[Corribus]

Its also interesting that the electrons in orbitals can be far away from the nucleus but the probability for this is very small. I wonder about the math, how low probability is it that a electron from an atom in my body is in the Andromeda galaxy?
Its not zero. Or am I wrong?

https://physics.stackexchange.com/questions/92565/is-it-that-electron-of-an-atom-can-be-found-anywhere-in-the-space

Strictly speaking this is true but even beyond the exponential falloff of the probability distribution, from a practical standpoint this assumes that there are no other electrostatic potential surfaces between here and, as you put it, the Andromeda galaxy. I.e., it assumes an empty universe. Obviously other atoms exist, and the potential energy function of one atom in your body would be influenced by that of the next atom over. Moreover it's worth reminding you that electrons don't have precise locations. Using language like "probability...that an electron from an atom in my body is in the Andromeda galaxy", which is predicated on macroscopic ideas like instantaneous observations at defined points in time and space, isn't really up to the task of disentangling the wave/particle duality and observable uncertainties of the quantum world.

Quantum mechanics is weird.   

[rolnor]

 Yes,  but an aproximation is possible. And, for simplification, lets assume its all empty space.

[Babcock_Hall]

@OP,

Thinking in terms of bond lengths and bond angles, what would you consider evidence that the resonance structure with two charges does or does not make a significant contribution to the overall structure of form amide?

[Corribus]

@Rolnor
All you need is the radial distribution function. (Keep in mind that analytical solutions exist only for hydrogenic atoms.). For an electron in the lowest energy orbital of the hydrogen atom, the probability drops off as a function of e^-2r/a, where r is the separation from the nucleus and a is the Bohr radius (about 5 picometers). You can estimate the probability that the electron exists in a region defined by r₁ to r₂ by integrating the radial distribution function (see: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydrng.html#c1). Let's forget the Andromeda galaxy and just estimate it for an distance more than 1 nanometer away from the nucleus - that's about 20x the Bohr radius . Using the approach above, the probability the electron is further than 1 nm away from the nucleus is about ~4E-13 to 1. The probability that it is more than 1 micron away from the nucleus is too small to be calculated by online worksheet, or even by Excel. So, maybe that gives some sense of scale.

[Corribus]

By the way, this kind of thing is true for any potential field that drops off exponentially with distance. A simple bar magnet in your living room technically will attract another bar magnet in the andromeda galaxy.... same thing with your personal gravitational pull. But does it really mean anything?

[rolnor]

Thanx,
I am not surpriced in anyway, electrons are to 90% found in the orbitals.
I just wanted to further explain resonance, that the molecules we draw are simplifications and that almost anything is possible, but often very improbable.
I guess that all particles in the universe can be found anywhere in the universe if we observe it for very long time. This is theoretically important but has no practical use for us. You mention forces and that is different from particles, forces are something else.

[Corribus]

Well forces act on particles and determine their properties. Position is one property. In the case of nuclei and electrons, the forces are electrostatic, which constrain position, momentum, and so on. In the case of planets, the forces are gravitational. I (a particle) am within the gravitational field of the Andromeda galaxy, and so those stars affect my position, velocity, and so on. As it happens, I'm sitting in a much stronger local field, imposed by our earth, which sits within an even stronger field (that of our sun), so Andromeda's grav fields are inconsequential to me. But if I and Andromeda were the only things that existed, I would be pulled toward it, despite how far away it is, because the field does extend to infinity. This is only if you ignore all the other stuff in the universe, of course

[rolnor]

I still think its different with particles or mass, if the universe life-span was infinite, my whole body could be in the Andromeda and this would happen an infinite number of times.