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 under pressure and high temperatere released energy: what is this process? [closed]

I am given hydrogen that is put into some pressure and high temperature conditions. After this it was found out that mass has decreased. It was also found that energy was released. Can someone, please,...
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Binding energy of Hydrogen = 0 = 13.6 ${\rm eV}$? [closed]

I was solving nuclear physics today.I used the binding energy formula on hydrogen.I found that B=0.But,B is also,as mentioned in my textbook,13.6eV. How?
CODE_FOR_PURSUIT's user avatar
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Fusion in the sun for 4 hydrogen to Helium-4. How is the energy produced

So please correct me if I am wrong but: First 2 proton’s (each with an electron) fuse together, The mass stays the same so no energy is produced? Then 1 of the protons turns into a neutron with a ...
Bobbie Space's user avatar
3 votes
1 answer
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Is metallic hydrogen solid or liquid?

If I squeeze hydrogen superhard with 400-500GPa of pressure, it becomes metal so is that solid or liquid? I know gallium melts on my hand and it's metal.
user6760's user avatar
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How can we estimate the frequency of the spin-flip transition?

I was reading the Hydrogen line explanation on Wikipedia when my attention was caught by the following sentence: This transition is highly forbidden with an extremely small transition rate of $2.9×10^...
Mark's user avatar
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Applying Kato-Rellich to the hydrogen atom model to prove stability of first kind [closed]

Trying to Understand the lower bound on the Schrodinger Operator of the Hydrogen atom. Using the kato-rellich theorem. My education has been in physics and i am slowly adding to my mathematics toolset....
Gedankenhooman's user avatar
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Is the axis of symmetry of electron orbitals arbitrary? Can it rotate?

The radial wavefunctions of electrons in hydrogen atoms, the electron orbitals or "clouds," is a topic covered in almost any quantum mechanics course or textbook. Something that has always ...
YaGoi Root's user avatar
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Can hydrogen be stored in the crystalline structure of ice?

I recently read that when ice freezes to form hexagonal crystals, the space within the hexagon is in fact a vacuum. Could this space potentially be used to store burnable hydrogen gas? If so, would ...
Robert Goddard-Wright's user avatar
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Why does $[Q,P]=i\hbar$ work for fermion? Shouldn't fermion satisfy anticommuting relation?

For hydrogen, we use $[Q,P]=i\hbar$ for electron, which is a fermion. Does it have a deeper reason such as that we're really considering the proton + electron system, which might be of bosonic nature?
Bababeluma's user avatar
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Antisymmetry of the total molecular wave function in case of orthohydrogen

If my understanding is right, the total wave function of any system containing electrons and protons (and any other fermions for that matter) must be antisymmetric under exchange of the respective ...
Tobi's user avatar
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Pauli exclusion principle in case of the $H_2$ molecule

Why do electrons in an $H_2$ molecule have opposite spins, while protons do not necessarily exhibit this behavior? Considering that both are fermions, shouldn't they both adhere to the Pauli exclusion ...
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When will an electron fired at a proton be captured instead of scattered?

Suppose electrons of energy $E>0$ are fired toward a proton. Since energy is always conserved in a central motion, and because an electron bound to a hydrogen atom must have negative energy $(E<...
Solidification's user avatar
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Is $n=1/2$ a valid hydrogen wavefunction?

The radial Schrodinger equation for the hydrogen atom is given by: $$\frac{1}{R}\frac{d}{dr}\left[r^2 \frac{dR}{dr}\right]+\frac{2m_e}{\hbar^2}\left(Er^2+ke^2r\right)=l(l+1).$$ Following the Bohr ...
John Eastmond's user avatar
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Moments of hydrogen orbitals/Transition dipole moments

I'm interested in calculating transition dipole elements for atomic transitions. This means I would like to calculate things like $$ r_{nlm,q}^{n'l'm'} = \langle\psi_{nlm}|r_q|\psi_{n'l'm'}\rangle $$ ...
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How can I calculate the column density of Hydrogen of a galaxy?

I have the following data: Mass of HI of the galaxy and radius. I thought using the following equation: $N_{HI} = \int n_{HI} ds \quad$ where the number density would be $n_{HI} = \frac{M_{HI}}{m_H V}$...
MJ_'s user avatar
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Why would a hydrogen atom form if proton and electron are left to attract each other, when they are very near? [closed]

In this question the OP asked, if electron and proton ,which are very near to each other,are left to attract in a straight line then what will happen? The answer was that a Hydrogen atom will form. ...
SacrificialEquation's user avatar
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Strange fine structure splitting of the two-body Dirac equation

This question is a follow-up of the discussion about one of my answers. Marsch proposed a two-body Dirac equation for hydrogen in order to treat the proton recoil effects in a non-perturbative way (...
dennismoore94's user avatar
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1 answer
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How is the proton accounted for in the relativistic solution of the hydrogen atom?

