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 get Bohr model from Schroedinger equation? [duplicate]

New theories must in some approximation must reduce to older approximately correct theories. In what approximation exactly does the angular momentum quantization condition from Schroedinger's equation ...
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Is the radiation problem actually solved in the classical quantum model of hydrogen?

It's often said that in classical physics a electron-proton system is not stable due to "Bremsstrahlung" and that one instead has to look at it quantum mechanically. This doesn't make sense ...
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What do maufacturers do to ensure that a valve is capable of containing hydrogen gas? [closed]

I am a researcher working to develop a hydrogen fuel system for use in a specialized internal combustion engine. The biggest challenge from an engineering standpoint with a project such as this is the ...
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Forces during the formation of hydrogen molecules

In my book it is given that for the formation of hydrogen molecules, hydrogen atoms come closer due to net attractive forces. It is written that initially when the atoms were approaching towards each ...
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Hydrogen Atom in Second Quantization and Two-Particle Bases

Context: In non-relativistic QM and many-body theory, the second quantization formalism allows us to write a Hamiltonian for a many-body system with up to two-body terms as (up to a re-ordering ...
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Is $e^-$ in 1st excited state in the $\rm H$-atom in superposition of possible ($l,m,s$ for $n=2$) substates/in superposition of all possible states?

I want to know how we can determine the probability of various states of hydrogen as there are infinite of them, or electron in a hydrogen atom is in the superposition of which states, maybe it is in ...
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Question about the radial hydrogen eigenfunctions

When calculating the selection rules for electronic transition in the hydrogen atom in dipole approximation, we always focus on the angular integrals. But why the integral $$ \int_{0}^{\infty}[rR_{nl}(...
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Origin of $\ell \leq n-1$ orbital rule

I am wondering about the origin of the $\ell \leq n-1$ orbital filling rule. For the hydrogen atom, I believe the reason is because in the spatial wave function there is the term $$\psi \propto \sqrt{(...
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Hydrogen Emission vs Absorption Wavenumbers

I am used to using the formula $ R_H (\frac{1}{n^2_{final}}-\frac{1}{n^2_{initial}}) $ to calculate the transition wavenumbers when an electron in a Hydrogen atom emits a photon. Can you use the same ...
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Schrödinger's equation for hydrogen atom (azimuthal part) [duplicate]

Now, The azimuthal part of the Schrödinger's equation for a hydrogen atom (after separating variables) is: $$ \frac{d^2 \Phi}{d \phi^2} + m^2 \Phi = 0$$ Which has solution $A e^{im\phi} + B e^{-im\phi}...
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How to calculate radius of the $n$th Bohr orbit if the nucleus is not at rest relative to the center of mass?

I've been dealing with a couple of questions regarding Bohr's model except where the mass of the nucleus is not negligible compared to the mass of the (revolving) electron. According to my book (...
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Transition $2p \rightarrow 1s$ of Hydrogen Atom

I am reading Mukhanov and Winitzki's book Introduction to Quantum Effects in Gravity and in second paragraph of Sec. 1.4.2 they say that : The spontaneous emission by a hydrogen atom is the transition ...
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Nodes in Spherical Harmonics

In Rydberg Atoms book by Thomas F. Gallagher, Page 14, the author provides the general equation of spherical harmonics which is well-known. He states that there exist $l-m$ nodes in the $\theta$ ...
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Schrodinger Equation of a Hydrogen Atom in a Rydberg State

I am not a mathematician, so I really appreciate it if someone could explain it in a simple way. In Rydberg Atoms book by Thomas F. Gallagher, the Schroedinger equation for the H atom in atomic units ...
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Wave Function Collapse During Reactions

When a proton and electron combine to form Hydrogen gas after the big bang, would the wave function of the electron collapse as they bond together?
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Why do we normalize the radial and the angular parts of a spherical wavefunction separately?

I'm trying to revise the Quantum Mechanical model of the Hydrogen atom, and I understand all the methods involved, including separating the wavefunction into its radial and angular parts, solving all ...
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Hydrogen atom at $T=0K$ [closed]

If I have an hydrogen atom at $T=0K$ from Boltzmann distribution I can have only the G.S populated, so if I send to this atom photons at all energies is impossible to excite the atom, is this right? ...
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Why do we ignore the proton when computing relativistic correction in the Hydrogen atom?

