This week I showed my high school students that if you add the mass of a proton and the mass of an electron the result is higher than the mass of a hydrogen atom, because of the binding energy being negative. I used very precise measurements of the masses, and some student asked how these measurement are actually done. I did some research and found out how you can do it with Penning traps, but in the case of an electron you actually use a carbon ion with only one electron, as it is described here : https://www.mpg.de/7961020/electron-mass
It seems to me that if you use an electron bound to a nucleus, there is binding energy involved. If you get rid of it by quantum physics calculations, then you cannot use this result to show that adding the masses of a proton and an electron gives a mass lower than the mass of an hydrogen atom. It would be a circular argument.
Is there another way to determine the mass of an electron very precisely (not the way Millikan did), without any binding energy involved ?