In the non-relativistic limit, the Schrodinger equation for the hydrogen atom can be solved using reduced mass techniques to account for the motion of both the electron and proton. I am wondering if a ...
Ghorbalchov's user avatar
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Does free neutron decay create a hydrogen atom?

When a free neutron decays, it is transformed into a proton, an electron, and a neutrino. Does this electron begin to "orbit" the proton, forming a hydrogen atom? Or does the electron run ...
Robert Goddard-Wright's user avatar
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2 answers
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How is there so much ionized hydrogen in the sun?

To my understanding, the sun contains large amounts of ionized hydrogen compared to the amount of hydrogen in the first excited state. I am curious about the explanation, at the quantum scale, for how ...
Relativisticcucumber's user avatar
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"Good" eigenstates for hydrogen atom in first excited state in an electric field

Consider a hydrogen atom in the first excited state that is being kept in an external electric field of strength $\lambda E_{ext}\mathbf {\hat{k}}$ . This electric field causes the splitting of the ...
Muralidhar Rao's user avatar
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2 answers
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Why can we ignore other charged particles when dealing with the Hydrogen atom?

Introductory treatments of the Hydrogen atom use the following Hamiltonian: $$H=\frac{|\textbf{p}_p|^2}{2m_p} +\frac{|\textbf{p}_e|^2}{2m_e}-\frac{Ke^2}{|\textbf{r}_p-\textbf{r}_e|}$$ However, given ...
Pol's user avatar
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Quantum Collapse during the Measurement of the spectrum of hydrogen [closed]

We have hydrogen inside a tube, and we induce a voltage on it; a current passes through it and light is emitted. The frequencies of light correspond to the differences of the eigenvalues of the energy ...
Zatrapilla's user avatar
2 votes
1 answer
112 views

Can Gravity alone produce a simple Hydrogen or Helium atom?

Imagine there is no EM or Nuclear Force, and Gravity is the only force. Can gravity alone produce an atomic structure similar to a basic atom? In this scenario, the nucleus is just a single particle. ...
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Why is there an exponential in the radial component of the hydrogen electron orbital wavefunction?

The solution for the Schrödinger equation for an electron in a (spherically symmetric) potential well shaped like $V=1/r$ is described by a wave function of the form $\Psi_{nlm}(r, \theta, \phi) = R_{...
acdr's user avatar
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What is the interpretation of these hydrogen probability density diagrams?

In the diagram above, what is the interpretation of all of the individual renders? Does the hydrogen atom continuously change between these states? For example, will $(n, l, m_l)$ become $(2, 0, 0)$ ...
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Darwin Term (Fine Structure) and the Taylor expansion of the electric potential energy

I am trying to derive the Taylor expansion for the potential $U(\vec r + \delta \vec r)$. The general expression for the Taylor expansion is: $$f(x)=\sum_{n=0}^{\infty}\frac{f^{(n)}(x_0)}{n!}(x-x_0)^n....
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Linear Stark effect in Hydrogen: Why do states $\langle 2,0,0|H_1|2,0,0\rangle$ and $\langle 2,1,0|H_1|2,1,0\rangle$ vanish?

I was reading sec. 10.4, example (4), about the 'Linear Stark effect in Hydrogen' in the book 'Quantum Mechanics: A Modern Development' by Leslie E. Ballentine (Also related to example (ii) in ch. 13....
Rasmus Andersen's user avatar
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What is the entropy of a hydrogen atom?

What is the entropy of a hydrogen atom, a bound proton and electron? First attempt: The standard molar entropy of hydrogen gas is 130.68 $J \, mol^{-1} K^{-1}$ at $298 K$. $1 \, mol = 6.02214076×10^{...
Jackson Walters's user avatar
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1 answer
180 views

How much information is in a hydrogen atom?

How much information is contained in a hydrogen atom (a bound electron and proton) at room temperature? There are bounds that set limits on the amount of mass/energy that can exist in a given region ...
Jackson Walters's user avatar
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1 answer
218 views

Symmetry of the hydrogen molecule wave function

Due to their overlapping wave functions, electrons in an $H_2$ molecule must posses opposite spins. The nuclei (two protons) on the other hand are far enough apart for the Pauli exclusion principle to ...
Tobi's user avatar
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2 answers
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Are the protons in dihydrogen in the same quantum state?

The electrons in the hydrogen molecule experience the same potential and are thus in the same state, so the Pauli exclusion forces them to have opposite spins. Since the protons are identical by ...
TunaSandwich's user avatar
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For hydrogen atom wave function, why eigenstate of Hamiltonian isn't only spherical harmonics if $H$ commutes with square of angular momentum? [closed]

I was reading quantum mechanics and I read about CSCO. So, commuting operators should share common eigen states, does that mean same eigen states? because in hydrogen atom wave function, Hamiltonian ...
Shuvajit Dutta's user avatar
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How does the pressure inside a pipe drop for a compressible gas (hydrogen)?

