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I'm a high school drop out so excuse my grammar. I have done extensive reading in Astronomy and Cosmology, and came across this article With the title "Physicist Are Dumbfounded why we don't fall through a chair when we sit.

They said if they expand the atom that makes up a wooden chair to the size of baseball stadium and place the Nucleus in the middle of the stadium the Electron, Proton,And Neutron would be outside the stadium. what in all that space is keeping the chair together?

Qmechanic
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To keep you from falling through the chair, the atoms do not need to "take up space." They merely need to provide a force. In particular, they need to provide exactly enough force to oppose the force of gravity pulling on you.

Fundamental forces like electrostatic forces and gravity don't require "touching" in the intuitive macroscopic sense. They get to convey force at a distance. So they don't need to "fill" the space, as much as they just need to convey enough force.

Where this becomes unintuitive is in the distances involved. The electrostatic forces rise sharply as you get closer to the atoms in the chair (why this happens is another topic entirely). As a result, the difference between a separation that yields a very small force from the chair and a separation that yields a gargantuan force from the chair is very small. We're talking nanometers, or even less. So to our macroscopic-oriented minds, it "feels" like we're making contact, and that contact is hard and unyielding. In reality, the atoms in our body are still a distance away from the atoms in the chair, and there's a little bit of springiness to the interaction. Its just over such small scales that you and I don't intuitively realize it's there.

Its just one of the examples where the intuition that serves us well in daily life just doesn't quite do the job when we start looking at the really small. (The same happens when we start looking at the really large, like planets or stars)

Cort Ammon
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Well, wood is not made of a single type of atom like the fundamental elements of the periodic table are, however, wood is primarily composed of organic compounds like lignin and cellulose which are carbohydrate molecules. Molecules are complex structures made up of tightly bound atoms. Molecules have the ability to attract each other through a type of interaction known as Van Der Walls forces. The result is that the molecules that make up wood are not easily separated from one another, this tight network is able to then support the force of body weight so that the chair doesnt disintegrate. The reason why atoms do not simply collapse onto each other as a result of all the "empty space" is that the electrons which orbit the nuclei of atoms form a kind of virtual repulsive force field due to a principle from quantum mechanics known as the Pauli exclusion principle. All the things I have written here is a vastly over simplified view that leaves many details out, as the question you have asked is truly a deep one not easily understood without a lot of grounding in physics.