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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How to find the electrostatic potential of a hydrogen-like charge density?

So I've been trying to find the scalar potential that would correspond to the charge density of a ground state hydrogen atom. The result is known, and the inverse of my problem can be found e.g. in ...
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What is electrochemical water splitting by photovoltaics?

What can be the best way for production of hydrogen ? I have read about different methods like photocatalysis, PEC and so.. But can some one explain in brief?
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Quantum mechanics - Solved problem list [closed]

Im trying to find all the solutions to the energy and wave function of all the problems in quantum mechanics. Unfortunately I find non correlation solutions. Someone can write here the solutions ( ...
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How much hydrogen does Earth lose in an hour? [on hold]

CONTEXT: Escape velocity is the minimum speed needed for a free, non-propelled object to escape from the gravitational influence of a massive body. The escape velocity from Earth is about 11186,1 m/s. ...
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Eigenspaces of the hydrogen atom as representations of $SO(3)$

When we computing the discrete spectrum of the hamiltonian of the hydrogen atom $$H=\Big(-\frac{\hbar^2}{2m} \Delta - \frac{e^2}{r} \large),$$ by some explicit computation we get that eigenspace $...
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Does hydrogen gas laser exist? If not, why?

I have searched the internet, and this forum, but can't find a mention of hydrogen gas laser. There does, however, exist the hydrogen maser that used the 21cm radiation. Also there exist Nitrogen gas ...
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Black hole nucleus in hydrogen

The hydrogen atom gets the spectrum it has because you analyze the Schrodinger equation in spherical symmetry with the potential given by $V=-\frac{1}{4\pi\epsilon_0}\frac{e^2}{r}$. Yet the same ...
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82 views

How can i obtain the correction to the eigenvalues as a result of adding the gravitational potential to the hydrogenlike atom?

In treating the hydrogen-like atoms, we normally neglect the gravitational potential for the system. I am able to justify the above statement by comparing the gravitational potential to the ...
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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 ...
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Interpretation of 21 cm intensity mapping

I'm currently trying to understand the following plot from Astrophysics for physicists by A.R. Choudhuri. I think I understand the basic concept of measuring the line-of-sight velocities with the ...
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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 ...
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What are estimated magnetic properties of liquid metallic hydrogen?

I understand that liquid metallic hydrogen isn't easy to produce, or keep it stable on Earth, but can be liquid metallic hydrogen magnetised? Does it have magnetic properties at all?
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Can a hydrogen atom temporarily attract an additional electron to form a negative ion?

Negative ions should be a kind of temporary substance form that exists widely. Can a hydrogen atom temporarily attract an additional electron to form a negative ion? Other elements or molecules can. I ...
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Has man ever observed the spectrum of a single hydrogen atom?

Were there this kind of experiment done before? The spectrum we observed is radiated by huge number of hydrogen atoms in the gas, not by single hydrogen atom. I know it's very hard to test a single ...
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Are parahydrogen and orthohydrogen identical particles?

I have no formal physics background, just aerospace engineering, and I'm working on a DSMC project simulating relaxation of hydrogen in non-equilibrium, rarefied, 1D flow via translational and ...
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Dependence of radial probability function on quantum numbers

I was reading the book "Quantum Physics" from Eisberg & Resnick about the expected value of the electron radial coordinate, which it defines as \begin{align} \overline{r_{nl}} = \int_{0}^{\infty}...
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Recombination of hydrogen

Suppose a slow-moving electron and a slow-moving proton are injected into a chamber, such that the two approach each other and are likely to combine to form an atom of hydrogen. How would one ...
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Where can I find relativistic corrections to 2s and 2p levels of Hydrogen Atoms?

I am currently studying for a Quantum Mechanics test, and I want to calculate the 2p and 2s hydrogen atom corrections for the relativistic, spin-orbit and darwin corrections, using perturbation theory....
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Trying to solve TDSE for Hydrogen atom, but I cant determine initial condition

I am trying to solve TDSE for a hydrogen atom in the b-spline basis set. $$i\dfrac{\partial}{\partial t}\Psi(t)=[H_{0}+D(t)]\Psi(t)$$ with initial condition $\Psi(t=-\infty)=\Psi_{g}$, where $\Psi_{g}$...
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More than two linearly independent solutions to the (linear second order) radial wave equation?

