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.

Filter by
Sorted by
Tagged with
3 votes
1 answer
163 views

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:...
  • 821
6 votes
1 answer
204 views

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 ...
  • 821
6 votes
2 answers
448 views

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 ...
  • 821
0 votes
1 answer
98 views

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 ...
7 votes
5 answers
284 views

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 ...
  • 1,337
1 vote
1 answer
98 views

Zeeman effect in hydrogen atom

Was the Zeeman effect observed for hydrogen atoms experimentally? Is there any reference?
  • 1,856
0 votes
2 answers
237 views

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 ...
1 vote
1 answer
69 views

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 ...
2 votes
0 answers
38 views

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 ...
  • 49
4 votes
5 answers
195 views

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 ...
  • 41
0 votes
0 answers
44 views

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 ...
  • 2,012
0 votes
0 answers
52 views

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 $$\psi_+=\frac{1}{\sqrt{2}}\left[\psi_{1s}(r_A)+\psi_{1s}(r_B)\right]$$ ...
3 votes
1 answer
84 views

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 ...
  • 41
0 votes
2 answers
87 views

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 ...
2 votes
1 answer
63 views

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 ...
4 votes
4 answers
2k views

Can the Schrödinger equation be solved for deuterium?

Or does the added neutron complicate things too much?
  • 189
2 votes
2 answers
110 views

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 ...
0 votes
1 answer
77 views

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 ...
1 vote
1 answer
127 views

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 ...
0 votes
0 answers
22 views

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 ...
-2 votes
2 answers
117 views

(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 ...
0 votes
2 answers
242 views

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 ...
-2 votes
2 answers
85 views

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....
1 vote
1 answer
370 views

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 ...
2 votes
2 answers
97 views

Hydrogen line spectrum [closed]

lately I have come across the hydrogen line spectrum, I quite understand it as I could easily solve all numerical questions. However, conceptually I feel stuck at two points. If an electron absorbs ...
1 vote
1 answer
95 views

Where is this extra energy in the Hydrogen Atom coming from?

...
2 votes
1 answer
72 views

Are hydrogen spectral differences guaranteed to be unique?

I was shown an interesting question that goes something like this: Consider the energy released by the transition in Hydrogen when the electron falls from $n=4$ to $n=3$. Explain how we know that ...
  • 2,206
1 vote
1 answer
91 views

Collision of an electron with an atom

What exactly happens when we say an electron collides with an atom? When we say atom, does the incoming electron collide with the nucleus of the atom (electromagnetic repulsion from the nucleus ,...
0 votes
2 answers
141 views

What is the precise internal structure of Jupiter?

I've been trying to find out exactly where the layers of molecular hydrogen, and metallic hydrogen are precisely, inside Jupiter, in kilometres from the centre. Ideally with an error margin of 1-10kms....
0 votes
0 answers
47 views

Precise theoretical energy of the dihydrogen molecule as a function of internuclear distance?

I am currently looking for the most state-of-the-art theoretical prevision of the energy of the dihydrogen molecule as a function of internuclear distance as a means of comparison with numerical ...
1 vote
1 answer
90 views

How much energy is stored in the field of a hydrogen atom?

How much energy is in the electric field of a single lone hydrogen atom that has no neutrons and exists at the lowest energy state possible? Well in a universe where nothing else exists.
  • 589
4 votes
1 answer
84 views

Why is Cosmic Microwave Background Radiation thermal? [duplicate]

Cosmic Microwave Background (CMB) Radiation is known to be thermal to very good approximation. This means that when it was created, this radiation has already been thermal. This is because the ...
0 votes
2 answers
57 views

Spin of hydrogen orthonormal

In this video lecture, the lecturer wrote spin up is $|\alpha\rangle = [\frac{1}{2}, \frac{1}{2}]$ and spin-down is $|\beta\rangle= [\frac{1}{2}, -\frac{1}{2}]$. He then wrote that $\langle\alpha|\...
  • 103
1 vote
1 answer
139 views

Hydrogen atom orbital projections resemble to some Chladni figures! Mathematical reasoning?

Chladni figures are formed by sprinkling salt on a vertically vibrating membrane, f.e. [. Some of them are purported to be projections of hydrogen atom orbitals f.e. 1s, 2s, 2p, 3d, etc., e.g. . One ...
26 votes
2 answers
2k views

Why can't hydrogen and helium fuse?

In the hearts of stars, hydrogen atoms fuse together to make helium. After the hydrogen in the core is depleted, the star changes state and conditions at the heart of the star make it possible for ...
1 vote
2 answers
71 views

It more efficient to generate heat burning electrolyzed hydrogen, or through an electric resistance?

