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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 Equation. Hydrogen atoms are the only atoms which could exist even n a world with fine - structure constant 1.

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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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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 ...
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Is metallic hydrogen an example of exciton?

I know that in exciton an electron is excited and goes from valence band to conducting band leaving an electron hole which is positively charged, soon Jupiter came into my mind and then this question. ...
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1answer
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Why does $2p$ have highest RDF at $4a_{0}$?

I was reading notes from my first class in Quantum Physics that I received and left confused at the following statement: For each principal quantum number $n$, the orbital set with the highest $\...
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What is the resistivity of solid non-metallic hydrogen?

If I were to use solid hydrogen (assuming temperature of 10K, pressure 1 atm) as a resistor of sorts, what would it's resistivity be? (Note: If someone can give me a good resource on info like this ...
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Lamb Shift and virtual particles [closed]

Can someone explain about the Lamb Shift?
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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
56 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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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
56 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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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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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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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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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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112 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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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
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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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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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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
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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
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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
257 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
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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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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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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
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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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0answers
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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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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), ...