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In classical mechanics, there is a famous effect called Sling-shot effect (the link will support a demonstration), by which the satellite orbiting the huge planet will steal some kinetic energy from the planet (combining the laws of conservation of energy and momentum ).

So my naive question is: Is there any corresponding effect can exist in the atom? I mean the electron plays the role of satellite and the nucleus plays the role of a planet, or electron can steal the speed of nucleus (I believe the conservation of energy and momentum will still work in an atom)?

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  • $\begingroup$ This might be worth a look. $\endgroup$
    – BLAZE
    Commented Jan 19, 2017 at 8:34

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There are a couple of points to consider. Firstly a spaceship using a slingshot maneuver can take kinetic energy from a planet, but not from the Sun. That is bacause in the centre of mass frame of the Solar System the Sun is (almost) stationary so it has no kinetic energy to steal.

In the atom analogy the nucleus is the Sun, so an electron could not take kinetic energy from it. The analogous process would be two electrons slingshotting each other and exchanging kinetic energy. Even though electrons repel each other (unlike gravity which is always attractive) this process could happen if the electrons behaved like orbiting bodies.

The problem is that the second point we need to consider is that electrons do not behave like orbiting bodies. The electrons do not whizz around the nucleus like little balls. They are delocalised over the whole atom and they do not have a position in the way that macroscopic objects have a position.

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  • $\begingroup$ The last paragraph has strange claims. First, what do you mean by the interaction being averaged away to zero? If there were no interaction, we'd have very high degeneracy like that which we'd have if electrons didn't repel. Next, the wavefunctions being orthonormal only tells us relations between different states, not any information about each individual state. And if you mean to speak of wavefunctions of each electron, it's completely wrong: electrons do interact, and this interaction makes the wavefunction not separable into product of $\psi(\vec r_{1})\psi(\vec r_{2})$. $\endgroup$
    – Ruslan
    Commented Jan 19, 2017 at 13:29
  • $\begingroup$ @Ruslan: that's an attempt to gloss over the self-consistent field calculation. I thought going into the details of how a Hartree-Fock SCF calculation is done would be a bit too much. The SCF approach does give use an overall wavefunction that factors into wavefunctions for each electron. Though it's true that we'd normally follow this with a CI calculation using the HFSCF orbitals as a basis, and that does mix up the orbitals to produce a wavefunction that can't be factored. $\endgroup$ Commented Jan 19, 2017 at 13:35
  • $\begingroup$ If the nucleus has no kinetic energy, can you explain to me what this article is claiming: "In 1986, a group working at the Daresbury Laboratory in Great Britain succeeded in measuring the largest angular momentum reported until then for a nucleus. They found dysprosium‐152 to be rotating with a spin of 60 ℏ—or about 2×1020 revolutions per second in a classical estimate." "Superdeformed Nuclei Rotate So Fast They Make Heads Spin," physicstoday.scitation.org/doi/abs/10.1063/1.2811312?journalCode=pto $\endgroup$
    – HyperNym
    Commented Dec 7, 2022 at 4:49
  • $\begingroup$ @HyperNym In that experiment a nucleus was bombarded with heavy ions to put it into an excited state, and that made it rotate on its axis. The figure quoted is the rotation rate of the nucleus on its axis. $\endgroup$ Commented Dec 7, 2022 at 5:29

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