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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 ...

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Lamb Shift and the meaning of “Lamb shift, which they produce in the spectrum energy of light from excited hydrogen atoms”

I cannot understand this paragraph. "Indirect effects of virtual particles can nonetheless be measured, and their existence has been confirmed by a small shift, called the Lamb shift, which they ...
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3answers
114 views

What is the meaning of natural line broadening?

I have recently found one exercise in an exercise book: During the transition from the first excited state of a hydrogen atom into the ground state, photons with a wavelength of 121.5 nm are ...
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1answer
43 views

Has hydrogen ever been used in Quantum Computing?

What I'm talking about is hydrogen atom quantum dots, where a hydrogen atom is embedded in a semiconductor. The reason for asking is because the Hydrogen atom is a Quantum mechanical system with a ...
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55 views

What is the point of talking about three axes for hydrogen orbitals?

The hydrogen orbitals are usually described using polar coordinates ($\Psi(r, \theta, \varphi)$). I understand that $r$ is the distance from the center of the atom, but how are the angles defined? ...
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1answer
48 views

Relation of Hydrogen orbitals to its spectral series?

I'm looking for the link between the Rydberg formula for hydrogen spetcral series $$\frac{1}{\lambda_{\mathrm{vac}}} = R\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$$ and this image. Is it right to ...
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156 views

What is the current measured (i.e. model independent) density of hydrogen $H$ in the universe?

The question came up in this thread: What is the current value for the temperature at which Recombination took place? I was under the impression that we had an independent measurement of Hydrogen in ...
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28 views

Assignment of $m_\ell$ values to $p_x, p_y$ and $p_z$ states

For the orbital angular momentum quantum number $\ell=1$, there are three possible $m_\ell$ values, namely, $-1,0$ and $+1$. Which $m_\ell$ value is associated with which of the three p spates, namely,...
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24 views

Resistance to a nanoscale system like hydrogen atom? [closed]

Can we talk about the resistance to a nanoscale system? For example, the hydrogen atom. It is obvious that the conventional resistance formula $$R=\rho \dfrac{L}{A}$$ be unable to characterize the ...
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A question on the colours of the hydrogen spectrum

Why does hydrogen have 4 lines in the atomic spectroscopy and not more? I mean when an electron get excited it has more than 4 possible ways to return to the ground state. So why we see only 4 lines?...
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1answer
111 views

How to numerically solve the Schrodinger equation for the hydrogen atom?

From the analytical solution for the hydrogen atom I remember that the energies were obtained by boundary conditions and then the energy depends on n*n in which n is interpreted as different energy ...
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How to find many body states whose total $L_{z}$ eigen values are zero?

I am trying to solve construct matrix representation of Helium atom. The hamiltonian is , $$H=-\frac{1}{2}\sum_{i=1}^{2}\nabla^{2}_{i}-\sum_{i=1}^{2}\frac{2}{r_{i}}+\frac{2}{|\vec{r_{1}}-\vec{r_2}|}$$ ...
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1answer
48 views

Questions on Stark Effect on Hydrogen

Suppose that a hydrogen atom is subject to a weak uniform electric field $\vec{E}=\epsilon \hat{z}$. Let's neglect the effect of electron spin. The perturbation added to the original hamiltonian $H_0$ ...
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72 views

Expected momentum of ground state hydrogen $<p>$

I am trying to calculate the expected momentum of an electron in the ground state of hydrogen atom. This is the wave function. So far I have done this:$$\iiint_V \Psi^* (-i\hbar) \frac {d\Psi} {dr} ...
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1answer
27 views

How much UV does a hydrogen flame emit?

