Imagine that science has figured out how to make the ultimate slicing tool, for use in… whatever the hell they’d need it. For simplicity, let’s say it’s made of tungsten.
If you held the blade vertically, sharp end up, it would be shaped like two-dimensional pyramid. The tip of the blade is one atom thick. Two atoms below the tip, three atoms below that, etc.
Three questions:
1: How many atoms thick would it have to be before I could see anything? I’m guessing it would be in the quadrillions of atoms.
Looking at the blade with the naked eye, would I be able to see a definitive edge to the blade, like I can with a run-of-the-mill Gillette blade? Or would it look… I dunno, fuzzy?
What would happen if I put my finger to it? I imagine that it would slice so cleanly and painlessly that I wouldn’t notice anything amiss until my finger was severed.
I’ve actually wondered about this myself. Here’s the tricky part:
Unless I’m mistaken, the two sides end up being at right angles to each other. Perhaps this “blade” would not really be particularly sharp at all, on account of the sides being at such a wide angle. Or, perhaps, because the sides are so smooth, and go all the way to being just one atom across, it would indeed be incredibly sharp. Which?
Think of it this way, how many atoms could you fit into a square inch. If you put 1# pressure on the blade you would have billions of PSI at the tip. I have heard that some Dr’s are now using Obsidian flakes for scalpels now.
This will depend on the crystalline structure of the material involved. If the material uses a close-pack structure, the angle between the two faces of the blade would be about 55 degrees.
Plastic surgeons who work on facial features sometimes use obsidian-bladed scalpels. They supposedly cause less scarring, because they are so sharp. The blades are only useful for soft tissue, though, because they break very easily.
#1 and #2 are probably hard to answer, since the “atomically sharp” area of the blade would be microscopic. So it’s basically moot; the part of the blade you’d see would probably look like a normal razor blade. Existing razor blades are already too sharp to see the “sharpness” with a naked eye.
An atom is 1 is, on average, 1 angstrom long. Or close enough that we’ll go with that. An angstrom is 10^-10 meters in length.
How small can you see? Let’s call it 1/2 the diameter of a human hair which is 45 microns or 4.5*10^-5
OK, so just divide one into the other and you come up with 22,222. That’s how many atoms across you could just barely see at the limits of your eyesight.
It’s actually a lot less than you think; the bond distance between tungsten atoms is 274 picometers and the smallest thing your eye can see is about 50 micrometers, which is only about 182,000 atoms. There’s also some minimum thickness before the material becomes opaque (very thin metal is transparent), probably a lot thinner than this.
You’d probably still see a sharp line since the blade goes from transparent to opaque over a very small distance, especially since the angle is so wide (90 degrees as previously stated)*.
Only the very tip would be super-sharp; a blade big enough to see with the progression in thickness you stated would basically have the cross-section of a cube*, so you’d have a very wide base going through your flesh. In fact. I doubt it would really cut that well, much less be able to sever your finger, unless you used a much thinner blade (it’d still be painful though, simply because you are injured, if less painful that if a saw or ordinary knife was used). Of course, such a thin tip would likely dull down very rapidly.
*Unless you meant that the tip started out with one atom, then two, then three, then stopped getting wider after some point.
Anyway, part of your question was what would happen if you touched it. Supposedly blades that sharp can separate cells (including dead skin cells?), rather than crushing any of them.
Holding a knife by hand would bend or break off a lot of really thin stuff. I don’t even know what kind of machine could apply force properly to avoid that. But that’s what happens with a regular knife, little bits get deformed and come off on whatever you cut. So the molecule thin blade would rapidly decline to the point of something no sharper than the best conventionally sharpened blades now. Well after the first cut anyway.
Not definitive but most craftsmen and machinists can touch or see 1/1000 of an inch or roughly 30 microns (0.03 mm) i personally attained this dimension when i was grinding mineral thin sections for a petrographic laboratory. We measured the cutting edge of various “sharp” blades and they are less than 0.5 microns (0.0005 mm) right at the tip. Needless to say, you can’t see it.
With regard to knives, you come to bevel angles right at the cutting edge. axes, machetes and big knives have a cutting bevel of 25 to 40 degrees on one side. Most pocket knives today can be sharpened down from 20 to even 9 degrees per side. A well-sharpened pocket knife can split a single strand of hair.
The sharpest “ground” edge i know are diamond scalpels. A single scallop of glass flaked from a bigger chunk might even be sharper. I’m not sure. What I’m sure of is it’s definitely easier to flake glass or obsidian than to grind down diamond.
