## Introduction: How Big Is an Atom? Let's Measure It...

Even in ancient Greece, scholars thought about the structure of the matter surrounding them. According to legend, the philosopher Democritus, who lived in the 5th century BC, the originator of the first particle model. In the absence of technical possibilities, his theses were based on a pure thought experiment.

Democritus is said to have sat at the foot of the Acropolis in Athens and thought about the whereabouts of the weathered rock. He mused that the effects of the weather would turn large rocks into small rocks, from them large, then small stones, and from this, in turn, sand and ultimately dust. But the dust particles would also have to continue to weather, i.e. disintegrate, only that they can no longer be seen. However, this should not mean that they are no longer there, but simply no longer visible. And now Democritus asked himself the crucial question: How long can a piece of matter continue to be divided?

Democritus came up with two possible answers:
First: Matter can be divided indefinitely, until nothing is left. However, he found this conclusion absurd due to the fact that there was a lot of "something" around him, and not "nothing".

So the second possibility had to apply: Matter cannot be broken down indefinitely, at some point there will be one (or of course several) last, smallest, indivisible particle. He called it atom (ancient Greek atomos = indivisible.)

Democritus assumed that every substance around him was made up of such tiny, indivisible particles. So there should be stone atoms, water atoms or air atoms. That he was wrong here would only be found out much later, as well as what these atoms would look like, how big they would be and after how many “divisions” one would have reached the atom. In addition, the name he chose is misleading, since an atom is still divisible.

## Step 1: Parts You'll Need

It's hard to believe, but the size of an atom can be determined with home remedies. You only need for this

• petrol
• sunflower oil
• a pipette
• a very small 1 mL syringe (1 mL = 1 cm³)
• a baking sheet with a raised rim
• water
• Bear moss spores (Lycopodium)
• 2 Plastic jars with screwable lid: One for the petrol-oil-mixture and one for the lycopodium-powder

## Step 2: The Experiment

To carry out the experiment: At the beginning you need 100 cm³ of petrol/gasoline.

Since I did not have a vessel with a 100 ml marking, I simply filled a glass with exactly 100 g of water and marked the water level with a pen. Then I emptied the water and filled the glass with petrol up to the mark. So I had almost exactly 100 ml of petrol.

Then only 0.1 cm³ (= 0.1 ml) of oil is added to the petrol.

The next step is to determine the volume of a drop from the pipette. To do this, fill the pipette with petrol and then drip into an opened 1 ml syringe until it is full. Specifically, I needed 67 drops from the pipette until the 1 ml syringe was full. Therefore 1 drop from the pipette has a volume of 1/67 cm³.

Now fill the baking sheet about 1 cm high with water. The bear moss spores are filled into a plastic jar with a screw-on lid. This lid is poked about 5-10 times with a thin needle. Then sprinkle the water with bear moss spores so that it is covered with spores fairly evenly but thinly.

Now you fill the pipette with the petrol / oil mixture and then let a single drop fall onto the water / the bear moss spores. If everything was done correctly, an oily circular area without spores should form. Their radius r is determined with a ruler. Specifically, I was able to determine r to be 7 cm.

## Step 3: Some Calculations

How can one determine the atomic size from this?

Well, we know the volume of a drop of a pipette to be 1/67 cm³. Due to the mixing ratio of 1: 1000, there is only 1/67000 cm³ of oil within one drop.

The oil volume also corresponds to the circular area * oil layer thickness h, i.e. 7² · π · h = 1/67000. From this follows for the oil layer thickness h = 9.7 · 10 ^ –8 cm = 9.7 · 10 ^ –10 m.

Sunflower oil consists largely of oleic acid (triolein, C57 – H104 – O6). It is now assumed that the oil layer thickness h corresponds exactly to the edge length of the oleic acid molecule with its 167 atoms.

These 167 atoms therefore require a volume of h · h · h. Accordingly, 1 atom (we are now assuming all 167 atoms of the same size) needs exactly the volume h · h · h / 167. The edge length d of an atom (this is also assumed to be a cube) is thus h / 3rd root of 167 , specifically

d = 1.76 · 10 ^ -10 m = 1.76 angstroms.

This atomic diameter corresponds surprisingly well with the literature values.

Here you can find many other interesting physics-experiments: my homepage with physics-experiments

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