It's convenient and simple to use electricity to generate heat, doubtlessly, say in en electric kettle or boiler or heater, but is it more efficient to generate heat burning electrolyzed hydrogen, or ...
-2 votes
3 answers
153 views

How to understand the hydrogen energy level and its wave function?

I have difficulty to understand this Hydrogen atom's energy level and its wave function. My difficulty is regarding the hydrogen atom itself, not the energy level and the wave function their selves, ...
1 vote
1 answer
207 views

Could water be converted into hydrogen and oxygen using very strong magnetic fields?

Had a crazy thought experiment and was wondering if this is possible/feasible. You place water in a electrically neutral container like glass. Then the glass container is placed between two opposing ...
  • 329
1 vote
1 answer
552 views

Viscosity of liquid hydrogen and its effect

The dynamic viscosity of saturated liquid hydrogen at atmospheric pressure is roughly $\mu_{LH_2} = 1.3\times10^{-5}~Pa.s$. For the same conditions, its density is $\rho_{LH_2}=70.8~kg/m3$, so the ...
1 vote
0 answers
203 views

Dirac equation for hydrogen atom

I went over a calculation of the hydrogen wavefunction using Dirac equation (this one) and I am a bit confused by the angular part. The final result for the wavefunction based on that derivation is ...
1 vote
2 answers
136 views

The most precise analytic solution of the hydrogen energy levels [closed]

Consider the problem where we want to calculate the energy levels of an electron in a hydrogen atom and we want to find the most precise analytic (i.e. a closed-form solution) solution that matches ...
  • 109
6 votes
0 answers
154 views

Question about Sakurai's $SO(4)$ symmetry section

In Sakurai's Quantum mechanics book, he says the hydrogen atom has $SO(4)$ symmetry by explicitly exhibiting operators $I_i,K_i$ that satisfy the commutation relation of the Lie algebra $so(4)$. ...
0 votes
1 answer
35 views

Do all of the energy levels listed in Hydrogen Spectral Series assumed to be s ('sharp') sublevels?

When reading about the hydrogen spectral series (Lyman, Balmer, etc.) I noticed that nowhere are suborbital or sublevels (azimuthal) mentioned; only principal quantum numbers n .... Are there any p or ...
  • 3,735
2 votes
1 answer
90 views

Can the amount of heavier elements in the Sun's core be approximated?

Can the amount of heavy and other types of elements as impurities inside the Sun's core be approximated? If these elements are present, do they disturb the process of hydrogen fusion, since they ...
1 vote
1 answer
68 views

Is the atomic shell model valid considering electron-electron interaction?

In atomic physics the shell model is motivated by starting looking at the H-atom. Solving Schrödinger's equation leads to atom orbitals labled by quantum numbers n,l,m. Taking Pauli's principle into ...
  • 70
7 votes
5 answers
2k views

Proton Electron Merger

Can somebody explain what would happen if an electron & a proton, very close to each other are left to "fall" to each other in a straight line?
  • 165
0 votes
2 answers
651 views

How to compute the Clebsch Gordan-coefficients for spin-angular momentum coupling of Hydrogen?

Consider a hydrogen atom with Hamiltonian $H$, angular momentum $L$ and spin operator $S$ and total angular momentum $J:= L+S$. Since $H,L^2, J^2$ and $J_z$ all commute with each other, we can find a ...
  • 229
0 votes
1 answer
78 views

Doubt in energy of electron in first shell of hydrogen atom [closed]

Let us calculate the energy of the electron in the first shell of the hydrogen atom. Since hydrogen is a single electron species we can use Bohr's postulates. The kinetic energy (KE) of an electron in ...
0 votes
1 answer
293 views

Find the expectation value of angular momentum $L_z$ of a wave function in energy eigenstates

$\psi_{nlm}(r,\theta,\varphi,t)$ as expansion in energy eigenstates: $$\psi(r,\theta,\varphi,t) =\sum_{n=1}^{\infty}\sum_{l=0}^{n-1}\sum_{m=-1}^{l}c_{nlm}ψ_{nlm} (r,θ,ϕ) \exp \left(-\frac{iE_n t}{\...
1 vote
0 answers
27 views

Formula for wavelength emitted taking into account the quantum orbital number $l$

Rydberg's formula can be used to find the wavelength emitted due to an electron moving from one energy level $n_i$ to another one $n_f$. But when the Schrödinger's model of the atom is introduced we ...
  • 35

1
2
3 4 5
14