Inconveniently complicated truth
It’s atomic physics with the first years and we are working our way through the models of the atom in chronological order. When we got to Thomson and the discovery of the electron I made a statement something like this: “The electrons couldn’t have been atoms because their mass was far too small so were considered to be like small plums in a pudding”. This provoked the obvious question “How did they know the mass of an atom”. Hmm, not quite sure about that. I know how they do it now (mass spectrometer and all that) but how did they do it then?
In 1811 Avogadro came up with the idea that equal volumes of gas at the same pressure and temperature should contain the same number of atoms. If this is the case then it is possible to measure the relative masses of different gases by simply measuring the mass of equal volumes, so 1litre of Helium has a mass 4x the mass of 1 litre of Hydrogen etc. But to know the mass of 1 atom you have to know how many atoms there are and Avagadro didn’t know that even though the number is named after him.
Around 1865, by considering how far gas atoms move between collisions and the pressure they exert on their container, Johann Loschmidt calculated how many atoms there are in 1 cm3 this enabled him to estimate the mass of a gas atom. The derivation looks a bit tricky which is probably why we tend to leave this bit of history out of the story.
Thomson discovered the electron in 1897 so would have known the approximate mass of the atom.
I was going to post a photo of Loschmidt but when I saw what Avogadro looked like I just had to post his photo instead.