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Lorentz force (atomic)


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Is it possible the Lorentz force regulates a the ground state in hydrogen.. If no, why not?

 

Using the Bohr magneton it seems some atoms actually have pretty strong magnetic fields, which could have enough force to be a "ground state" energy source/regulator.

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I don't think so. Would it explain stable orbits? Energy levels?

 

I think it might. Using the Bohr radius 5.29e-11 m , and 2.18e6 (m/s) as the ground state electron velocity, with the Lorentz force equation the ground state Lorentz force in hydrogen is right around 1.65e-7 N and (n=2) is half of that (unless I made a mistake)

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It might have something to do with the fractional hall effect and a filling factor of 1/2 (ratio of electrons to magnetic flux quanta). .. I'm still thinking about this. What are some atoms with no nuclear dipole moment?

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It might have something to do with the fractional hall effect and a filling factor of 1/2 (ratio of electrons to magnetic flux quanta). .. I'm still thinking about this. What are some atoms with no nuclear dipole moment?

 

K38m (m means metastable, i.e. an isomer)

 

It has no hyperfine structure, which is what happens when there is no nuclear dipole moment (and means you can laser trap it with a single frequency of light) but there is most assuredly atomic structure.

 

I think there's an isotope of Ca as well, and probably others.

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In a ground hydrogen atom, would the Lorentz force equation look something like this?

 

F = qE + qv x B

 

qE = (1/(4*pi*electric_constant)) * (1.60217e-19 C)^2 / (5.29177e-11 m)^2

 

qE = 8.2387e-8 N

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Thanks for the help swansont. Sorry these questions are probably boring to you.

 

qE is the electrostatic force on a charge, then (qv * B), is the magnetic force on a moving charge.

 

In ground state hydrogen would it looks something like this?

 

ub = bohr magneton = (e*hbar)/(2*electron_mass) = 9.27400e-24 (A m^2)

v = 2.18769e6 (m/s)

 

B = (((1/2) * electron_mass * v^2) / ub = 235051 T

 

(qv * B) = (1.602e-19 C) * (2.187e6 m/s) * (235051 T) = 8.2387e-8 N

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Thanks for the help swansont. Sorry these questions are probably boring to you.

 

qE is the electrostatic force on a charge, then (qv * B), is the magnetic force on a moving charge.

 

In ground state hydrogen would it looks something like this?

 

ub = bohr magneton = (e*hbar)/(2*electron_mass) = 9.27400e-24 (A m^2)

v = 2.18769e6 (m/s)

 

B = (((1/2) * electron_mass * v^2) / ub = 235051 T

 

(qv * B) = (1.602e-19 C) * (2.187e6 m/s) * (235051 T) = 8.2387e-8 N

 

 

1. Why are you using the electron magnetic moment? You are proposing the interaction of a moving electron in the proton's magnetic field.

 

2. Where did you get your equation for B?

 

3. What will the field from the proton be, at the position of the electron?

 

4. What will be the direction of such a force?

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You didn't use the proton's magnetic moment, and you didn't find the magnetic field properly. Where did you find an equation that said the magnetic field was the magnetic moment multiplied by the kinetic energy?

 

(This is all ignoring your use of the Bohr model, of course)

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That equation was based on the thought (flawed most likely) that all particles have a very strong intrinsic internal magnetic fields (undetectable outside of its radius, normally) and a much weaker detectable magnetic field or magnetic dipole moment (which may be a part of the normally 'invisible' internal field). I know this is all probably speculative nonsense, but don't quarks sometimes have very strong magnetic fields in QCD (or chromomagnetics)?


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If the magnitude of a magnetic field (within an atom or shell) can be measured by the radius of its shell curvature.

 

Then,

p=qBr

 

The electron vibrational or orbital momentum for ground state hydrogen is:

 

p = (electron_mass * 2.187e6 m/s) = 1.9928e-24

r = 5.29e-11 m

q = elementary charge

 

B = (p / (e*r)) = 235051 T

 

This is basically where I got the equation above.

