# 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.

761 questions
Filter by
Sorted by
Tagged with
147 views

### Energy eigenvalue of hydrogen-like atoms using Laplace-Runge-Lenz vector

I have a basic question about a few calculations involving the quantum mechanical Laplace-Runge-Lenz vector. In classical mechanics there is the Laplace-Runge-Lenz vector, which for a hydrogen-like ...
33 views

### Hydrogen radial equation solution's boundary condition for $r \to 0$ [duplicate]

I am studying the hydrogen atom and I am analysing the radial equation: $$\left[\frac{-\hbar^2}{2m} \frac{\partial^2}{\partial r^2} + \frac{\hbar^2l(l+1)}{2m}+ V(r)\right]u=Eu$$ with $V(r)$ equal to ...
• 41
128 views

### Is the factorization method of Hamiltonian related to the theory of Lie groups?

I was learning about algebraic methods to solve the H atom, when I came across the factorization method. It is mentioned in various textbooks, notes and papers, like the one from Infeld and Hull. I am ...
• 105
1 vote
23 views

### Why do closed shells have a SOC split?

Why do the energy states of closed shells behave like in the one electron case? Imagine an atom with one electron in the $2p$ orbital. $l=1$ and $s=1/2$, so spin orbit coupling leads to two levels ...
1 vote
30 views

### Can hydrogen aquire magnetic moment?

Is the orientation of the electron inside its orbit around the proton inside the hydrogen atom dependent of the proton spin orientation... (as the spins of the two particles are cancelled out.)So if ...
• 2,255
108 views

### Hydrogen atom in a very strong magnetic field

An atom of hydrogen is placed in a very strong magnetic field. The magnetic moment of the orbit of the electron may either align with the external field or may oppose it. What will happen with the ...
1 vote
80 views

### Incorrect factor in radial wavefunction $R_{2,1}$ of hydrogen atom

First of all, let me state that this isn’t a homework question but rather my personal annoyance. I can provide a proof in the comments if you think otherwise. The general equation for radial wave ...
78 views

### Can we use Internal Combustion Engine exhaust to give heat for electrolysis to get hydrogen from water, to be used as fuel in the ICE?

Can we use exhaust from an Internal Combustion Engine to provide heat for the process of the electrolysis (to get hydrogen from water). And then use the H2 as fuel for the ICE so we use very little ...
1 vote
51 views

### Distribution of states of H$_2$ gas for a given temperature

How can I calculate the population distribution of vibrational and rotational states of H$_2$ gas, for any given temperature? I think the vibrational states are more important, since the rotational ...
30 views

### Electric dipole transitions: why is $\langle \vec{d} \rangle$ for stationary states 0 but not for superpositions?

We've learned in lecture about electric dipole transitions for hydrogenic atoms, and our professor claimed that $\langle\vec{d}\rangle=0$ for stationary states, but not for superpositions of states. ...
• 187
1 vote
69 views

### Evaluation of $\langle nlm|\frac{1}{r^2}|nlm\rangle$ [closed]

I am trying to prove that $$⟨nlm|\frac{1}{𝑟^2}|nlm⟩=\frac{1}{𝑛^3*𝑎^2*(l+\frac{1}{2})}$$ (where $𝑎$ is the Bohr radius) for the $|𝑛𝑙𝑚⟩$ state of hydrogen. I know how to do this using Hellmann–...
839 views

### Can the protium nucleus be in an excited state?

An electron in protium can absorb a photon and jump to an orbit of higher energy. Is an analogous procedure possible for the nucleus of protium (a single proton)? Can this nucleus be in an excited ...
• 253
108 views

### Positronium radius more than expected

I am trying to derive the basic properties of positronium. Usually it is stated that we can just set reduced mass of hydrogen atom as $\dfrac{1}{2}m_e$ and obtain: r_n=\dfrac{8\pi\...
1 vote
43 views

### Expectation Value Involving $s$-Wave Solutions to Central Potential

I previously posted a question regarding the expectation value described below, but it was closed because the question was not developed enough. Since I was given the option to delete it, I deleted it;...
• 199
1 vote
31 views

### 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,...
• 153
1 vote
118 views

### 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?
55 views

### 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 ...
79 views

### 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.
• 13k
77 views

• 11.7k
159 views

### 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 ...
• 5,925
102 views

### 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 $$r_{nlm,q}^{n'l'm'} = \langle\psi_{nlm}|r_q|\psi_{n'l'm'}\rangle$$ ...
• 14.4k
43 views

### 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 $n_{HI} = \frac{M_{HI}}{m_H V}$...
• 1
104 views

### 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. ...
101 views

### 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 (...
• 2,385
1k views

### 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 ...
• 2,122
2k views

### 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 ...
1 vote
391 views

### 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 ...
• 1,261
68 views

### "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 ...
98 views

### 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 ...
• 151
70 views

### 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 ...
• 145
126 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. ...
• 21
3k views

216 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 ...
293 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 ...
70 views

### 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 ...
• 138
1 vote
55 views

### 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 ...
134 views

### 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 ...
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 ...