Feasibility of Bohr orbit quantization for multi-electron

[nameab]

We know that the satellites are rotating around the earth, but when there are multiple satellites, we almost do not considerthe interaction between the satellite. When the atoms within the two electrons,Can they both rotate around the nucleus?

 

We know The rotation of electron around the nucleus is planar motion. the conditions of plane motion is the force direction
and the movement direction in the same plane. Within the atom, electrons and protons, the force of the same value, and thus
between the electrons can not be ignored, because the protons and another electronic accumulative force of this electronic is
not in the plane of rotation of the electrons around the nucleus.So when the atoms within multiple electrons can not
simultaneously rotate around the nucleus.

Therefore, due to the repulsion between the electrons, the electronic may be rotated next to the atomic nucleus(Energy
minimization) .When the nucleus on the electron attractive F, but his only contribution to the rotation orbits f.There are
some special radius of his rotation angular momentum satisfy the Bohr quantization condition . Means that when the atoms
within multiple electronic, electronics not in rotation around the nucleus but in the next to the atomic nucleus rotation,
and rotation of the angular momentum obey Bohr quantization condition

 

 

[imatfaal]

a. your photos do not show up for me

b. we do look at the effect of one satellite upon another - it is just pretty difficult so if we can simplify we do so. The moons of the gas giants and the rings are a particularly fruitful area where this is necessary.

c bohr atom is a bit out of date - we really use quantum mechanics to describe these ideas in any detail. although the Bohr model is used to introduce the ideas; it is not the state of the art.

[nameab]

photos show up for you

[imatfaal]

nope

[nameab]

photos address http://lvripple.blog.163.com/blog/static/2150610222013921112252959/

[imatfaal]

Thanks for photo address - but they don't add a great deal and take up a lot of space. I think I have made my points in my first post

[Enthalpy]

Until satellites collide, they have very little influence on an other's trajectory, because they're so light as compared with the planet. It's completely different for electrons, whose repulsive force is similar to the attraction by the nucleus.

 

You must forget any "plane orbit", and even trajectories, for electrons on stable orbitals around a nucleus. This image is not only outdated, it is also false and misleading. Electrons occupy some volume near a nucleus.

http://winter.group.shef.ac.uk/orbitron/

 

The orbital gives a probability to find an electron around each possible position around a nucleus, but it does not tell "the electron is here at that time, there later". The historical improvement by quantum mechanics was this. It explains why electrons occupy a permanent volume instead of falling on the nucleus, and give numerically accurate values for the energy differences between the orbitals.

 

With several electrons, you have one single wavefunction that gives the probability to find electron 1 around this position AND electron 2 around that position AND electron 3 ...etc. One wavefunction for all electrons gives the possibility, for instance, that every electron of a spherical orbital can be at any angle around the nucleus with equal probability density, BUT that two electrons are improbably near to an other, because they repel an other.

 

From that single wavefunction for several electrons, one can deduce a probability density to find one electron - or rather any of the electrons - around a position near the nucleus, but this probability density does not include the information about electron correlation - that their repulsion keeps them apart.

 

As far as I know, no algebraic solution exists for two electrons around a nucleus (a helium atom, say). Numerical solutions exist for a few electrons. As the numerical computation complexity must increase very quickly with the number of electrons, I expect algorithms to make simplifying assumptions, for instance that orbitals deep near the nucleus are little influenced by outer shells, or maybe that multi-electron orbitals resemble a weighted sum of few single-electron orbitals, multiplied by a correlation function that represents the repulsion between the electrons... Some trick is mandatory, because just 10³ finite volume elements per electron and only 6 electrons for the 2p orbitals would require to solve over 10¹⁸ hypervolume elements, which is just impossible.

[nameab]

As the attractiveness of the nucleus, h can not be too far away.Since the repulsion between electrons, h is not too close.Therefore, there is a specific value H, the minimum energy of the electron

[Enthalpy]

Even a single electron cannot be too close to the nucleus as a mean value. This is because a more compact electron, as it is a wave, has more kinetic energy. Past the optimum size, which defines the orbital, the kinetic energy increases more than the electric attraction brings.

[nameab]

The same attraction and centrifugal force, their energy is the same

[hypervalent_iodine]

!

Moderator Note

nameab, no one seems to be able to view your images. Please use another service to share them, or upload them directly to your posts.

[nameab]

ok?

[swansont]

Electrons do not orbit like satellites. Any ideas based on this are likely to be fatally flawed.

[Enthalpy]

Electrons do not orbit like satellites. Any ideas based on this are likely to be fatally flawed.

I wish to take advantage of the present context to express my full and complete agreement with Swansont, as usual.