A hydrogen flame is invisible but emits ultraviolet (and infrared) radiation. How much UV does a hydrogen flame emit for a given reactant flow or a given heating power? Could a hydrogen flame be used ...
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1answer
41 views

Formula for number of atomic orbitals for a given $n$

In my studies, it is stated that an atomic orbital is usually described in terms of three quantum numbers: $n$, the principal quantum number, $l$, the orbital quantum number and $m$, the magnetic ...
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Hydrogen energy state transition times and probabilites

How correlated is the energy absorbed to the later energy emitted, and hence to the transition type? What is the scale of time it takes to make a downward transition in energy level? In a very cold ...
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18 views

What happens when a photon does not excite the eletron in hydrogen [duplicate]

Let's say the energy carried over (photon) is not enough to change energy level of electron in hydrogen, or, it is a tad too much and we instead refer to the extra energy as the insufficient carrier ...
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44 views

How do I proceed with the following coulomb integral?

I am trying to solve the $H_{2}^{+}$ ion problem using Fourier transform approach. The Hamiltonian that I am trying to solve is as follows, $$H=-\frac{\hbar^{2}}{2m_{e}}\nabla^{2}_{e}-\frac{e^{2}}{4\...
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1answer
34 views

Are there any materials that have more tensile strength than diamond?

I'm looking up materials for worldbuilding, specifically for keeping metallic hydrogen in containment in zero gees. Are there any materials that have more tensile strength than a diamond anvil cell? ...
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1answer
128 views

Is the probability density of an electron in a hydrogen atom static?

Probability densities are illustrated in text books and on Wikipedia as static pictures. Is the probability density of an electron within an isolated Hydrogen atom static or does it oscillate in some ...
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1answer
128 views

Calculating the Radial Distribution Function

I've been reading a book "Why Chemical Reactions happen" which devotes a chapter to the concept that each of hydrogen's orbitals can be expressed with a wavefunction, which is a function of $(x,y,z)$, ...
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1answer
71 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, ...
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1answer
34 views

A question about Helium spectrum

I'm starting to read about two-electron atoms from physics of atoms and molecules by Bransden. Analyzing Helium spectrum I noticed that the energy of $He^+(1s)+e^-$ is greater than the energy of He, ...
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29 views

Finding the expansion coefficients of the decomposition of a 3D Gaussian wavepacket in the eigenfunctions of the Hydrogen atom

I'm having trouble with trying to find the expansion coefficients of a superposition of a Gaussian wave packet. First I'm decomposing a Gaussian wave packet $$\psi(\textbf{r},0) = \frac{1}{(2\pi)^{3/...
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1answer
92 views

Hydrogen and the neutron

I have a question about Hydrogen and the neutron. So a neutral hydrogen atom has structure ${}^1H\equiv[p^+ e^-]$, a bound proton and electron. From a quantum theoretical viewpoint, one would write ...
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30 views

What are all the wavelengths of the dueterium spectra?

What are all the wavelengths in the spectrum of deuterium? I've searched and came up with an abstract that only lists the visible part of deuterium's spectrum (see http://myslu.stlawu.edu/~jmil/...
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2answers
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How do alpha particles emit the heleum spectrum without electrons?

By definition, alpha particles do not have any electrons. This, in turn, should mean they do not emit a spectrum because a light spectrum is caused by electrons jumping between orbitals. Yet it is by ...
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1answer
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If I jump from space using a spacesuit filled with hydrogen could I survive the fall? [closed]

If I fill a spacesuit to its maximum volume with hydrogen while wearing it (who cares about the breathing part anyway) and jump from space (let's say, from 100km above sea level, a.k.a. Karman Line), ...
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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?
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80 views

How one can use the Klein-Gordon equation to deal with the hydrogen atom? [closed]

I'm not familiar with physics jargons compare to those who study physics professionally, but to remark my knowledge regarding this question, the Klein-Gordon equation is a relativisitc equation for ...
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1answer
134 views

How is hydrogen able to emit a light spectrum with only one electron?

When light is shined through hydrogen gas, three colors of light appear. The issue I have with this is that hydrogen has one electron, meaning somehow the electron has to be emitting all three of ...
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How much electricity does it take to create hydrogen from water depending on the water's pressure?

