Is the Proton Always Confined at the Core of an Atom?

[TrickyDicky]

I have next to zero knowledge about nuclear physics but after giving some thought to the dynamics of the electron cloud in the atom and its kinetic energy I realized that the motion of the nucleons in the atom is not so frequently discussed and I was wondering ,for instance,
in the case of the simpler hydrogen atom with a single proton, in idealized pictures the proton is always quiet at the core of the atom, but the nucleus is in motion right?
does the proton reman confined in the center of the atom or is it free to move arond the whole atom volume?
how is the kinetic energy of the proton compared to the electron?

I only consider the hydrogen atom to keep it simple, I'm aware there are nuclear shell models for the nuleus but they are above my understanding of the matter.
Thanks for any comment on this

 

[bcrowell]

If your question is about hydrogen-1, then the answer is that by conservation of momentum, the center of mass of the atom doesn't accelerate, and the momenta of the electron and proton are equal in magnitude and opposite in direction, so the ratio of the kinetic energies is equal to the inverse ratio of the masses (because K=p^2/2m). The effect on the states of the electron is to replace the mass of the electron with the "reduced mass" mM/(M+m), where m is the mass of the proton and M is the mass of the electron.

 

[TrickyDicky]

If your question is about hydrogen-1, then the answer is that by conservation of momentum, the center of mass of the atom doesn't accelerate, and the momenta of the electron and proton are equal in magnitude and opposite in direction, so the ratio of the kinetic energies is equal to the inverse ratio of the masses (because K=p^2/2m). The effect on the states of the electron is to replace the mass of the electron with the "reduced mass" mM/(M+m), where m is the mass of the proton and M is the mass of the electron.

That makes sense for this two body system, I guess if the electron's moment was bigger than the proton's it would fall out of the atom.
So due to the huge difference in mass the electron velocity in the atom is much faster than the proton and it's only natural that the electronic characteristic frequencies of motion are much higher than the proton's.
Might this mass and velocity asymmetry between nucleus and electrons be part of the reason why electrons are so easily shared between atoms (with all the chemichal consequences) and also their ability to flow in metals (electric currents)? Or are these totally unrelated properties?

 

[bcrowell]

That makes sense for this two body system, I guess if the electron's moment was bigger than the proton's it would fall out of the atom.

I don't think it really has anything to do with the fact that the system is bound. All the same things would be true if it was unbound.

So due to the huge difference in mass the electron velocity in the atom is much faster than the proton and it's only natural that the electronic characteristic frequencies of motion are much higher than the proton's.

Their frequencies are equal, since their motions are identical functions of time except for spatial scaling and mirror-inversion about the center of mass.

 

[TrickyDicky]

Their frequencies are equal, since their motions are identical functions of time except for spatial scaling and mirror-inversion about the center of mass.

Are you sure? Maybe I misunderstood this:
http://quantum.bu.edu/notes/QuantumMechanics/MolecularStructure.pdf
Read the first paragraph.

 

[TrickyDicky]

So are the frequencies of electrons and nucleus equal or different? anyone?

 

[TrickyDicky]

Their frequencies are equal, since their motions are identical functions of time except for spatial scaling and mirror-inversion about the center of mass.

From the link
"While electrons are very much lighter than nuclei, both experience comparable (Coulombic) potential energies.
The result is that electrons move much faster than nuclei. This in turn means that the characteristic frequencies of electronic motion are much higher than those of nuclear (vibrational and rotational) motion, and so electronic spectroscopic transitions occur in more energetic regions of the spectrum (visible, UV, and X-ray) than do vibrational (IR) and rotational (microwave) spectroscopic transitions."

bcrowell, do you have objections to this? This is basically what I said in post #3, maybe you have a different view on this.

 

[TrickyDicky]

I'm not sure this is the right thread to address questions about nuclear physic, if it is perhaps someone can clarify the above mentioned doubt. Otherwise suggest which would be the right thread. Thanks

 

[Astronuc]

I'm not sure this is the right thread to address questions about nuclear physic, if it is perhaps someone can clarify the above mentioned doubt. Otherwise suggest which would be the right thread. Thanks

The answer involves both atomic and nuclear physics.

