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 ...

learn more… | top users | synonyms

-3
votes
1answer
36 views

Angular momentum Bohr's model

I have been trying to derive speed, radius etc. in hydrogen atom using Bohr's postulates and not neglecting the coulombic attraction on proton. I know that they will be revolving around their centre ...
3
votes
1answer
66 views

Spin-orbit coupling from the rest frame of the proton?

When we calculate the spin-orbit interaction in a Hydrogen atom we just work in the electron's frame of reference: the proton is moving and produces a magnetic field which the electron's spin ...
1
vote
2answers
84 views

Calculating the most probable radius for an electron of a hydrogen atom in the ground state

This link describes a method for determining the most probable radius of an electron for a Hydrogen atom in the ground state. It states that : The radial probability density for the hydrogen ...
10
votes
5answers
1k views

How does the hydrogen atom know which frequencies it can emit photons at?

At university, I was shown the Schrodinger Equation, and how to solve it, including in the $1/r$ potential, modelling the hydrogen atom. And it was then asserted that the differences between the ...
1
vote
1answer
30 views

Calculate the average temperature needed for hydrogen fusion reaction [duplicate]

my question is simple. How can we calculate the temperature needed in order to do the nuclear fusion things , and also the temperature after the reaction successful. If you can describe it, it ...
1
vote
2answers
26 views

How to measure the wavelengths of ultraviolet lines in the hydrogen spectrum?

how to measure the wavelengths of ultraviolet radiation isn't it invisible? it's possible to measure visible radiation but how to measure invisible radiation?
0
votes
1answer
32 views

Can a laser be designed to ionize muons so as to prevent a-sticking?

Muon catalyzed fusion is currently little more than a lab curiosity today in part because of how many hydrogen nuclei can be fused before the muon is carried away by an alpha particle. ...
0
votes
1answer
42 views

Can scientists tell the energy levels of the atom?

In the hydrogen spectral series how did the scientists know the number of the energy level which the electron is moving from or to?
4
votes
1answer
38 views

How did Lyman discover his series?

How did Lyman discover his series in hydrogen atom? How did he know that the final energy level is the first level and not the second or the third or etc.? Or how did the other scientists know which ...
0
votes
2answers
31 views

requirements for hydrogen fusion

What are the requirements for hydrogen atoms to go through fusion? Is it a ratio of heat to pressure or are there specific heat and pressure values that must be met (per atom or per mole?) Are there ...
1
vote
1answer
21 views

Excited Energy levels of Hydrogen vs Solids

My question has to do with Excited Energy Levels. I keep reading and learning that all objects/most solids emit infrared radiation. But to emit radiation, an object's particles must first enter a ...
0
votes
1answer
12 views

Hydrogen Adsorption distance

In chemical adsorption of H2 molecule, the distance is limited. In the physical adsorption, the distance of adsorption is limited or can be any value? Is there any correspondence to adsorption ...
2
votes
0answers
41 views

Limits of integration for the radial wave function of the Hydrogen atom in the WKB approximation

I am working a problem where we have to find the energy eigenvalues for the radial wave function of the hydrogen atom for $\ell=0$ using the WKB approximation. I am sure that I set up the integral ...
0
votes
0answers
69 views

Difference between expectation values of $L^2$, $L_z$ and measuring $L^2$, $L_z$

I was given with this hydrogen radial wavefunction $$ R_{21} =\left(\sqrt{\frac{1}{3}}Y^0_1 + \sqrt{\frac{2}{3}}Y^1_1\right) $$ and was asked to find a) What are the expectation values of the ...
0
votes
1answer
70 views

Expectation value of energy from the position state of hydrogen atom [closed]

I was given with the position state of hydrogen atom: $$ R_{21} =\left(\sqrt{\frac{1}{3}}Y^0_1 + \sqrt{\frac{2}{3}}Y^1_1\right) $$ I am getting confused about getting the expectation value of ...
1
vote
3answers
80 views

What makes water heavier than air?

I apologize in advance if this is too basic for this site. Considering that hydrogen is lighter then oxygen, and water is 2/3 hydrogen, and only 1/3 oxygen, and our "air" is comprised mainly of ...
3
votes
2answers
213 views

What is the expected distance of the electron from the nucleus in the hydrogen atom?

