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  1. Problems
  2. /An atom of hydrogen has a radius of about 0.1 nm…
MediumChemistryHigh School (9–10)GeneralAtoms and Molecules › Laws of Chemical CombinationNumericalBoard Exam

An atom of hydrogen has a radius of about 0.1 nm…

StemPy LabContributed by StemPy Lab

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

An atom of hydrogen has a radius of about 0.1 nm0.1\ \text{nm}0.1 nm. How many hydrogen atoms, placed in a straight line touching each other, would make a line 3 mm3\ \text{mm}3 mm long? (1 mm=106 nm1\ \text{mm} = 10^{6}\ \text{nm}1 mm=106 nm.)

Check your answer

Work it out on paper, then type your number. The answer itself stays hidden.

Need a reminder? The key ideaShowHide

Dalton: matter is made of atoms, which are not created or destroyed in a reaction; atoms of one element are alike; they join in small whole-number ratios. An atom is about 0.1 nm0.1\ \text{nm}0.1 nm in radius, and 1 u=1.66×10−24 g1\ \text{u} = 1.66 \times 10^{-24}\ \text{g}1 u=1.66×10−24 g.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

Step 1. The width of one atom. 2×0.1 nm=0.2 nm2 \times 0.1\ \text{nm} = 0.2\ \text{nm}2×0.1 nm=0.2 nm.

Step 2. The line in nanometres. 3 mm=3×106 nm3\ \text{mm} = 3 \times 10^{6}\ \text{nm}3 mm=3×106 nm.

Step 3. The number of atoms. 3×106 nm0.2 nm=1.5×107\dfrac{3 \times 10^{6}\ \text{nm}}{0.2\ \text{nm}} = 1.5 \times 10^{7}0.2 nm3×106 nm​=1.5×107.

Answer: about 1.5×1071.5 \times 10^{7}1.5×107 atoms, fifteen million, in just three millimetres.

Common mistake. Using the radius as the width gives twice too many atoms.

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  1. Dalton's atomic theory and atomic massLaws of Chemical Combination and Atoms

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