Equality of Gravitational and Electrostatic force

[PhysicsEnjoyer31415]

TL;DR Summary

So i was experimenting around with formulae and i thought to myself "could a planet rip a electron off a single electron system?" So i used this formula and i want to know if this is correct? . I know that gravity is magnitudes weaker than electrostatic force but if it were forced anyway would this be correct?

 

[anuttarasammyak]

I feel two points
1 How we can arrange the experiment so that only electrons no ion cores are under influence of gravity ? Free fall of atoms is the most familiar situation. I do not know how we can fix the position of the cores with no influence to electrons.
2 If we can fix the cores, forgetting about EM force, I wonder which is bigger gravity from the Earth or gravity from the ion core to the electrons ?

 

[Drakkith]

For a hydrogen atom with a radius of 37 picometers, placed near the surface of the Earth, I get the following results for the forces on the electron:

Tidal Force: 1.185x10^-16 newtons
Electrostatic Force: 1.68x10^-7 newtons

Even if my electrostatic force is an order of magnitude off due to being a classical calculation and not a quantum one, we're looking at a difference in force in the realm of nine orders of magnitude. A planet is absolutely not ripping an electron off of an atom unless the electron is only bound to the atom in the loosest possible sense of the word 'bound'.

 

[Ibix]

Tidal Force:

It's worth noting that the tidal force calculation addresses @anuttarasammyak's objection about the nucleus apparently being unaffected by gravity in the OP's calculation. This tidal force approach is the correct way to go about this, not the OP's calculation.

I wonder which is bigger gravity from the Earth or gravity from the ion core to the electrons ?

Earth. Atomic masses are of order $10^{-27}\mathrm{kg}$, electrons about three orders of magnitude lower, and atomic radii $10^{-10}\mathrm{m}$. That gives you a gravitational force around $10^{-48}\mathrm{N}$. Assuming Newtonian gravity is remotely valid for atoms.

 

[PhysicsEnjoyer31415]

For a hydrogen atom with a radius of 37 picometers, placed near the surface of the Earth, I get the following results for the forces on the electron:

Tidal Force: 1.185x10^-16 newtons
Electrostatic Force: 1.68x10^-7 newtons

Even if my electrostatic force is an order of magnitude off due to being a classical calculation and not a quantum one, we're looking at a difference in force in the realm of nine orders of magnitude. A planet is absolutely not ripping an electron off of an atom unless the electron is only bound to the atom in the loosest possible sense of the word 'bound'.

I think you are right and this is only a theoretical possibility , i thought it could become true only if we have mass in 50s of magnitude , neglect gravitational force of proton ,and have radius not more than magnitudes of 6 or 7. Also i was using the bohrs model where radius of hydrogen atom wpuld be 0.529 angstrong

 

[anuttarasammyak]

I think you are right and this is only a theoretical possibility , i thought it could become true only if we have mass in 50s of magnitude , neglect gravitational force of proton ,and have radius not more than magnitudes of 6 or 7. Also i was using the bohrs model where radius of hydrogen atom wpuld be 0.529 angstrong

In order to get large tidal force, putting an atom very closed to a tiny densed mass instead of planet would be interesting.

 

[PhysicsEnjoyer31415]

In order to get large tidal force, putting an atom very closed to a tiny densed mass instead of planet would be interesting.

Would definitely love to see that

 

[PhysicsEnjoyer31415]

In order to get large tidal force, putting an atom very closed to a tiny densed mass instead of planet would be interesting.

I think it still might not be enough to pull a electron even if we hold down the proton somehow. That would require a huge density which i am not sure is possible or not , maybe a neutron star or something but it would surely be interesting

 

[Mister T]

I think you are right and this is only a theoretical possibility.

Actually, he demonstrated that it's a theoretical impossibility.

 

[PeroK]

I think it still might not be enough to pull a electron even if we hold down the proton somehow. That would require a huge density which i am not sure is possible or not , maybe a neutron star or something but it would surely be interesting

There's a little thing called Quantum Mechanics that may be relevant here. You don't get far with a Newtonian model of the atom.

 

[PhysicsEnjoyer31415]

There's a little thing called Quantum Mechanics that may be relevant here. You don't get far with a Newtonian model of the atom.

Yes