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
0
votes
1answer
50 views

No $L = 0$; $S = 0$ states of Deuteron. Is this due to internal $np$-scattering?

Quick question regarding the L = 0; S = 0 states of Deuteron. In my notes I have stated that the state is unbound by 60keV np scattering. Am I right in saying this is the internal scattering of the ...
2
votes
2answers
2k views

The stark effect on ground state of Hydrogen

When considering the Stark Effect, we consider the effect of an external uniform weak electric field which is directed along the positive $z$-axis, $\vec{\varepsilon} = \varepsilon \vec{k}$, on the ...
3
votes
1answer
811 views

Quantization of kinetic and potential energy of electron in H atom

The total energy of electron in an hydrogen atom is quantized.The Bohr radius in the ground state is just an average value of the distance of the electron from the nucleus. This means that the ...
3
votes
1answer
592 views

Physical picture of spin-orbit coupling

I just want to confirm my understanding of spin-orbit coupling of a Hydrogen atom. Is the idea that the spin of the electron has a magnetic dipole moment and the orbit of the electron has a dipole ...
1
vote
1answer
1k views

Why electron spin being anti-parallel to the orbital angular momentum gives lower energy than the electron spin being parallel to the angular

Take hydrogen atom as example. The 2P orbital will split due to spin-orbit coupling to the $^{2}P_{3/2}$ and $^{2}P_{1/2}$ terms. The term $^{2}P_{1/2}$ has anti-parallel orientation of electron spin ...
0
votes
1answer
57 views

water molecular structure [duplicate]

If someone claim that chemical formulation for the water isn't $H_2O$, how we can prove for he/she that water has constituted of $H_2O$ molecules. Generally based on what evidences we sure that water ...
1
vote
1answer
1k views

Expectation value of $1/r^3$ in the $2p$ state of a Coulomb potential

I've been having difficulty calculating this quantity. We have an electron in the 2p state of a hydrogen atom (Coulomb potential). As a preliminary step to finding the energy difference between the $...
0
votes
2answers
2k views

If Hydrogen's nucleus lacks a neutron, then what is keeping the nucleus stable and the proton inside it?

I have two questions : In a simple hydrogen atom $(^1_1H)$, there is no neutron. So, if there is no nuclear force to hold the nucleus together then what is the thing that is holding the atom together?...
1
vote
1answer
2k views

Effective potential of radial equation of Hydrogen

In QM, the study of the hydrogen atom, why does it follow that for the radial equation given as $$-\frac{\hbar^2}{2m}\frac{d^2 u}{d r^2} + \bigg( -\frac{e^2}{4 \pi \epsilon_0} \frac{1}{r} + \frac{\...
0
votes
2answers
167 views

Exact electron energy levels in hydrogen

I was wondering, if you wanted to write down the exact expression for electron energies in a hydrogen atom, what would you have to include? There's principal splitting, fine structure and hyperfine ...
0
votes
0answers
81 views

Would a transition from liquid metal to solid metal hydrogen exhibit thermodynamic characteristics of freezing?

Hydrogen is proposed to have (at least) two metallic states. I believe the liquid metal state has been observed for a short time under high pressure and temperature conditions, and solid metal ...
0
votes
1answer
157 views

Q: Laser cooled hydrogen

Is it possible to cool down hydrogen some much (using lasers) to get a metalic form of the element? Or to try to produce it no such cooling is required?
1
vote
1answer
354 views

Using the Heisenberg Uncertainty Relation to Estimate Ground State Energies

In Shankar's Principles of Quantum Mechanics, he applies the HUP to estimate the ground state energy of the Hydrogen atom. In the proof, it is said that the first step to minimizing the expectation ...
0
votes
0answers
151 views

Degeneracy of Hamiltonian for Hydrogen Atom (Coulomb Problem)

It can be proven that the commutation relations $$\Big[ N,H\Big]=0$$ $$\Big[ L,H\Big]=0$$ $$\Big[ N,L^2\Big] \neq 0$$ Where $N$ is the Runge-Lenz vector. I'm wondering if it is possible to write ...
0
votes
1answer
756 views

Series solution to Legendre equation: QM interpretation

I can't figure out how Legendre polynomials can be interpreted to give the angular part of the wavefunction of hydrogen orbitals. The recurrence relationship is $a_{n+2} = $$\frac{(n-l)(n+l+1)}{(n+1)(...
2
votes
1answer
444 views

Metallic deuterium and metallic tritium as a fuel instead of metallic hydrogen?

