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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Benefit of Hydrogen Electrolysis

I was considering building a simple solar hydrogen generator for fun and it led me to the question Does the hydrogen produced have more potential energy than the electricity used to get it? Obvious ...
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If water vapour is a green house gas , then how is using hydrogen fuel cell stopping global warming?

Hydrogen fuel cells produce water vapour then aren't they also contributing towards global warming ?
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Natural frequency of electrons and the Hydrogen atom

Natural frequency is the frequency of a system when it vibrates freely without damping. I am in need of clarification about the definition of natural frequency at the atomic and molecular levels. Let'...
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Why is there a non-zero probability density of finding an $l=0$ electron at the origin of a Hydrogen-like atom?

A well known result for the $l=0$ hydrogenic functions is that $$\psi_{nlm_l}=R_{nl}(r)Y_{lm_l}$$ $$|\psi_{n00}|^2=\frac{Z^3}{\pi a_0^3n^3}$$ where $R_{nl}$ and $Y_{lm_l}$ are the radial function and ...
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Hydrogen atom quantum numbers distribution

The wave function of the hydrogen atom is given by $\psi_{n \ell m} \left( r, \theta, \varphi \right) = R_{n \ell} Y_{\ell}^{m} (\theta, \varphi)$ which depend on the quantum numbers $n, \ell, m$. I ...
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Perturbed hydrogen atom transition probabilities

Given the perturbed hydrogen atom having Hamiltonian $$ \hat{H} = \frac{\vec{p}^2}{2m}-\frac{e^2}{|\vec{r}|}+\lambda \vec{S}\cdot \vec{r} $$ (1) say which operators commute with the Hamiltonian among $...
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How to take care of singularities or discontinuities in a numerical Time-Dependent Schrodinger Equation simulation using the Split-Operator method?

I am currently trying to numerically simulate a two-dimensional Hydrogen atom using a split-operator method (elaborated below). I have tested that the code produces a good result for an isotropic ...
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How are Hydrogen Atoms Described in Standard Model? [closed]

Specifically, in order to calculate the quantities like emissivity or the cross section of photon resonant scattering by hydrogen atoms, what logical deduction route should we follow, starting from ...
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Coulomb potential vs Coulomb potential energy

I know that the Coulomb potential in a hydrogen atom is $V(x)=\frac{-e^2}{4 \pi \epsilon_{0} r}$. Usually the potential is given by the potential energy divided by the charge, so I would expect $V(r)=\...
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Inconsistency between the Lamb shift and vacuum polarization

According to Griffiths' Introduction to Elementary Particles, one of the contributions to the Lamb shift is the lack of vacuum polarization. In chapter 2, he explains how vacuum polarization can be ...
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Calculation of the rate of transition of the Hydrogen electron from $|2lm\rangle$ to ground state

This is how it was calculated in my book: We take the electromagnetic field to be part of the system. The initial state of the system is the direct product $|2,l,m\rangle \times |0\rangle$. $|0 \...
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Generating hydrogen from moving water

I am a high school student and I have planned to participate in national innovation award of my country. In this competition, prototype of innovation is needed. I have created a design but I lack ...
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Partition Function of a Hydrogen Atom - How it is derived?

It is well-known that the Partition Function of Hydrogen Atom diverges if we calculate in naive manner. And I could find the partition function named Brillouin-Planck-Larkin partition function which ...
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Can hydrogen be generated from flowing water?

Imagine water (water is made conductive using salt) flowing at a great speed is passed through a high magnetic field. Then due to changing flux , can we induce electric current in water? If electric ...
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Electron capture and overlapping wavefunction

I'm sorry if the following question sounds a little homework-ish, but I need help understanding how to even proceed with the following problem. In a hydrogenic atom of atomic number $Z$, the ...
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Hydrogen atom as a free particle moving on a three dimensional sphere?

