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How much do neutrons "weigh" and how would one go about "weighing" a neutron?

We know the charge of an electron from Millikan's experiment, and the charge/mass ratio from Thompson's apparatus, hence the mass of an elecgtron. Now we know there are 6.23 x 10^23 atoms per gram of hydrogen (Avogadro) and each consists of an electron and a proton, so we know the mass of a proton.Helium atoms consist of two electrons, two protons, and two neutrons, and we know the density of helium relative to hydrogen, so we can calculate the mass of a neutron.