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Question Video: Calculating the Number of Nanoparticles That Fit across a Given Diameter of the Human Hair Chemistry

A human hair has a diameter of 80000 nm. How many nanoparticles with a diameter of 50 nm would fit across the human hair? Give your answer to the nearest whole number.

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Video Transcript

A human hair has a diameter of 80000 nanometers. How many nanoparticles with a diameter of 50 nanometers would fit across the human hair? Give your answer to the nearest whole number.

Human hair varies in thickness by quite a lot, but it’s typically 100 micrometers wide, which is about 100000 nanometers. The particular hair we’ve been given is 80000 nanometers in diameter, which is just a little bit thinner. Nanoparticles are particles with a diameter of 1 to 100 nanometers. The nanoparticles we’ll be using have a diameter of 50 nanometers. I’ve assumed, in this case, we’re dealing with spherical nanoparticles.

Our job is to work out how many of these nanoparticles placed end to end would fit across the human hair. This means we need to work out how many particles in a line are 80000 nanometers long. And we shouldn’t overthink it and place the nanoparticles on the surface of the hair. To figure out the number of nanoparticles we need, we simply have to take the diameter of the hair and divide it by the diameter of the nanoparticle.

We plug in our values to get 80000 nanometers divided by 50 nanometers. We don’t necessarily need a calculator for this because we can see that 50 goes into 800 16 times, which means 50 goes into 80000 1600 times, giving us our answer of 1600 nanoparticles. And we already have our answer to the nearest whole number.

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