I have heard on various occasions that the Hamiltonian/Lagrangian of the Hydrogen atom or that of a particle moving in $1/r$-potential can be transformed into that of a free particle moving on the ...
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About normal Zeeman effect and Hydrogen atom

I think that the normal Zeeman effect is experimentally observed only when we can neglect the spin i.e. if we consider a spin-singlet state with total spin $S=0$. Since in the hydrogen atom there is ...
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Problems with selection rules and polarisation

On this website http://bingweb.binghamton.edu/~suzuki/QuantumMechanicsFiles/2-4_Polarization_of_photon_emitted_from_an_excited_atom.pdf#page72 they want to explain the selection rules and the ...
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Expectation value of $r^{-3}$ for $\ell=0$

I'm trying to calculate the hyperfine structure energy for Hydrogen. From Jackson's Electrodynamics book eq. 5.73 we have: $$H_{HFS}=\dfrac{\mu_{0}}{4\pi}\left[\dfrac{-8\pi}{3}\mu_{N}.\mu_{e}\delta(r)+...
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Atom orbitals physics vs. chemistry

Why draw chemists always $|2p_x\rangle$, $|2p_y\rangle$ and $|2p_z\rangle$ orbitals instead of $|2,1,m\rangle$? Since $|2p_x\rangle$ or $|2p_y\rangle$ are a superposition of energy eigenstates they ...
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Is this really $SO(4)$ algebra?

The commutation relations involving the components of Runge-Lenz vector of the Hydrogen atom problem, ${\vec A}$ and the angular momentum ${\vec L}$ are given by $$ [L_i,L_j]=i\hslash\varepsilon_{ijk}...
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Probability of Finding an Electron Close to the Nucleus of a Hydrogen Atom

I am trying to calculate the probability of finding an electron in a small volume element close to the nucleus of a ground state hydrogen atom. I then need to calculate the same but replacing the ...
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Probability of finding the electron of a hydrogen atom within a cone of a given angle

I am working on a question where I must find "the probability of an electron being located within a cone of semi-angle 20 degrees w.r.t the z-axis" for the 2s and 2p states of a Hydrogen ...
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Spherical harmonics visualization as oscillations on sphere

I‘ve watched this video where they visualize the spherical harmonics as oscillations. Since the spherical harmonics determine the spatial shape of the orbitals of the hydrogen atom their time ...
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Current distribution in hydrogen atom

In the Bohr model of hydrogen, the electron orbits the proton at selected radii such that the angular momentum is quantized in integer multiples of $\hbar$. We can then associate a current with such a ...
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How can hydrogen have negative enthalpy?

According to the data found here, the enthalpy of hydrogen at very low temperatures can be negative. I fail to wrap my head around how this can be in line with $H = U + pV$, where $U$, $p$, and $V$ ...
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How do we obtain radial part and angular part with spherical harmonics?

In a website (sorry, I can't find it anymore) I've read this when talking about spherical harmonics: if we want to determine simultaneous eigenfuntions of $L^2$ and $L_z$ we have to solve this system:...
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Trying to understand the relationship between Hydrogen atom, spherical harmonics and central field force in quantum mechanics

I have a problem understanding three arguments in quantum mechanic: When we talk about a particle in a central field we have this kind of Hamiltonian: $$H=\frac{p^2}{2m}+V(r)$$ if we use spherical ...
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Separable Hamiltonian systems in quantum mechanics

Why is it that in separable Hamiltonian problems the total eigenfunction is equal to the product of the individual eigenfunctions, but the individual Hamiltonians must commute? In mathematics, when ...
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To which orbital does an excited electron in a hydrogen atom go?

For atoms other than hydrogen, each subshell within an energy level has distinct energy. For hydrogen, however, all orbitals within an energy level are degenerate (have the same energy). So, when the ...
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Atom and Light interaction

I want to qualitatively get a picture of what happens when a hydrogen atom interacts with electromagnetic waves. If we consider that the hydrogen atom is in state $\phi_{100}$ (ground state) then the ...
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Zeeman effect in hydrogen atom

Was the Zeeman effect observed for hydrogen atoms experimentally? Is there any reference?
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What is a good definition for Radial Probability Density?

Hi Physics Stack Exchange, I’m a student with first year university chemistry knowledge and high school mathematics and physics knowledge (e.g. am familiar with complex numbers). I’m having some ...
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Confusion with some of the states of addition of angular momentum 1 +1/2

In the hydrogen atom, for $n=2$, I want to find all possible states. For $l=0$ this is easy, and so it is with most of $l=1$. There are two states, however, that I don't understand. They are: $$\Psi_1 ...
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There is any kind of research on the use of a "Light-Gas Gun" on the production of Metallic Hydrogen?

