1.30 - The sizes of atoms and molecules

1.30 - The sizes of atoms and molecules

Atoms and small molecules are far too small to measure with a classroom ruler. You will learn their approximate scale, convert between metres and nanometres, and use that scale in a simple estimate.

The scale of atoms and small molecules

Atoms and small molecules have typical sizes of the order of 10−10 m10^{-10}\,\mathrm{m}. A useful reference size is 0.1 nm0.1\,\mathrm{nm}, equal to 1×10−10 m1\times10^{-10}\,\mathrm{m}.

Order of magnitude

An order of magnitude describes an approximate scale using a power of ten.

The reference value is not an exact diameter for every atom or molecule. Different atoms have different sizes; small molecules may be a few tenths of a nanometre across. For example, 0.2 nm0.2\,\mathrm{nm} and 0.3 nm0.3\,\mathrm{nm} are still on the atomic scale.

Converting nanometres to metres

The prefix nano means one billionth. Nanometres are convenient because they avoid writing many zeros.

Nanometre conversion

1 nm=1×10−9 m1\,\mathrm{nm}=1\times10^{-9}\,\mathrm{m}

To convert a length in nanometres to metres, multiply its numerical value by 10−910^{-9}.

For the reference atom size:

0.1 nm=0.1×10−9 m=1×10−10 m0.1\,\mathrm{nm}=0.1\times10^{-9}\,\mathrm{m}=1\times10^{-10}\,\mathrm{m}

For a small molecule 0.3 nm0.3\,\mathrm{nm} across:

0.3 nm=3×10−10 m0.3\,\mathrm{nm}=3\times10^{-10}\,\mathrm{m}

The unit conversion is always the same. One nanometre is ten times the reference atom size of 0.1 nm0.1\,\mathrm{nm}; it is not itself the typical atom size.

Using the scale to estimate

[DIAGRAM: asset_name: Atom and small molecule order-of-magnitude scale - diagram 1; asset_slug: 036_1_30_typical_size_order_of_magnitude_of_atoms_and_small_molecules_diagram1; file: 036_1_30_typical_size_order_of_magnitude_of_atoms_and_small_molecules_diagram1.png; recommended_method: deterministic_drawn; description: Deterministic monochrome log-scale comparison showing a typical atom or small molecule at about 10^-10 m / 0.1 nm, 1 nm at 10^-9 m, and a human hair near 10^-4 m. The visual teaches the order-of-magnitude recall value and prevents confusion between 0.1 nm and 1 nm. It is an exact assessed scale visual, so deterministic drawing is used.]
Diagram

Each equal gap on the scale represents a factor of ten. The drawings are symbols, not objects drawn at their relative sizes. A hair about 10−4 m10^{-4}\,\mathrm{m} wide is about a million times wider than an atom of size 10−10 m10^{-10}\,\mathrm{m}.

To estimate how many atom-widths fit along a length, divide the total length by the size of one atom. Use the same unit for both lengths.

Atom-widths across one millimetre

Using 1×10−10 m1\times10^{-10}\,\mathrm{m} for one atom and 1 mm=1×10−3 m1\,\mathrm{mm}=1\times10^{-3}\,\mathrm{m}:

number of atom-widths=10−310−10=107\text{number of atom-widths}=\frac{10^{-3}}{10^{-10}}=10^7

About ten million atom-widths fit along one millimetre. This is an estimate treating atoms as adjacent widths; it is not an exact count in a real material.