Imagine creating bubbles of hydrogen and oxygen underwater at a particular depth using electricity. Then reusing the energy of the bubbles going upward to the surface ( buoyancy ). How is the energy ...
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1answer
39 views

Compute degeneracy in energy levels of a wavefunction which is a sum of other wavefunctions

Given a hydrogen atom-like wavefunction at time $t=0$, say: $\Psi(r,t=0)=A(2\psi_{100}+\psi_{210}+\sqrt{2}\psi_{211}+\sqrt{3}\psi_{21-1})$ How can I compute the degeneracy of the energy levels for ...
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1answer
58 views

How well are the energy differences between ortho and para hydrogen and deuterium known

For a while i have been investigating whether neutrinos could feel a fifth force, that is axial, (opposite charge for opposite spin). But charge conservation means that either proton and neutron are ...
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38 views

Optimal Deuterium-Deuterium fusion pressure equation?

I am building a Hirsch-Farnsworth Fusor (a simple D-D fusion reactor) and was wondering if there is an equation or algorithm that could be used to calculate the optimal pressure for deuterium-...
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2answers
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What happens if Jupiter is ignited?

I was wondering, what would happen if there was a large amount of oxygen released into Jupiter's atmosphere, than igniting it? Because Jupiter is 90% gas, therefore being a big fire waiting to happen (...
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1answer
77 views

Could we create an artificial sun? [closed]

based on dyson spheres.. imagine we construct an sphere of high radius R , then we fill the sphere with hydrogen, if the sphere is huge and the hydrogen is too then the gravity will make the ...
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1answer
52 views

Why is Jupiter gaseous rather than solid or liquid?

Why is Jupiter made up of gas? If the gravitational pull was strong enough would it compress to form a solid body?
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1answer
97 views

Can you combine protium and tritium to produce Helium-4?

Can you combine protium and tritium to produce Helium-4? I think they're a perfect match like a piece of puzzle since tritium just need another proton and electron to make a stable helium-4 atom. Also,...
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33 views

So(4) synmetry in hydrogen atom

How it that invariance of rotations in 4 dimensional space leads to a degeneracy of energy of hydrogen atom in l and m values.
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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, ...
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Shankar's Hydrogen Fine Structure

In Shankar's section on the Hydrogen Fine Structure, it appears he sets the magnetic vector potential to be zero. Why does he do this?
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3answers
296 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{...
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1answer
99 views

Why Hydrogen bomb is called “Thermonuclear Bomb”?

Why do we call Hydrogen bomb as "Thermonuclear Bomb" ?
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3answers
469 views

Why doesn't hydrogen have a neutron?

Why doesn't hydrogen have a neutron?
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1answer
78 views

Ionisation of hydrogen

Is ionization of hydrogen gas atoms possible? I separated hydrogen from water by electrolysis but I want to obtain H+, how do I ionize that hydrogen gas? Is it possible to do it?
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18 views

Screened Coulomb Potential effect on Hydrogen [duplicate]

How does a screened coulomb potential affect the ground state energy of hydrogen atom? Just by looking at the perturbed potential, can we make a prediction about the energy shift? The screened ...
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0answers
94 views

Does separation of variables find all solutions to the 3-dimensional spherical time independent Schrödinger equation for a hydrogen atom?

I understand why it's OK to separate $\mathbf x$ and $t$ in the time-dependent equation. What's not clear to me is why, in the case of the 3-dimensional hydrogen atom, it's sufficient to find ...
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1answer
79 views

Evaluation of hydrogen atom matrix elements

Consider the operator $$\mathcal{P}=L_y L_z$$ and the hydrogen atom states $\left|n,l,m\right\rangle$. Evaluate the ratio $$\mathcal{R}=\frac{\left\langle3,1,-1|\mathcal{P}|3,1,0\right\rangle}{\...
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Can electronic energy be independent of nuclear coordinates in the two non interacting hydrogen atom?

I was trying to solve two non interacting hydrogen atoms both nucleus fixed at the the positions $\vec{R_{1}}$ and $\vec {R_{2}}$. I have considered the ground state wave functions of the two ...