Well, if it was that simple, there would already be some research on it, but I couldn't find any. Light-Gas Gun: If you don't know, a Light-Gas Gun is basically an apparatus that is able to shot ...
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Why do two hydrogen atoms bond?

I was wondering (with my limited classical physics knowledge) why two hydrogen atoms tend naturally to a bonding configuration, I mean, given two hydrogen atoms with zero relative velocity between ...
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Confusion about this explanation of the radial hydrogen Schrodinger solution

I was reading this page about solving the radial part of hydrogen's energy eigenstates. They explain how to solve for the asymptotic behavior $R_{\infty}(r)$ first by taking the limit of the ...
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Why does the hydrogen molecular ion has no bound state except the bonding state?

Using LCAO method, we can determine the ground state of the hydrogen molecular ion. It is the spatially symmetric state given by $$\psi_+=\frac{1}{\sqrt{2}}\left[\psi_{1s}(r_A)+\psi_{1s}(r_B)\right]$$ ...
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Bohr model of hydrogen atom

According to Bohr model of hydrogen atom, the electron orbits in circular orbits around the nucleus. when I'm asked to find the energy needed to ionize the hydrogen atom, I calculate the energy stored ...
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What power is required (in terms of watts) to produce 1 lpm flow of Hydrogen @ STP using electrolysis at 100% efficiency?

I know that the energy is usually expressed a joules but the test set up I have at the moment comprises of just voltage, current and temperature measurements along with a hydrogen mass flow gauge. I ...
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Why aren't triplet states in Hydrogen molecule bound by Pauli's principle?

I am learning about the wavefunction of two electrons in a Hydrogen molecule and I came across following spin states: |↑↑⟩ and |↓↓⟩, which form two of the triplet states in the molecule. This confuses ...
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Can the Schrödinger equation be solved for deuterium?

Or does the added neutron complicate things too much?
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Is it possible securely detonate a hydrogen bomb inside a very, very thick iron armor to get the armor only rise its temperature and not break apart? [closed]

Is it possible securely detonate a small hydrogen bomb inside a very, very thick iron armor, preferabely a sphere, to get the armor only rise its temperature and not break apart? Would it be a hazzard ...
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Stationary waves as eigenfunctions of the Hamiltonian operator in the ground state of the hydrogen atom

Taking the Hamiltonian operator $H = T + V$, I know that the eigenfunctions are stationary waves, this means that the wave function $\Psi$ is eigenfunction of T + V, this is also true in the case of ...
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What is the Hydrogen and Helium composition of the Sun in terms of their different states?

What is the Hydrogen and Helium composition of the Sun in terms of: Hydrogen: (1) molecular, (2) metallic and (3) ionized compositions? and Helium: (1) atomic, (2) metallic and (3) ionized ...
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How much energy is released in high orbital hyperfine transitions?

The famous 21 cm Hydrogen Line happens due to the hyperfine transition of the 1s electron spin in Hydrogen orbital cloud. If a hyperfine transition were to happen in other elements highest orbital ...
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(Cold?) fusion by combining protons and electrons?

How does one remove electrons from hydrogen nuclei? Using a tokamak? In any case, do we really need millions of degrees centigrade of temperature to get an electron to fuse with a proton? To make a ...
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Is energy of electron of any atom at infinity zero?

Is energy of electron of any atom at infinity zero? As I know it's zero for hydrogen-like atom (ion) according to Bohr's model, but what about 2-electron atom or 3-electron or more? Will it also be ...
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Why am I failing to calculate the Bohr radius correctly? [closed]

This is the formula that I'm using: $$r_n=\frac{h^2}{4\pi^2me^2}\times\frac{n^2}{Z}$$ Here, $r_n$ = radius of nth orbit $h$ = Planck's constant $(6.626\times10^{-34}Js)$ $m$ = mass of an electron $(9....
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Is hydrogen atom with a single unpaired electron diamagnetic?

I know that paramagnetism is caused because of the net magnetic dipole moment of an atom with unpaired electrons. On the other hand, all substances exhibit diamagnetism, but the effect is weak and ...
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