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The magnetic moment of the proton is well-known.

 

If you want to try and take the tactic of inferring the magnetic field from the "shell curvature" (by which I assume you mean the Bohr orbit) then you need to reconcile this with the Hyperfine splitting of Hydrogen — the energy difference between the two orientations of the electron magnetic moment in that field — being h * 1420 MHz. (or ~10^-24 J)

 

Since the Bohr magneton is ~ 10^-23 J/T, that implies about 0.1 T

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The magnetic moment of the proton is well-known.

 

Yes, but what about the possibility of a strong internal magnetic fields within the proton between gluons and quarks? Doesn't QCD predict something like this?

 

If you want to try and take the tactic of inferring the magnetic field from the "shell curvature" (by which I assume you mean the Bohr orbit) then you need to reconcile this with the Hyperfine splitting of Hydrogen — the energy difference between the two orientations of the electron magnetic moment in that field — being h * 1420 MHz. (or ~10^-24 J)

 

Since the Bohr magneton is ~ 10^-23 J/T, that implies about 0.1 T

 

 

Maybe all properties including, electron energy, mass, magnetic field, and radius scale down with the hyperfine splitting?

 

What does quantum theory predict happens to the orbital of a hyperfine split H atom vs a normal ground state H atom?

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Yes, but what about the possibility of a strong internal magnetic fields within the proton between gluons and quarks? Doesn't QCD predict something like this?

 

Not sure. QCD isn't my field.

 

Maybe all properties including, electron energy, mass, magnetic field, and radius scale down with the hyperfine splitting?

 

I think at this point you're grasping at straws. Either the atom follows the physics that has been discovered, or you disregard basically all of physics. Proposing that we essentially understand nothing about atomic physics in order to accommodate your hypothesis is a nonstarter.

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Not sure. QCD isn't my field.

 

I think at this point you're grasping at straws. Either the atom follows the physics that has been discovered, or you disregard basically all of physics. Proposing that we essentially understand nothing about atomic physics in order to accommodate your hypothesis is a nonstarter.

 

I agree it is pointless to try to reinvent the physics of how things work. But I feel there is something missing when it comes to understanding what things really are (and where they come from). It seems strange that most physicists are perfectly content believing an atom is just a mathematical construct floating through space.

 

As for the hydrogen hyperfine structure, I don't have enough understanding of quantum spin (what it physically represents) to even touch it.

 

I've just been playing with classical concepts and properties of the Bohr hydrogen atom.

 

 

Here are a couple more concepts that have led to my questions. I

 

 

Hall Voltage in Hydrogen?

 

V(Hall_Voltage) = ((-I*B) / d) / (n * e)

 

I = current

B = magnetic field strength

d = depth of conductor

n = charge per volume

e = elementary charge

 

Calculate the current:

 

If the electron orbital frequency in hydrogen might be:

f = (2.187e6 m/s) / (2*pi*5.29e-11 m) = 6.5796e15 Hz

 

The (orbital?) current might be:

I = f * e = .001054181 A

 

For the conductor depth I used the Bohr radius: d = 5.29177e-11 m

(just to see what would happen)

 

The charge per volume is:

n = (1 electron) / ((4/3) * pi * bohr_radius^3) = 1.61104e30 (1/m^3)

 

Calculate the magnetic field strength within the electron orbital using this equation:

 

B = E / ub

(or p=qBr )

 

Where,

E = kinetic energy of ground state electron = 2.1798e-18 J

ub = Bohr Magneton = 9.27400e-24 (J / T)

 

B = (2.1798e-18 J) / (9.27400e-24 J / T) = 235051.76 T

 

Solve the equation:

 

V(Hall_Voltage) = ((-I*B) / d) / (n * e)

 

V(Hall_Voltage) = (((-1) * (.001054181 A) * (235051.76 T)) / (5.29177e-11 m)) / ((1.61104e30 1/m^3) * (1.60217e-19 C))

 

 

V(Hall_Voltage) = -18.1409185 Volts

 

This was pretty close to the Rydberg constant (13.605 eV)

 

-18.1409185 / 13.60569 = 1.3333333 or (4/3)

 

If the charge per volume (n) is changed to:

n = (1 electron) / ((pi * r^3) = 1.61104e30 (1/m^3)

 

 

The solution becomes: -13.60568 V

 

 

 

Here's another one:

 

Inductance, Capacitance, and LC resonance in Hydrogen?