I'm puzzled by the following radial wave equation: $$ \left(\frac{\hbar^2}{2m_r}\left(-\frac{d^2}{dr^2} -\frac{2}{r}\frac{d}{dr} + \frac{l(l+1)}{r^2}\right) + V(r)\right)R_{nl}(r) = ER_{nl}(r)$$ ...
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How can I calculate the hyperfine structure of a $p$-orbital?

I have a little problem with the calculation of the hyperfine structure of the 3p orbital in the hydrogen atom. The Hamiltonian is: Were represents the magnetic moment of the proton and the ...
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How does the ratio of hydrogen to helium help prove the big bang theory?

From what I have read one of the key pieces of evidence for the big bang theory is the ratio of hydrogen to helium in the universe. I have not seen any explanation as to how the big bang theory ...
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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 ...
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About the size of the orbitals $s$, $p$, $d$, etc, in $H$ atom

Can we define a size for the H atom orbitals which are not spherically symmetric, e.g. $p, d$ etc? For example, is it meaningful to say that the $(n+1)p$ orbital is larger in its extent than $np$ ...
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Hydrogen: Whether it's a metal or non-metal

I know hydrogen is a non metal, but when I just study about some introductory elementary band theory I find the band structure of hydrogen has a half filled valence band just like alkali metals, and ...
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Why is the “fine structure” correction called that way?

I'm working on the fine structure correction to the Hydrogen atom. I have more of a conceptal, maybe historical question, why is this correction called this way? and why is the fine structure constant ...
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Where does this Differential Equation comes from?

Im studying Stark Effect and im trying to prove that the second order correction to the ground state of hydrogen like atoms goes like \begin{equation} \delta E^{(2)}_{100}= -\frac{1}{4}a_o^3 E^2(4+5Z^...
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Why hydrogen lines are less visible in the Sun spectrum than in supernovae clouds?

Supernovae clouds are very colorful, and if I trust documentaries I watched, the colors are due to excitation of elements, as in fireworks. Since the Sun is mostly made of hydrogen, I suppose those ...
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Question about Electric Dipole Transition Selection Rules [duplicate]

I learned that the selection rules for electric dipole transition in a hydrogen-like atom is \begin{align} \delta l & = \pm1 \\ \delta j & =0,\pm1 \\ \delta m_j & =0,\pm1 \end{align} I ...
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Can one add a discrete set of functions to complete the bound states of the hydrogen atom?

Though being an infinite orthonormal set of functions, the bound states $\Psi_{nlm}$ of the hydrogen atom do not form a basis of the Hilbert space $L^2(\mathbb{R}^3)$ due to the continuous spectrum, i....
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Expectation value of $x,y,z$ for general $nlm$ state of hydrogen atom

How to calculate expectation value of $\langle x\rangle, \langle y\rangle,\langle z\rangle$ for the general $\psi_{nlm}$ state? $x$ has $\sin(\theta)\cos(\phi)$ angular part which can be expressed as $...
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Can hydrogen plasma react with oxygen?

What if you put hydrogen in a vacuum and turned it into a plasma? There is no oxygen in the vacuum, but once you eject the plasma would it react drastically with the oxygen? Would it explode? Would ...
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Quantum energy levels of a point mass rotating about a fixed point

The question is: A particle of mass m is attached to a fixed point in space by a massless rigid rod of length a and can freely rotate about this point. Find the quantum energy levels of the system. ...
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Probability of finding hydrogen atom in its ground state given an initial state

So I came across this question that asked what is the probability of a hydrogen atom which is prepared in an initial state $\Psi (\vec{r},t)$ to be in the ground state $\psi_{100}(\vec{r}) =2exp(-r)Y_{...
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Plasma inside deuterium spectrum tube?

