In science fiction works, there is a mention of an ultra-strong and ultra-thin filament one atom thick.

| September 26, 2021 | education

In science fiction works, there is a mention of an ultra-strong and ultra-thin filament one atom thick. What would be the length of such a 20g filament made of carbon? Compare this length with the distance from the Earth to the Sun. Consider a carbon atom as a ball with a radius of 7.7 * 10-11m.

Data: m (mass of the thread in question) = 20 g.

Constants: r (radius of a carbon atom) = 7.7 * 10 ^ -11 m; MC (atomic mass of carbon) (MC = 12 g / mol); Na (Avogadro’s number) = 6.02 * 10 ^ 23 mol-1; S (distance from the Earth to the Sun) = 1.496 * 10 ^ 11 m.

1) The number of carbon atoms: N = m * Na = 20 * 6.02 * 10 ^ 23 = 120.4 * 1023 atoms.

2) The length of the thread in question (we assume that there is no distance between the atoms): L = N * 2r = 120.4 * 10 ^ 23 * 2 * 7.7 * 10-11 = 1854.16 * 10 ^ 12 m.

3) Comparison of distances: k = L / S = 1854.16 * 10 ^ 12 / (1.496 * 1011) = 12394 p.

Answer: The length of the thread in question is 1854.16 * 10 ^ 12 m, which is 12394 times the distance from the Earth to the Sun.



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