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 ...

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408 views

tritium beta decay - probability of being in 1s state

Hydrogen-like wavefunctions have the form: $$R_{10} = \left(\frac{Z}{a_0}\right)^{\frac{3}{2}} 2\space e^{-\frac{Zr}{a_0}}$$ $$Y_{00} = \frac{1}{\sqrt {4\pi}} $$ where $a_0 = \frac{4\pi \epsilon_0 ...
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3answers
674 views

Why are hydrogen energy levels degenerate in $\ell$ and $m$?

Is there a good physical picture of why the energy levels in a hydrogen atom are independent of the angular momentum quantum number $\ell$ and $m$?
3
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1answer
70 views

State with non-zero angular momentum - cannot be described by spherical harmonic?

For a state with non-zero angular momentum, why is it that it cannot be described by the spherically symmetric spherical harmonic?
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1answer
116 views

Is it possible to find the hydrogen atom's radial wavefunctions?

Is there a way to actually find the equation of $R(r)$ without looking at a table with these equations already given? I'm given $n$, $\ell$, and $m$.
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1answer
25 views

Lowest Frequency De-excitation problem

Before the formation of the molecule it is possible for the muonic hydrogen atom to be formed in an excited state and for radiation to be observed from a single transition to the ground state. ...
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1answer
49 views

modern physics :emission spectrum [closed]

If in a hydrogen atom all possible transactions take place. The ratio of maximum frequency to minimum frequency is 135/7.what is the principal quantum number of excited state. The max frequency case ...
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2answers
118 views

Why does hydrogen give up its electron to a platinum catalyst?

All descriptions of a Hydrogen fueled fuel cell (such as this one) Start with $H_2$ giving up its electrons to a platinum coated anode. Then the $H^+$ ions (protons really) travel through the ...
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1answer
104 views

Obtain the eigenfunction of Jz for the wave function of an electron in a hydrogen atom? [closed]

The wave function of an electron in a hydrogen atom is given by Is this wave function an eigenfunction of Jz , the z-component of the electron’s total angular momentum? If yes, find the ...
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1answer
88 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 ...
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2answers
252 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 ...
2
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2answers
1k 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 ...
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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 ...
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1answer
152 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 ...
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2answers
48 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?
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2answers
95 views

Can a laser be designed to ionize muonic atoms 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. ...
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1answer
52 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?
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1answer
89 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
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2answers
109 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 ...
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1answer
38 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 ...
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1answer
22 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
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0answers
116 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
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0answers
119 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
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1answer
268 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 ...
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3answers
1k 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 ...
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2answers
520 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 ...
3
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2answers
267 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 ...
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0answers
108 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
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1answer
496 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 ...
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3answers
360 views

Is there 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
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2answers
326 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
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1answer
112 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
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1answer
112 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?
5
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3answers
773 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?
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2answers
682 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?
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0answers
220 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 ...
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1answer
50 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?
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4answers
3k 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
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1answer
615 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 ${}^1H$?
5
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2answers
2k 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?
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1answer
256 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
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1answer
171 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
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1answer
1k 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
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1answer
1k 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. ...
1
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1answer
105 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? ...
5
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1answer
723 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
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1answer
87 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
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1answer
67 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 ...
7
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2answers
371 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
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1answer
262 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 ...
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1answer
453 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 = ...