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Chapter 1: Problem 15

A hydrogen atom is about \(0.1 \mathrm{nm}\) in diameter. How many hydrogen atoms lined up side by side would make a line \(1 \mathrm{cm}\) long?

Short Answer

Expert verified
The number of hydrogen atoms that will make a line \(1 \, cm\) long when lined up side by side is \(1 \times 10^8\).

Step by step solution

01

Convert \(cm\) to \(nm\)

To start solving this problem, the unit of the total length which we want to obtain by lining up hydrogen atoms, which is given in \(cm\), needs to be converted into \(nm\). The conversion factor is \(1 \, cm = 1 \times 10^7 \, nm\). Thus, \(1 \, cm = 1 \times 1 \times 10^7 = 1 \times 10^7 \, nm\).
02

Calculate the number of hydrogen atoms

Now, knowing the total length in nm, the number of hydrogen atoms that would result in this total length if lined up can be calculated. The diameter of each atom is given as \(0.1 \, nm\). So, the number of atoms is calculated as the ratio of the total length to the diameter of one atom. Therefore, the number of hydrogen atoms can be calculated as \(\frac{1 \times 10^7 \, nm}{0.1 \, nm} = 1 \times 10^8\). This division is done because the size given is for one single hydrogen atom and we need to find out how many of these individual atoms can fit in the total length. Division will thus give the number of times the single atom's size fits into the total length, which is the number of atoms required.

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