Does gravity hold electrons in orbit around atomic nuclei?

Question

If the forces are unified then it must, mustn't it?

Answer 1

The answer is roundly negative.

We can measure the energy of electrons. That energy is just too high for a gravitational potential. Remember that we already know the masses of electrons, protons and neutrons, so we can compute the gravitational force. The energy of the electron in those "orbits" requires a tremendously stronger force.

When we use the electromagnetic one, it works. Quantum mechanics, in fact, predicts the behaviour of the hydrogen atom pretty well using only electrostatic interaction. With more sophisticated models, still based on electromagnetism, the atomic theory works. So I don't think there's much more to add.

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If the forces are unified then it must, mustn't it?

No, it must not.

• First of all, the forces are not unified. Three of them can be explained with the same theory, but not gravity (at least not yet).
• They were only unified a few instants after the Big Bang.
• Do not try to apply dictionary definitions to science. Do it the other way round: correct the dictionary from what you know. Dictionaries are quite bad at science haha.

And finally, do not believe you understood what you heard. I'm against "popular science" because of that. People think they understood, but they didn't, and that's dangerous. I prefer teaching instead.

As others point out, "it means that they come from a common gauge group".

Understanding what that means requires, I think, many years of learning maths and physics. I encourage you to learn them, but my advise is not to try to grasp too advanced concepts without background.

Answer 2

The short answer is no. The thing responsible for bounding the orbit of the electron mainly the electrostatic potential. If you compare $\frac{V_{elec}}{V_{grav}}$ you will get an insanely large number.