[talanum1 (OP)]

Why does the nuclear positive charge of a neutral atom get totally canceled by the electrons even though they do not cover an impenetrable sphere around the nucleus?

[Bored chemist]

Imagine an atom and near it, but not very near, there's an electron.
The electron is attracted to the nucleus of the atom.
But it is also repelled by the electrons around the nucleus.
Those two forces are equal and opposite.
So, from a distance, it seems that the nuclear charge is screened.

[chiralSPO]

As Bored chemist says, the charge from the nucleus is equal and opposite to that of the electron cloud.

Because the electrons are only separated from the nucleus by an Ångstrom or so (10^–10 meters), any particle that is more than 100 times this distance (10 nm) away essentially feels no difference in the electrostatic attraction from one and the attraction of the other (essentially same magnitude of force, and same direction, except one is attractive and one is repulsive).

There is some net force possible for particles that are very close. For example, London dispersion forces, which can be thought of as mutual distortions of the electron clouds in close neutral molecules.

[evan_au]

electrons ... do not cover an impenetrable sphere around the nucleus

In high school, the structure of the atom is often introduced as like a tiny solar system, with electrons spinning in orbits around the central nucleus.

This analogy might give the idea that the nucleus is shielded in the plane of the electrons, but not "North" and "South".
- In fact, the electrons do surround the nucleus in three dimensions
- Unlike planets, electrons are not hard objects, but have a more obvious "wave" nature, which spreads out their location so it surrounds the atom on all sides.
- For some atoms, the electrons are in a symmetrical sphere
- For other atoms, the electrons are in a non-so-symmetrical shape, while still surrounding the atom in 3 dimensions (an example of this is the oxygen atom in a water molecule, where the electron concentration gives the water molecule a boomerang shape)

For atoms at room temperature, the electrons do form a fairly impenetrable shell. That's why, when you try to squash a solid or liquid, the pressure rises enormously - that represents the electrons pushing back on adjacent atoms.

To seem diagrams representing some of the shapes of the electron cloud surrounding a nucleus, see: https://en.wikipedia.org/wiki/Atomic_orbital#Orbitals_table

Why does the nuclear positive charge of a neutral atom get totally canceled by the electrons

It's true that in most atoms and molecules, the number of protons equals the number of electrons, giving zero net charge.

But many chemical processes (and many life processes) rely on charged ions, where the positive and negative charges do not balance.

One example is common salt, sodium chloride. In this chemical, the sodium gives its outer electron to the chlorine
- This means the sodium atom now has a neat spherical shell of electrons - but one less than the number of protons, giving it an overall positive charge
- This means the chlorine atom now has a neat spherical shell of electrons - but one more than the number of protons, giving it an overall negative charge
- These charged ions exist quite stably in solid and liquid states, or dissolved in water

Probably the most extreme example is the H⁺ ion, which occurs naturally in drinking water.
- In this case, the Hydrogen atom gives its only electron to a OH^- group
- This leaves the Hydrogen atom with no electrons - just a bare proton, with a very intense electric field (which then attracts nearby water molecules)
- That's why chemicals which have lots of free protons (like strong acids) are very powerful at disrupting other chemicals

See: https://en.wikipedia.org/wiki/Self-ionization_of_water

[talanum1 (OP)]

The electrons are wavelike when not observed, but quantum mechanics say the outermost electron is at a point when observed. Shouldn't the nucleus positive charge then leak out?

An observed chemical will act differently than an unobserved one.

[Bored chemist]

quantum mechanics say the outermost electron is at a point when observed.

That's more or less the opposite of what QM says.

Shouldn't the nucleus positive charge then leak out?

It's not a matter of "leaking out" it's a matter of adding the electrostatic fields from the electrons and the nucleus and finding that , from a distance they add up to zero.

An observed chemical will act differently than an unobserved one.

What might that even mean?
I can stare at a test tube, but I can't actually observe the molecules reacting.

[evan_au]

An observed chemical will act differently than an unobserved one

When two molecules approach each other, they start to disturb each other - effectively, they "observe" each other.
- In the extreme, if they have the right formula, and hit at the right angle and right speed, the two molecules may react with each other, forming different molecules.

If they don't approach each other at all, then they won't disturb or "observe" each other, and no chemical reaction can occur.

What makes you think that observation in quantum mechanics requires a conscious observer?