A lot of news come these days about metallic hydrogen and its possibility of releasing 20 times more energy than just oxygen-hydrogen reaction. Like here: https://www.nasa.gov/pdf/...
0
votes
0answers
747 views

Quantized energy levels of Bohr hydrogen atom

When considering the quantized velocity of the electron in the Bohr model of the hydrogen atom at the various energy levels we have: $$v_{n} = \bigg(\frac{e^2}{4 \pi \epsilon_0}\bigg)\frac{1}{n \hbar}$...
3
votes
1answer
100 views

What's the possible changes for future physics due to the discovery of metallic hydrogen?

In recent days scientists in Havard find a way to turn hydrogen into a metal. So What's the meaning of such a discovery (you know this relative paper has published in science) and what's the influence ...
1
vote
2answers
192 views

What makes solid hydrogen, or any other material, metastable?

Recently, there's been some talk of potential lab results in an attempt to create pure, solid hydrogen in a stable form, which, if true, would be a first. Much of the excitement seems to be about the ...
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 ...
13
votes
2answers
546 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 ...
-2
votes
1answer
75 views

How is possible to create a pressure greater than Earth core's pressure in laboratory? [duplicate]

Recently is been reported than metallic hydrogen has been observed in the laboratory at a pressure of around 4,890,000 atm. This as far as I know is even greater than Earth's core theorized pressure. ...
3
votes
2answers
183 views

For the recently reported production (January 2017) of metallic hydrogen in the laboratory - what is the evidence exactly?

My google news page has burst forth the news that metallic hydrogen has been produced in a laboratory using a diamond anvil cell. Only one service mentions (at this particular moment) that it has been ...
2
votes
1answer
40 views

Do H$_2$ fuel cells function the same as H?

Are the 2 hydrogen molecule broken apart first? or does the $H_2$ directly react with the dialetric/anode/cathode to produce electricity? i.e. http://www.fuelcellstore.com/horizon-aerostak-a200
1
vote
1answer
191 views

Definition of energy levels of a hydrogen atom

I just want to confirm my understanding of energy levels of a hydrogen atom, since many times they introduce it without stating exactly what it is. It is given as $$E_{n} = -\bigg[\frac{m}{2 \hbar}\...
1
vote
2answers
427 views

Momentum space representation of the hydrogen atom Schroedinger equation

The Schroedinger equation for the hydrogen atom is $$\Big(-\frac{\hbar^2}{2m} \Delta - \frac{e^2}{r} \large)\Psi(\mathbf{r}) = E \; \Psi(\mathbf{r}).$$ I have found that the momentum representation ...
0
votes
1answer
57 views

Radiation issues dealing with the formation of Hydrogen from an isolated proton and electron

Please excuse me if this question has been asked and/or even partially answered here before... (I did search about, and did not see it specifically asked) In particular, and being purposefully '...
1
vote
2answers
1k views

About the Stability of hydrogen Isotopes

Shouldn't tritium be more stable than a hydrogen atom with no neutrons? Why does tritium do alpha decay but not hydrogen atom with no neutrons? I suppose that when the number of neutrons increases the ...
2
votes
0answers
41 views

Why is the fine stucture not included in the energy correction for problems with external magnetic field?

In problems regarding the effect of an external magnetic field on a hydrogenlike atom, it is assumed that the total energy splitting of the $1s$ level is due to the hyperfine structure and the Zeeman ...
0
votes
1answer
315 views

Solving the radial part of the Schrodinger equation for a central potential with two radial terms

a "hydrogen-like" atom has the following modified coulomb potential $$V(r)=\frac{-Ze^2}{r}+\frac{\alpha}{r^2}$$ Where Z is the number of positive charges and $\alpha$ is a positive energy constant. ...
-2
votes
3answers
547 views

The pros and cons of hydrogen vs. nuclear energy [closed]

If nuclear energy causes such a toxic effect to our environment, then why do we shy away from hydrogen? I understand that hydrogen is extremely volatile. To my understanding, hydrogen gives off ...
0
votes
1answer
122 views

Decay of hydrogen nucleus?

