Question

How are the atoms actually weighed? Are they weighed by some kind of weighing machine accurately or is their weight just approximately calculated?

Answer 1

There is no way to determine the atomic mass or molecular mass directly. They are determined from vapour density ( molecular mass = 2 x vapour density) and other methods. Another one factor is atomic mass is not at all related with mass of an atom. Mass of an atom will come in the order of 10^-23g but atomic mass data we are giving in numbers without any exponential terms. So atomic mass is the ratio of mass of one atom to the mass of 1/2 of Carbon-12 atom. It is simply ratio.