Specifically, I would like to know the general formula, in terms of $n$ and $l$, assuming the electron is in an orbital (i.e. simultaneous eigenstate of $H$, $L^2$, and $L_z$). I understand that it ...
1
vote
1answer
58 views

Hydrogen atom: potential well and orbit radii

I happened to open up an old solid-state electronics book by Sah, and in it he says: "it is evident that the electron orbit radius is half the well radius at the energy level En" The orbit radius is ...
0
votes
0answers
60 views

Perturbation of a Hydrogen Atom in a Quadrupole Field

Question: A hydrogen atom is located in a quadrupole field, which gives it a perturbation $$H_1=A(x^2-y^2)$$ where $A$ is some constant. Calculate the ...
2
votes
1answer
59 views

Is a free proton a positive Hydrogen-1 ion?

The Hydrogen-1 isotope is a form of hydrogen with 1 electron, 1 proton, and 0 neutrons. If that isotope were to lose its electron (thus being a Hydrogen-1 ion with a positive charge) what would be ...
0
votes
3answers
167 views

Is any time-dependent hydrogen atom Schrödinger equation solvable analytically?

It's well-known that hydrogen atom described by time-independent Schrödinger equation (neglecting any relativistic effects) is completely solvable analytically. But are any initial value problems for ...
2
votes
2answers
101 views

Spin orbit coupling and fine structure of the Hydrogen atom

At university we have just derived the expression for the energy split due to spin-orbit coupling in the Hydrogen atom, i.e. what is known as the FINE structure of Hydrogen. To do this, we ...
0
votes
1answer
69 views

Angular momentum of hydrogen from $n,l,m$ values

Given a wavefunction for hydrogen $\psi(n,l,m)$ it is possible to calculate its associated energy from $E=-13.6/n^2$. Does a similar equation exist for $L^2$ and $L_z$? That is, if we are given the ...
1
vote
1answer
66 views

energy difference uniqueness in hydrogen atom

Is the energy difference between two energy levels unique for that particular pair of levels for a hydrogen atom ? If so how can one prove it?
4
votes
3answers
612 views

Why is a proton assumed to be always at the center while applying the Schrödinger equation?

Why is a proton assumed to be always at the center while applying the Schrödinger equation? Isn't it a quantum particle?
6
votes
2answers
276 views

How can one see that the Hydrogen atom has $SO(4)$ symmetry?

For solving hydrogen atom energy level by $SO(4)$ symmetry, where does the symmetry come from? How can one see it directly from the Hamiltonian?
1
vote
0answers
91 views

Step in derivation of solution to Dirac equation for hydrogen

My text, when solving hydrogen in the Dirac equation, makes the claim $\varphi_{j m_j}^{(+)} = \frac{\mathbf{\sigma} \cdot \mathbf{x}}{r} \varphi_{j m_j}^{(-)}$ where $\varphi_{j m_j}^{(\pm)}$ are ...
0
votes
1answer
42 views

Visible Lines for Hydrogen

Say H atoms are excited to 4th level, n=4 that is, how many lines do we see? How to decide the number of the lines?
-1
votes
2answers
484 views

Collision between electron and proton?

What would happen if an electron collided with a proton such that the two do not collapse? Would the two become a unit, or would some force prevent them from bonding thus forcing the electron to orbit ...
4
votes
1answer
112 views

Fusion: Why deuterium and tritium?

I would like to know why scientists try to use deuterium and tritium for fusion and not just the ordinary isotope of Hydrogen ${}^1H$?
4
votes
2answers
361 views

What made Bohr quantise angular momentum and not some other quantity?

Bohr's second postulate in Bohr model of hydrogen atom deals with quantisation of angular momentum.But, I was wondering why he quantised angular momentum and any other quantity?
2
votes
1answer
110 views

Strömgren Sphere of Sun

I have a homework problem: The Sun emits $ \sim5 x 10^{23}$ photons per second with $hν > 13.6$ $eV$. If the density of hydrogen atoms in interplanetary space is $n =$ $109 m^{-3}$, what ...
2
votes
1answer
107 views

Possible Outcomes from Measuring a Hydrogen Atom

A hydrogen atom is characterized by the wavefunction $$\mid \psi \rangle =\sqrt{\frac{2}{7}}\mid 4\,2\,1\rangle +\sqrt{\frac{1}{7}}\mid 2 \,1\,\bar{1}\rangle+\sqrt{\frac{4}{7}}\mid 3\,2\,0\rangle$$ ...
5
votes
1answer
256 views

