>eli5: On an atomic level, how does an atom ‘know’ it belongs to (for example) a sheet of paper but not the sheet of paper below it.
It doesn’t. Look up vacuum welding, it’s fascinating. When you have two very clean surfaces of, say, aluminium, and touch them together in a vacuum, they will weld themselves together because yes the atoms don’t ‘know’ which piece of metal it’s a part of. The reason they don’t in your everyday experience is because our environment is full of oils, and dirt, and oxygen corroding the metal, so there are multiple dividing layers between the actual metal.
Of course paper is less simple since it’s actually a bunch of fibres mashed together.
>Also how do scissors interact with the paper on an atomic level to cut it into two pieces.
The scissors blades compress the paper fibres until they break apart. Scissor blades aren’t lined up for a reason, what they’re doing is basically pulling the paper apart, just in a very small area. It’s why very blunt scissors don’t cut, they bend the paper instead; the area on which they’re pulling is too large, and the force of your hand isn’t great enough to pull that many fibres apart
To add to the other answers already here, on the atomic level, it’s electrons that are responsible for holding atoms ‘together’. This doesn’t make much sense in terms of our scale of reality, but the electrons “in” an atom, despite being very small, occupy a much larger volume than the nucleus. They can be ‘shared’ from one atom to another, and that’s how atoms stick together and form molecules. Individual atoms in the paper are stuck to adjacent atoms this way, but those big molecules are in turn just kind of mushed together and held together by a mess of fibres and adhesives all kind of tangled together – not the strong connections made by the sharing of elections. The metal in the scissors on the other hand is mostly held together by the sharing of electrons between all the iron atoms in a big ‘electron sea,’ a property specific to metals. This is basically what’s happening when scissors cuts paper: It’s very unlikely that anything in the paper would be strong enough to dislodge the iron atoms from each other, but the vastly weaker connections between “paper molecules” (really, the paper fibres) are very easy for the cutting edge of the scissors to get between and mechanically separate.
To create a bond between atoms you need to put energy into the system. Paper consists of molecules that are formed through some process that uses energy to bind atoms. In a tree, this energy is stored through photosynthesis for example – which utilizes the energy of sunlight to create carbohydrate molecules. Breaking a bond releases energy – that is what happens when you burn things for example. It’s also why your body ‘burns’ sugar – the energy released from breaking bonds in a sugar molecule is what powers the rest of your body. However, if you put two sheets of paper on top of eachother, the atoms don’t interact with eachother much, because you are not putting energy into the system, so they cannot ‘fuse’ so to speak. So the atoms don’t ‘know’ that they are part of any particular sheet of paper, but they necessarily have to remain bonded to the other atoms that are part of the sheet of paper, because they are ‘energetically bonded’ to them in a way.
At the atomic level, a single atom “belongs to something” as long as nothing kicks it out of place. It’s like playing with a grape inside a bowl:
If someone gives you a grape on a bowl, as long as you’re careful, you can move the bowl and the grape and it will never fall off and “the grape belongs to the bowl.
If you’re not careful or if you move the grape or the bowl too fast, the grape *might* fall of, and then “the grape no longer belongs to the bowl”
**Atoms are like grapes** and **molecules are like bowls**, but ***the bowl is also made of grapes that also are bowls***. Weird, right? We need to read that sentence again to try to understand!
If we think about paper, a single atom of paper is “inside a bowl made of paper atoms”, and unless you kick it with enough force you won’t be able to take that paper atom out. That’s because “the paper atoms that make the bowl” don’t let the paper atom escape.
Scissors work by pushing the atoms in the paper with enough force to take them out of their bowls. They do it in a way where only a few stops in the paper are pushed, and they are all close enough that you can separate the paper into two pieces.
We can think about it as a bunch of eggs on carton holders, the kind that can hold 100 or 144 eggs at a time:
Think about every egg as a single paper atom. If you start pushing eggs from a line or column, your hand becomes like a scissor that cuts trough paper.
The interaction on an atomic level is minimal. The molecules that make up paper (mostly cellulose) are very stable, so the atoms are content where the are. Paper is more macroscopic. Think of it as a big knot pulled very tightly together. The knots are happy being their own separate knots, even when put close together.
Atoms need to be *really close* to each other in order to bond — on the order of the diameter of the atom itself (around one billionth of a foot). Jamming two sheets of paper together might *look* like they are “close” to our human eyes, but to atoms the two surfaces are actually barely even touching because the surfaces are extremely rough on the atomic scale, and there are other particles / air in between. (Also, atoms bond more easily with certain atoms than others — this is what chemistry is about!)
When two materials *are* bonded, they are bonded with a certain mechanical strength that is a property of the material, determined by the kinds of atoms and the structural arrangement they form. Cutting paper with scissors is one way of breaking the bonds between atoms in the paper. It works oin large part because the mechanical strength of the scissors is stronger than the paper — your hands push on the atoms in the scissors, which then translate that force into the paper.
The reason that an atom knows what sheet of paper it belongs to is due to the fact that the atom is *bound* to a molecule. A molecule is a bunch of atoms that bond *very* strongly to one another. The atoms can be arranged in a chain, in rings, or in one of many other ways.
Paper is made up of various different molecules, most importantly [cellulose](https://en.m.wikipedia.org/wiki/Cellulose) in case you want to look it up. Many of these molecules make up fibres and many fibres make up the sheet of paper.
As I said, the bond between the atoms and the rest of their molecule is very strong. Breaking that bond would require a lot of work, that is missing when you simply push two sheets of paper together. The molecule really doesn’t want to give up the atom and there really isn’t a molecule on the other side that would like to adopt another atom.
Now when you cut a piece of paper with a pair of scissors it is very unlikely that you will break the bond between atoms. That is because, the bond between atoms inside of molecules is much stronger than the attraction between molecules. So when you cut a piece of paper you are much more likely to separate two molecules. Although, there is a chance you might also break a bond between atoms.
If you would like to know what bond I’ve been talking about look up “covalent bonding”.
There are four forces in the universe. Weak and strong nuclear (that’s the atomic ones you need) gravity and electromagnetism. They are if varying power. Breaking the strong nuclear one is what makes cities go bang. That’s what holds the paper together, as paper. What holds it together as a piece of paper, is the weak one. You can cut that.
Since you have two arms, let’s say you’re oxygen. You would neeeeeed to be holding hands with someone else with each hand to be happy, otherwise you’ll reach around like crazy looking for something to hold. In this description, “holding hands” represents covalent bonds. Hydrogen has one hand and carbon has four hands. As others described, paper is made of cellulose just an arrangement of hydrogen and carbon, where they’re all happily holding hands. The atoms “know” they’re part of one piece of paper and not another because they’re in different chains of hand holding.
I agree with those before that explained how the atoms are in fibers. Each piece of paper is made of small “strings” (fibers) that are all “knotted” (I’m avoiding the word entangled) together and kept in place with “glue” (adhesives), when you cut with scissors your concentrating the force in a very thin line and pushing some fibers up and some down. This rips them apart. This isn’t a hand holding issue though. The pieces of paper “know” they aren’t part of the same piece of paper because they aren’t “knotted” together, just like when you put two knitted blankets on top of each other they don’t spontaneously become knit together
The comments on cold welding aren’t relevant because metals make metallic bonds, which aren’t as “cleanly” defined as hand holding (covalent bonds)
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