of time on the Voyager Golden Record? Apparently, it has something to do with "a fundamental transition of the hydrogen atom". A high-level description was provided by NASA, as ...
7
votes
5answers
1k views

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 ...
7
votes
1answer
979 views

What are independent parameters in Hellmann–Feynman theorem?

A typical example in textbooks about the application of Hellmann–Feynman theorem is calculating $\left\langle\frac{1}{r^2}\right\rangle$ in hydrogen-like atoms. Wikipedia has a nice demonstration of ...
7
votes
0answers
70 views

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 ...
6
votes
6answers
3k views

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 ...
6
votes
5answers
3k views

Hydrogen radial wave function infinity at $r=0$

When trying to solve the Schrödinger equation for hydrogen, one usually splits up the wave function into two parts: $$\psi(r,\phi,\theta)= R(r)Y_{l,m}(\phi,\theta).$$ I understand that the radial ...
6
votes
2answers
6k views

Fusion: Why deuterium and tritium?

I would like to know why scientists try to use deuterium and tritium for fusion and not just the ordinary isotope of Hydrogen ${}^1H$?
6
votes
2answers
402 views

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 ...
6
votes
2answers
2k views

Jupiter Core is Solid Hydrogen

I was watching a show on the science channel about gas giants; there is something I do not understand. I am not a scientist, so this may be obvious to some. I learned that there a three states of an ...
6
votes
1answer
3k views

Reduced mass in quantum physics (Hydrogen Atom) [duplicate]

I've gone through an intermediate classical mechanics course, and in solving the two-body problem, we reduce it to a one-body between a larger stationary mass, and a smaller reduced mass. Most ...
6
votes
3answers
214 views

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 ...
6
votes
1answer
545 views

Why is metallic hydrogen degenerate matter?

Why is metallic hydrogen considered a form of degenerate matter, akin to neutronium and electron-degenerate matter? I can understand that for the other two, degeneracy pressure is the only force ...
6
votes
2answers
822 views

Spin-orbit coupling from the rest frame of the proton?

When we calculate the spin-orbit interaction in a Hydrogen atom we just work in the electron's frame of reference: the proton is moving and produces a magnetic field which the electron's spin ...
6
votes
0answers
245 views

Is it reasonable to interpret the Lamb shift as vacuum induced Stark shifts?

This is a pretty hand-wavy question about interpretation of the Lamb shift. I understand that one can calculate the Lamb shift diagrammatically to get an accurate result, but there exist "...
6
votes
1answer
156 views

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 ...
5
votes
4answers
1k views

How big is an excited hydrogen atom?

Suppose an empty universe with the exception of a single hydrogen atom (1 proton, 1 electron). The electron may be in its ground state or it may be excited a certain number of levels. Suppose it is at ...
5
votes
3answers
7k views

Using the uncertainty principle to estimate the ground state energy of hydrogen

I have been reading through this estimate of the ground state energy of hydrogen and others like it. In this one it says it is using the uncertainty principal but then proceeded to use the following: ...
5
votes
4answers
7k views

How can one describe electron motion around hydrogen atom?

I remember from introductory Quantum Mechanics, that hydrogen atom is one of those systems that we can solve without too much ( embarrassing ) approximations. After a number of postulates, QM ...
5
votes
3answers
583 views

Fine structure Hamiltonian from Dirac equation

The Hamiltonian for fine structure (the atom with $\text{Z}$ protons and with electron interaction terms included) is $$H=\frac{\text{Z}^2}{ r}+\underbrace{\frac{p^2}{m}+\frac{p^4}{m^3}}_{\text{...
5
votes
3answers
4k views

What is the expected distance of the electron from the nucleus in the hydrogen atom?

Specifically, I would like to know the general formula, in terms of $n$ and $l$, assuming the electron is in an orbital (i.e. simultaneous eigenstate of $H$, $L^2$, and $L_z$). I understand that it ...
5
votes
2answers
4k views

Neil deGrasse Tyson says that electrons “teleport” between energy levels?

This page: https://blog.afach.de/?p=62 Discusses the error Neil deGrasse Tyson made when talking about electronic transitions (video included there). Tyson clearly said in his Cosmos series that ...
5
votes
1answer
85 views

Can non-central hamiltonians commute with $\vec{L}^2$?

Central potentials $V(r)$ trivially commute with the operator $\vec{L}^2$ in quantum mechanics because the latter is a function of the angular coordinates $(\theta,\phi)$ only. Non-central potentials, ...
5
votes
3answers
769 views

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 ...
5
votes
1answer
5k views

Orthonormality of Radial Wave Function

Is the radial component $R_{n\ell}$ of the hydrogen wavefunction orthonormal? Doing out one of the integrals, I find that $$\int_0^{\infty} R_{10}R_{21}~r^2dr ~\neq~0$$ However, the link below says ...