It is about turbulent compressible fluid, in this case, hydrogen gas. I have hydrogen gas at Ti = 25 K, pi = 3 bars, and ṁi = 0.001 kg/s (so 2.214 m/s) at the inlet of the tube. The pipe is 12.7 mm in ...
Alike minute's user avatar
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Hydrogen atom in void

We have a hydrogen atom, in a gravitationally bound system nothing interesting happens to it. Let's put it in an empty world where there are only an electron and a proton. Several forces act on it: ...
Victor's user avatar
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QM - States with same orbital angular momentum quantum number but different magnetic quantum number are equiprobable

I'm studying the hydrogen atom. My professor says that in a spherically symmetric problem, the choice of the $z$-axis is arbitrary and so, given a fixed value of the orbital angular momentum quantum ...
Tom Avery's user avatar
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Hydrogen atom laser spectroscopy and Lamb shift

To sum up I am trying to figure out measuring Lamb shift with precission laser spectroscopy experiment, and I cannot quite put my mind on it. I know that 1S-2S measurement happened through 2PA,Balmer ...
Edvaeli's user avatar
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0 answers
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Why do orbitals in a subshell of hydrogen atom have same energy? [duplicate]

Why do orbitals of hydrogen atom have same energy? If we take $p$ and $s$ orbitals, they are located at slightly different distances from the nucleus. So ideally there must be an energy difference. ...
Nachiketas's user avatar
8 votes
2 answers
1k views

How can I justify the energy levels of a hydrogen atom heuristically?

In the future, I will need to teach students at school the proportionality $E_n\propto-\frac{1}{n^2}$ of the energy levels of a hydrogen atom. I could present this as an experimental fact, but I would ...
Vercassivelaunos's user avatar
1 vote
3 answers
168 views

Fine structure of spectral lines in the hydrogen atom

I'm studying atomic physics from the book "Physics of atoms and molecules" by Bransden. On chapter 5 it discusses the effects of relativistic corrections on the hydrogen spectral lines. It ...
FreeWill's user avatar
1 vote
2 answers
133 views

Why $n-\ell-1$ nodes?

Can someone tell, why the radial part of $H$-atom wavefunction has exactly $n-\ell-1$ nodes? I know this comes by solving but is there some physical reason attached to this also? There is a related ...
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Hydrogen spectrum for transitions of $\ell$, $m_{\ell}$

In this question, there is a spectrum exhibiting transitions corresponding to the azimuthal quantum number $\ell$ of a system corresponding to a spinning $\rm{Cs_2}$ molecule. Regarding hydrogen-like ...
Weier's user avatar
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Why does the minimum eigenvalue change dramatically when one basis function is added to the basis set? [closed]

Copy from here https://mathematica.stackexchange.com/questions/284809/why-does-the-minimum-eigenvalue-change-dramatically-when-one-basis-function-is-a I have a basis set which describes with high ...
Mam Mam's user avatar
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4 votes
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What is the physical origin of two Hydrogen atoms repelling at short distance?

Consider two isolated $\rm H$ atoms. They can be in different spin states, but the different states are degenerate. Now move these $\rm H$ atoms together. Now the singlet state will become ...
Guiste's user avatar
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Why is hydrogen considered the most efficient rocket fuel and how it relates to the concept of specific impulse (ISP)?

Why is hydrogen considered the most efficient fuel? I mean I know it is very light and can be accelerated very fast, but can’t you use a denser fuel but throw it at a slower speed bunch, and it’ll ...
acornator's user avatar
1 vote
1 answer
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Do excited states of hydrogen give cosmologically relevant hyperfine transitions?

In Griffiths quantum mechanics, there's a discussion of hyperfine splitting for the ground state of hydrogen - this gives rise to a small level splitting corresponding to an emitted wavelength of $21$ ...
user196574's user avatar
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3 votes
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Where is the Darwin term in Griffiths quantum mechanics?

I was reading the Wikipedia page on fine structure, and it had the following expression for the fine structure of Hydrogen: To recap the image, Wikipedia includes the spin-orbit interaction, the ...
user196574's user avatar
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Shape of atomic orbitals

I am a physics bachelor student and currently learning quantum mechanics. In my course we derived the wave function for the hydrogen atom. I know that the quantum number L is connected with the shape ...
Blue2001's user avatar
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Is there any sense in which "quantum fluctuations" are a true justification of the Darwin term?

"The Darwin term" is one of the three contributions to the fine structure of hydrogen (and other atoms). It is a perturbation to the hydrogen hamiltonian, which gives rise to a change in ...
AXensen's user avatar
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Confusion in the calculation of the Free Energy in a Fuel Cell [closed]

I am writing a thesis about fuel cells and trying to follow the calcultion of the Gibbs free enery of the reaction of some author. I am confused because he took the higher heating value (HHV) of the ...
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