Orthonormality of Radial Wave Function

Is the radial component $R_{n\ell}$ of the hydrogen wavefunction orthonormal? Doing out one of the integrals, I find that $$\int_0^{\infty} R_{10}R_{21}~r^2dr ~\neq~0$$ However, the link below says ...
1
vote
1answer
329 views

Writing a Wavefunction as a Linear Combination of Eigenstates

We have the following wavefunction for the hydrogen atom: $$\psi(r,\theta,\phi)=\frac{1}{\sqrt{4\pi}}\frac{1}{(2a)^{3/2}}\frac{r}{a}e^{-r/2a}\sin(\theta)\sin(\phi)$$ where $a$ is the Bohr radius. ...
0
votes
0answers
202 views

Orthonormality of Radial Wave Function in the Hydrogen Atom

Question: Show that the radial wave function for the hydrogen atom are orthogonal with no exceptions. Attempt: We know that ...
0
votes
0answers
40 views

Lifetime of 3d state shorter than 3s state in hydrogen atom

Can you say that the lifetime of the 3d state in the hydrogen atom is shorter than the one of the 3s state because the centrifugal energy associated with 3d is higher than the one associated with 3s? ...
4
votes
1answer
498 views

Reduced mass in quantum physics (Hydrogen Atom)

I've gone through an intermediate classical mechanics course, and in solving the two-body problem, we reduce it to a one-body between a larger stationary mass, and a smaller reduced mass. Most ...
2
votes
1answer
77 views

Why does bringing N 1-orbital atoms together yield N levels?

A common example of this is that when bringing N hydrogen atoms together into a ring. Far apart, assume each electron exists in the 1s state. As we bring them together, instead of each electron ...
0
votes
1answer
49 views

What Elements Is Mono-atomic Hydrogen Capable Of Penetrating?

I recently learned that monoatomic hydrogen passes directly through solid aluminum and even combines inside aluminum to form $H_2$ which cannot pass through solid aluminum and therefore causes ...
5
votes
1answer
114 views

How does one calculate where the “surface” of a gas-giant would be?

Okay, so Jupiter, Saturn, et. al are gas giants. I understand that they have large gassy atmospheres, which, due to the pressure would eventually become more and more dense as one approaches the ...
2
votes
1answer
107 views

Volume charge density of H-atom

I have a problem where I am supposed to calculate the volume charge density of a neutral hydrogen atom. The potential is given to be $$ \Phi = k \frac{e^{-ar}}{r} \left(1 + \frac{ar}{2}\right) $$ Now ...
1
vote
1answer
286 views

Hydrogen ground state energy calculation?

We want to find the energy of a hydrogen atom ($Z=1$) in the ground state $$ \psi_{100} = \frac{1}{\sqrt{\pi}}e^{-r}\ \ \ \ \ \ (\mbox{atomic units}) $$ with Hamiltonian $$ H = ...
0
votes
0answers
31 views

How to calculate the binding energy of electron of hydrogen atom by using uncertainty principle? [duplicate]

How to calculate the binding energy of an electron of hydrogen atom using uncertainty principle?
1
vote
2answers
130 views

Transition integral from 1-D cartesian into 3-D polar coordinate system

Lets say we have an electron which can be in two states. Its wavefunction for two states is then $\Psi=A\Psi_n + B\Psi_m$, where $\Psi$ is time dependent wave function. I know that the transition ...
1
vote
2answers
1k views

The probability of finding the electron in the H-atom

In the book Arthur Beiser - Concepts of modern physics [page 213] author separates the variables in the polar Schrödinger equation assuming: $$\psi_{nlm}=R(r)\Phi(\phi)\Theta(\theta)$$ then there a ...
2
votes
1answer
184 views

Orbital of Hydrogen molecule

does anybody here know an analytical approximation of the bonding hydrogen orbital MOLECULE? I am looking for a good approximation to this orbital, that might be in some textbooks to get an ...
4
votes
3answers
101 views

Hydrogen cloud at the universe's beginning?

What prevented all of the hydrogen at the universe's start from coalescing into one gigantic star?
0
votes
1answer
51 views

Photon propagation direction prediction possible after interacting with neutral hydrogen?

My current line of research deals a lot with hydrogen's Lyman-alpha emission and subsequent interactions of the Lyman-alpha photons with the surrounding hydrogen gas. My question is whether ...
0
votes
1answer
175 views

How to determine the region that would contain a quantum particle

(a) A hydrogen atom is in its ground state. If space is divided into identical infinitesimal cubes, in which cube is the electron most likely to be found? If instead space is divided into 31 ...