Hullo, In a deuterium spectrum tube there is a thin capillary in the middle (see picture) that glows purplish sort of. Now, I wonder what this glowing part actually consist of? Is it a completely ...
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Semi-classical Hydrogen Atom Angular Momentum under Magnetic Field

Suppose we have a semiclassical hydrogen atom in its ground state at the x-y plane with the proton being at the origin. Let there be a magnetic field $\vec{B}=B\hat{z}$. By deriving the orbital ...
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Is the $2p\rightarrow2s$ transition possible?

Selection rules in one electron atoms are: $\Delta n=$ any $\Delta l=\pm1$ $\Delta m_l=0,\pm1$ $\Delta s=0$ Parity must change Under strong spin orbit interaction: $\Delta j=0,\pm 1$, but $j=0\...
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Why do low concentrations of H2 in He gas exhibit lower thermal conductivity than either?

Thermal conductivity of He+H2 mixtures, as a function of molar concentration of H2, exhibit a minimum at around 14% H2. See Fig. 2 below from "Thermal conductivity of the hydrogen-helium mixture". ...
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virial theorem hydrogen atom

I calculated $\langle T \rangle$ and $\langle V \rangle$ as a function of time of a given state of the hydrogen atom $|\psi\rangle=a|1,0,0\rangle+b|2,0,0\rangle$ and I found that $$\langle V \rangle ...
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Finding the value of $r$ for which the radial function, $P(r)$, has a maximum? [closed]

In my (university) particle physics course, I am asked to find the values of $r$ for which the function $P(r)$ of a $2s$ Hydrogen electron has its maximum values. Here, $r$ denotes the distance in ...
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Radial term in the spin-orbit coupling

The spin-orbit interaction for the hydrogen atom is of the form $\hat{H_1} = A\frac{1}{r^3}\pmb{\hat{L}}\cdot \pmb{\hat{S}}$ Now in my course, we treated this interaction by working in the basis of ...
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Symmetries of a differential equation, its solutions and hydrogen atom

A symmetry of a differential equation need not be shared by its solutions. However, under that symmetry, the one solution goes to another. For example, consider the time-independent Schrodinger ...
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How does the hydrogen atom actually “look like”? [duplicate]

When deriving the solutions for the "simple" quantum mechanical hydrogen problem, one normally uses spherical coordinates $(r,\theta,\phi)$, since the problem has rotational symmetry. The solution has ...
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49 views

Transitions in Hydrogen Atom

Suppose we have a Hydrogen atom in a superposition of the 1s ground state, $\psi_1 = R_{1,0}(r)Y_{0,0}(\theta,\phi)$, and the $m_l = 0$ state of the 2p configuration, $\psi_2 = R_{2,1}(r)Y_{1,0}(\...
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$\langle r \rangle$ and orbital energy [duplicate]

Even though $\langle r_{2s} \rangle > \langle r_{2p} \rangle$ based on the following formula $$ \langle r_{n\ell} \rangle = \frac{{a}_{0}}{2}(3{n}^{2}-\ell(\ell+1)) $$ $2s$ has a lower orbital ...
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Relativistic hydrogen wave function for python/mathematica

Is there any library/module for mathematica or python that has the exact solution of the Dirac equation for a hydrogen atom implemented? Sympy has the wave functions the non-relativistic wave ...
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Understanding the radial distribution function [duplicate]

I am confused why the maximum of the radial distribution function for 2p orbital is closer to the nucleus than that for 2s orbital. Doesnt this mean that there is a higher chance of finding 2p orbital ...
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Difference between radial distribution function and probability density function

I want to be clear on the difference between radial distribution function ${P}_{nl}(r)dr$ and probability density function in the context of hydrogen wave function. Definition of ${P}_{nl}(r)dr$ is ...
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Expectation value of coordinate mixed operator with ground state

I have a Hamiltonian of the Hydrogen atom: $H=H_0+H_1+H_2$ , when: $H_0 $ is the hamiltonian from central force and from electron momentum , $H_1$ is the relativistic kinetic fixing, and $H_2$ is the ...
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Is there a mass spectrometer software that can measure the mass of a hydrogen atom [duplicate]

For a school project I need to measure the mass of a hydrogen atom either as a lab experiment or with a computer simulation. Since I don't have the appropriate equipment for the experiment, does ...