Posted by: Kash Farooq | November 17, 2012

Estimating the size of an atom (with a bath and a drop of oil)

Blogging while studying S207 – The Physical World.

How can you estimate the size of an atom when you haven’t got the technology to measure one?

When atomic theory was seriously being considered in the 1800s, this was one of the questions that puzzled scientists. If they existed, how small were atoms and molecules?

The English physicist Lord Rayleigh (1842 – 1919) came up with an ingenious, yet simple, method to provide an upper limit to the size of an atom.

If you carefully lower a drop of oil onto still water, the drop spreads to form a very thin circular layer. Rayleigh proposed that the oil film formed is one molecule in thickness (something that has since been confirmed). So, he got hold of a large bath tub, scrubbed it clean and started making measurements.

A circular patch of oil with radius R and thickness h sitting on still water. Remind me never to give up the day job.

We can approximate volume of the initial drop of oil; if we assume it is a sphere it has a volume of 43Πr3.

The patch of oil is approximately a very thin cylinder with volume ΠR2h.

The entire volume of the patch of oil obviously comes from the initial drop of oil, so:

43Πr= ΠR2h

h = 43r/R2

Realistic values for r and R could be, say, 0.5 x 10-3 m (i.e. 0.5 mm) and 0.4 m respectively.

This gives h ≈ 10-9 m.

As the patch of oil cannot be less than one molecule thick, we have found the maximum height of an oil molecule – and hence atoms must be even smaller than this.



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