The answer given is correct in the sense of the motion of the electon with respect to the nucleus (proton in the case of hydrogen atom). As an atom, the proton and electron maintain their separation, and the proton does not 'freely move around the volume' of the atom.

With respect to the comment - "The result is that electrons move much faster than nuclei. This in turn means that the characteristic frequencies of electronic motion are much higher than those of nuclear (vibrational and rotational) motion, and so electronic spectroscopic transition occur in more energetic regions of the spectrum (visible, UV, and X-ray) than do vibrational (IR) and rotational (microwave) spectroscopic transitions." - the electron transition refers to the binding energy of the electron with the nucleus. Photons (EM radiation) are absorbed and emitted in those wavelengths, which are characteristic of the potential energy of the electron with respect to nucleus.

http://hyperphysics.phy-astr.gsu.edu/hbase/hyde.html
Particularly - http://hyperphysics.phy-astr.gsu.edu/hbase/hyde.html#c4

Excitation of electrons in an atom can come from photons, or collisions with other atoms, or ions, or electrons.

The kinetic energy of the atom (in the case of translational motion, or vibration in an molecule) is mostly invested in the nucleus, but it is still the electrons that form the bond between atoms.

There is also nuclear (magnetic) resonance in which the nucleus can 'flip' in a changing magnetic field, and the frequencies are different for the heavier nuclei and the electron.

http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/nmr.html

 

[Bob S]

The charge center of the atomic electron cloud is normally the same as the center of the nucleus. Classically, if the electron cloud is displaced from the nucleus, the electrostatic restoring force causes the electron cloud to oscillate about the nuclear charge center, similar to two masses connected by a spring. Incident electromagnetic radiation can cause the atom to oscillate at the frequency of the incident radiation (electric dipole oscillation), and re-radiate at the frequency of the incident radiation. Rayleigh scattering of sunlight in our (clean) atmosphere is a good example of classical scattering of electromagnetic radiation by gas atoms (molecules). See

http://en.wikipedia.org/wiki/Rayleigh_scattering

This explains why the visible Rayleigh scattering spectrum of sunlight is smooth without any spectral lines, why it has a 1/λ⁴ intensity distribution, and why it is nearly completely polarized at 90 degrees.

Bob S

 

[TrickyDicky]

Thanks Astronuc and Bob S for your answers, I have now (I think) realized what is probably trivial and simple for a physicist but not so much when approaching the matter for the first time as I remarked in the OP.
The confusion I had was indeed (as astronuc suggests) that I was mixing the atomic(subatomic) realm and the molecular one, obviously the high frequencies we get from electronic transitions are related so much to the electron motion wrt the proton as to the proton wrt the electron, its just one oscillation and therefore one frequency.
The lower frequencies from vibrational and rotational nucleus-nucleus oscillations are at the molecular level.

 

[Bob S]

There are some electron-nuclear magnetic couplings that occur at very low frequencies. The hydrogen hyperfine structure line at 1420 MHz (21 cm) is due to the electron -nuclear spin magnetic moment coupling.

Bob S

 

[TrickyDicky]

There are some electron-nuclear magnetic couplings that occur at very low frequencies. The hydrogen hyperfine structure line at 1420 MHz (21 cm) is due to the electron -nuclear spin magnetic moment coupling.

Bob S

Sure, I was limiting my comment to the basic broad scheme.
But since you mention it, how would this magnetic moment coupling between the nucleus and electron be produced?

 

[Bob S]

Sure, I was limiting my comment to the basic broad scheme.
But since you mention it, how would this magnetic moment coupling between the nucleus and electron be produced?

The 21-cm line is observed in the interstellar and intergalactic neutral hydrogen gas, sometimes with a very large red shift. It has been used, for example, for mapping the spiral arms of the Milky Way galaxy. See

http://en.wikipedia.org/wiki/Hydrogen_line

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/h21.html

Bob S