How many atoms per meter are there in a carbon nano tube?

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SUMMARY

The discussion centers on calculating the theoretical number of carbon atoms in a carbon nanotube and how this relates to the thickness of paper needed to reach the moon through repeated folding. A carbon atom has a diameter of 0.22 nm, and the concept of folding paper 44 times to exceed the distance to the moon is explored. The number of atoms in a carbon nanotube varies based on its radius, making it essential to understand the specific properties of the nanotube in question. The calculations involve geometric principles, specifically the formula for distance as a function of paper thickness and the number of folds.

PREREQUISITES
  • Understanding of carbon nanotube properties and dimensions
  • Basic knowledge of geometric progression and exponential growth
  • Familiarity with atomic scale measurements (e.g., nanometers)
  • Concept of folding paper and its implications on thickness
NEXT STEPS
  • Research the properties of carbon nanotubes, including variations in radius and atomic structure
  • Explore geometric series and exponential functions in real-world applications
  • Learn about atomic measurements and their significance in nanotechnology
  • Investigate the theoretical implications of folding materials and their physical limits
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Students, physicists, and engineers interested in nanotechnology, geometric principles, and the properties of materials at the atomic level.

nalA
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I'm interested in the theoretical minimum number, so like the extruded buckyball ball?

I'm trying to work out if there are enough carbon atoms in a 'piece of paper' to reach the moon. :)

Which brings me to the next question : how many carbon atoms are there in a piece of paper? Or perhaps a better way of putting it would be, how big a piece of paper would you need - would a sheet of A4 paper get you there?

This all comes from me coming across that idea that if it was possible, you'd only have to fold a piece of paper 44 times to reach the moon! ie by doubling the thickness 44 times, you'd exceed the distance from the Earth to the moon.
 
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This is just a geometrical problem. Nano tube is a repeating pattern, find the "building block" - number of atoms, length - and then it is trivial.

Note that carbon nano tubes can have different radii, so the number of atoms depend on the properties of the particular tube.
 
That would be
Distance = thickness pf paper x 2^44
So that is easy to calculate.

Size of paper:
You can calculate the size of paper needed by knowing: ( best to start off with a square piece of papaer )
A carbon aom has a diameter of 0.22 nm ( 2,2 x 10^-10 m )

And that on each second fold, or folds of even powers of 2, result in another square ( odd folds have a rectangular shape )

So is A4 paper large enough or are you trying to fold an atom?
 

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