Amedeo Avogadro didn’t actually discover Avogadro’s number. It was named that in tribute to him as he first proposed that the volume of a gas is proportional to the number of atoms, regardless of the type of gas. A physicist called Jean Perrin first coined the term and defined it as the number of oxygen atoms in 32g of oxygen. To calculate it, he did several experiments. One method was by studying the Brownian motion of small spherical particles. He observed the diffusion of the particles and used this Avogadro’s number. He used an equation in a paper of Einstein’s to calculate it!
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