 

In an electronic LC circuit, the resonant frequency can be found with.

 

w = sqrt(1/L*C)

 

w = angular frequency (radians/sec)

L = Inductance (henries)

C = Capacitance (farads)

 

If this concept is applied to hydrogen:

 

The ground state electron in hydrogen might have a frequency of:

f = (velocity) / (wavelength) = 6.57968395e15 hz

where,

velocity = (fine_structure_constant * speed_of_light) = 2.18769 m/s

wavelength = (2 * pi * bohr_radius) = 3.324918e-10 m

 

The self-capacitance of hydrogen's ground state orbital/shell might be:

4 * pi * eo * R

where,

eo = vacuum permittivity = 8.8541878e-12 (A^2 s^4 / kg * m^3)

R = radius= bohr radius = 5.291777e-11 m

 

The hydrogen ground-state inductance might be (I'm not sure about this equation. Inductance of a sphere?):

L = ((r^2 * m) / e^2)

 

r = radius = bohr radius = 5.291772085e-11 m

m = electron_mass = 9.10938188e-31 kg

e = elementary charge = 1.60217e-19 C

L = inductance in henries

 

 

Calculate radians/sec from hertz:

w = (2 * pi * f) = 4.1341373522e16 rad/sec

 

Calculate Hydrogen (theoretical) Inductance:

L = (r^2 * m) / e^2 = (5.291772085e-11^2 meters^2 * 9.10938e-31 kg) / (1.60217e-19^2 Coulombs^2)

L = 9.937347518e-14 Henries

 

 

Calculate the Capacitance of Hydrogen:

C = 4 * pi * 8.85418782e-12 (Permittivity : A^2 s^4 / kg m^3) * r (meters)

C = 5.887805e-21 Farads

 

 

Hydrogen LC Resonant Frequency?:

w (angular frequency) = sqrt(1/LC)

 

4.1341373522e16 (rad/s) = sqrt( 1/ 9.937347518e-14 (m^2 * kg / C^2) * 5.887805e-21 (A^2 s^4 / kg m^2)

 

4.134167e16 (rad/s) = (f * 2 * pi)

 

 

Is just basically playing with numbers/nonsense?

 

This might just be basic algebra, and the solutions just come from "putting a variable in ... and you get it back out" .. But could it be something more?

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The Bohr model is not 100 percent correct, that is a fact. But aren't some aspects of it correct? The orbitals, energy levels, etc? You can't say it is 100 percent incorrect, imo, or just WRONG.

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The Bohr model is not 100 percent correct, that is a fact. But aren't some aspects of it correct? The orbitals, energy levels, etc? You can't say it is 100 percent incorrect, imo, or just WRONG.

 

seeing as it only manages to come close to describing singlet hydrogen-1 and even then fails quite a bit, yes we can say its wrong. its completely useless with anything with more than 1 electron. much better to use the current QM model.

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The Bohr model is not 100 percent correct, that is a fact. But aren't some aspects of it correct? The orbitals, energy levels, etc? You can't say it is 100 percent incorrect, imo, or just WRONG.

 

It gets the energy correct. That's about it. So you can use it for energy calculations.

 

 

It has orbits, not orbitals, and that's wrong. It gets the angular momentum wrong. At that point, you have to abandon it.

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The Bohr model is not 100 percent correct, that is a fact. But aren't some aspects of it correct?

I know that the mental pictue helps in constructing the Hamiltonian. How's that? :D

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