I have read a number of textbooks (e.g. Sakurai), and they all seem to say that the unperturbed Hamiltonian of hydrogen is: $$ H_0 = \frac{p^2 }{2m_e} - \frac{e^2}{r} \tag{1} $$ and the relativistic ...
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Associated laguerre polynomials for the hydrogen atom

The associated laguerre polynomial $L_k^N$ is a solution to the differential equation: $$ xy'' + (N + 1 - x)y' + ky = 0 $$ For the reduced radial equation for the hydrogen atom, we know that the ...
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Is the Bohr radius deprecated?

The Bohr radius ($a_0$ or $r_{\text{Bohr}}$) is a physical constant, equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state. It is named after ...
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Expectation value of $r$ [closed]

I am looking for an analytical expression for $$\langle r\rangle = \int dr r^2 R_{n'l'} r R_{nl}$$ where $R_{nl}$ are the radial wave functions, defined as $$R_{nl}(r)=N_{{nl}}\,r^{{l}}\,e^{{-{\frac {...
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Hydrogen atom and scale transformation for radial variable

While solving Schrödinger equation for Hydrogen atom we make a scale transformation for radial variable ($r=\frac{ax}{Z}$; where $a=$ Bohr radius, $x=$ dimensionless variable and $Z=$ atomic number), ...
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Is there a quick yet semi rigorous way to derive the Bohr radius of hydrogen?

I will be taking an oral exam, where I have to do some "airport physics", fast and easy magnitude estimations. Currently I try to come up with a good way to find the Bohr radius of the hydrogen atom ...
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Interpretation of probability current density of hydrogen atom wave function

I'm trying to understand the physical interpretation of the value of the probability current density of an electron in a hydrogen atom: $$j_r=0$$$$j_{\theta}=0$$ $$j_{\phi}=\frac{h}{rsin\theta}|\psi_{...
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Question about perturbation theory and even and odd wavefunctions

I was solving a question about perturbation theory and I came across something my teacher didn't mention and I can't seem to understand it. In the question there is an external electric field on a H-...
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Localizing position of electron in hydrogen atom

Consider the hydrogen atom, just taking into account the electrostatic force and not magnetism nor spin. Is it possible to take the wave functions of the energy eigenstates of that hydrogen atom, ...
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How can heavier elements be made from hydrogen atoms?

In a JRE podcast from a few years ago, talking about the idea of a universal constructor, Sam Harris said that we could go to a near-vacuum area of deep space, collect nothing but hydrogen atoms, ...
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Do the hydrogen atom's electron orbitals have Gaussian probability density functions?

In this article they show the following diagram: Are all the diagrams in the little boxes really just Gaussian probability density functions with mean and variance (or covariance)? If not, what kind ...
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How to get effective quantum numbers of a linear combination of $\rm H$-atom wavefunctions?

The convention for the Hydrogen atom's interpretation subject to the laws of quantum mechanics is that you can prove the quantization of $|L|$, $L_z$, and Energy through quantum numbers $\ell$, $m_\...
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In what sense are boron and carbon the simplest examples of degenerate atomic ground states?

According to this accepted answer, the most simple example of two atoms with degenerate ground states are boron and carbon. But hydrogen is the simplest of all which has the ground state configuration ...
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Two dimensional hydrogen atom

I was trying to solve for the wave function of an electron in a hydrogen atom confined to only two dimensions (in flatland). First of all I figured out the electrostatic potential energy in flatland. ...
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1answer
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Complex energy interpretation in perturbation theory

I'm working on time-independent degenerate perturbation theory for the Hydrogen first excited state. I have the following perturbation $H$: $H = \lambda V_0 \sin^2 \theta \sin 2\phi = \lambda V$. We ...
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Ground state of hydrogen molecule using Heitler–London method (H-L)

I am reading The Theory of Magnetism I, by Mattis. In Chapter 2, a hydrogen molecule is studied in the following way: We have a Hamiltonian of a hydrogen molecule: $$H = H^0_1 + H^0_2 + H^\lambda \...
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Why must energy transitions in hydrogen atom be between stationary states?