Very naive question. Nuclear decay is associated to more complex nuclei and explained through radiation. What about hydrogen and less complex nuclei? Will these nuclei eventually break apart? Or is it ...
0
votes
0answers
49 views

Find energy formula

I am struggling with this question my teacher gave me, Prompt Consider the hydrogen molecule, $^2H$, where each hydrogen atom has just one proton. The system has rotational, vibrational, and ...
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 ...
0
votes
2answers
1k views

Why Hydrogen is not solid in the outer space?

Why Hydrogen doesn't get solidified in the outer space?
2
votes
3answers
3k views

Magnetic quantum number for d orbitals

Online one can find many pictures of d-orbitals. I know that these states correspond to : n = 3, l = 2, m = -2, ...,2 but I don't know which one is which and I couldn't find a clear asignment ...
5
votes
2answers
583 views

Why are S-state solutions of Dirac equation for hydrogen atom allowed to be unbounded?

In this Wikipedia page there's a statement about 1S orbital as solved from Dirac equation: Note that $\gamma$ is a little less than $1$, so the top function is similar to an exponentially ...
0
votes
1answer
106 views

Energy states and electron excitation

We all know that in Bohr's model for hydrogen like species , electrons can revolve in only those orbits where its angular momentum is an integral multiple of $\hbar=h/2\pi$. But suppose we provide the ...
3
votes
0answers
213 views

On Virial theorem and its Quantum mechanical analog

The relation established by the virial theorem is well pronounced in the case of potential energies that are power law functions of distance. In quantum mechanics, a similar analog is present, ...
4
votes
2answers
2k views

Why is hydrogen or helium used in nuclear fusion?

I am not a Physics student. Just out of own interest, I'm studying about fission and fusion reactions. Where I found in fusion, the scientist are using either hydrogen isotope or helium-3 as fuel (...
-1
votes
1answer
838 views

Why is $\langle x \rangle =0$ for the ground state hydrogen atom?

From Griffiths, Introduction to Quantum Mechanics, 2nd ed: I found $\langle r \rangle =\frac{3a}{2}$ and $\langle r^2 \rangle =3a^2$. Now I need to find the expectation value of x. However, I don't ...
1
vote
1answer
375 views

(History) Who first solved the Schroedinger equation for the hydrogen-like atom (Coulomb potential)

My sense was that it was Pauli, but I can't seem to find any evidence to support this.
2
votes
2answers
382 views

How is Bohr's model related to electron cloud models via the correspondence principle?

I came across a discussion of atomic Rydberg states, which appear to be defined as having their outer electron in a highly excited state. In the same text, it mentioned that these excited electrons ...
-2
votes
1answer
191 views

H atom's excited state lasts on average $10^{-8}$ secs, is there a time gap (of max 2*$10^{-8}$ secs) betwn. two consec. photon absorpt.-emiss. pairs?

OK here is a description of what happens: time=0,timer starts first absorption happens, first emission happens absorption #2 happens emission #2 happens, stop timer timer==? According what I found, ...
2
votes
1answer
209 views

Are emission/absorption wavelengths of hydrogenic ions related to nuclear charge?

Is it possible to relate changing emission and absorption wavelengths of hydrogen-like ions to nuclear charge? Can one be expressed as a function of the other?
2
votes
1answer
191 views

Is there a list of hydrogenic transition matrix elements online?

Calculating transition matrix elements can be difficult, and I have found myself needing to use hydrogenic electric dipole transition matrix elements a fair bit. $$\mathbf{r}_{nlm}^{n'l'm'}=\langle\...
-1
votes
1answer
552 views

Calculating the most probable radius for an electron of a hydrogen atom

For the $\rm 1s$ state, the wavefunction is of the form: $\displaystyle{ Ne^{\Large{{-\frac{r}{a_0}}}}}$. So from this link and from what my professor said, the probability function will be $N^2e^{...
0
votes
1answer
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?
2
votes
3answers
1k views

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: ...
1
vote
2answers
4k views

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 ...