In Griffiths QM textbook, he said that a hydrogen atom in the ground state may undergo a transition to some other stationary state by absorbing a photon. Why must this transition be to another ...
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Solving the wave equation for one-electron atom

While solving the wave equation for a hydrogen atom, the first part of the solution is solving for the $\Phi(\phi)$. We have $$\frac{1}{\Phi}\frac{\partial^2\Phi}{\partial\phi^2}=-m^2$$ which has the ...
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Peak function decision

I am doing a lab of locating hydrogen's spectral lines and peak function fitting is required. It is suggested to use Lorentzian to locate the peaks. I wonder why don't we use Gaussian instead?
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Does the proportion of strong nuclear force in a star change during nuclear fusion?

I read that the SNF accounts for 99.9% of the mass of an atom. So if 4 hydrogen atoms become 1 helium atom during nuclear fusion does that change the proportion of SNF as we have 4 SNFs becoming 1 ...
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What causes a double peak for a single wavelength when using an optical spectrometer system?

I am doing an experiment to determine the Rydberg constant for the Balmer series using an optical spectrometer system (consisting of a monochromator with a photomultiplier detector and pulse counting ...
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Guessing eigenvalue solution

I am reading The Theory of Magnetism I, by Mattis. In Chapter 2, he proposes the following eigenproblem: $$ \left ( \begin{matrix} V & U \\ U^\dagger& V \end{matrix} \right ) \left ( \begin{...
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Why does the Bohr model give the correct energy levels for hydrogen even though it assumes a circular orbit?

I've been reading the answers for this question: Why did the Bohr Model Successfully calculate some of the energy levels in hydrogen? but it hasn't really satisfied my curiosity. Some answers suggest ...
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Zero Angular momentum at a Non-Zero distance in Quantum Mechanics

In Bohr atomic theory We learn that only those orbits are possible for which angular momentum is intger multiple of $h$.ie. $$mvr=\frac{nh}{2\pi}$$ Here n is used for angular quantum number,That can ...
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Bohr's hydrogen model confusion

As per Bohr model for hydrogen atom,energy of $n^{th}$ electron orbital is given by $\dfrac{-13.6}{n^2}$ eV. Energy of electron in the first orbit will be $-13.6$ eV and in second orbit will be $-3.4$...
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Quantitative contribution of kinetic and potential energies to the binding energy of the $\sigma$ orbital in $\text{H}_2$ or $\text{H}_2^+$

When a hydrogen molecule forms, 4.52 eV of energy is released, while for $\text{H}_2^+$ the binding energy is 2.77 eV. Such a binding energy is the difference of energies that have four terms in them: ...
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How can hydrogen spectrum be monomode (focusing on the lowest emission band)?

Consider you have an hydrogen atom. This atom can emit light under spontaneous emission for example, but the light it will emit will only be at some very specific frequencies: https://en.wikipedia.org/...
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Wavefunctions of the electron in a hydrogen atom [closed]

Can someone please explain those different electron distributions and what those (2,0,0), (3,0,0), etc. mean. Image source: https://commons.wikimedia.org/wiki/File:Hydrogen_Density_Plots.png
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Do emission and absorption lines complete each other

If you look at the spectral lines of hydrogen, the emission lines seem to be in the exact same spot where the absorption spectrum is black. Together, they build a full spectrum of visible light. Does ...
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Hydrogen atom ionization energy and infinity

We know that the ionization energy of hydrogen atom is 13.6 eV. What bothers is this energy corresponds to infinite seperation between the electron and proton. If we assume that this is true then in ...
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Measuring the size of the proton from the hydrogen atom spectrum?

I was reading that besides measuring the angle of ricocheted electrons bouncing off the proton to pin down its size, it is also possible to excite the electron and then measure the frequency of the ...
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Hydrogen wave function and angular momentum operators [closed]

I'm working my way through an old exam assignment for my Introduction to Quantum mechanics and a few (parts of) questions have me a little confused. The assignment is about the hydrogen atom and its ...
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Is hydrogen produced in the universe? [duplicate]

Since stars use hydrogen initially for fusion which then produces heavier elements. Where does all this hydrogen come from? Does all the hydrogen come from the birth of universe? If yes then will new ...

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