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What is the difference expressed in kilograms between the mass of a proton and a mass of an electron?
A simple approach can be used to estimate this mass using basic thermodynamics and the ideal gas laws.
1 mole of H2 has a mass very close to 2 grams. H (atomic rather than molecular hydrogen) is made of one proton and one electron, the mass of the electron is negligible when compared to the mass of the proton. 1 mole of H2 contains N H2 molecules where N is the Avogadro constant N = 6.022E23 g per mole: that is 1 mole of H2 has a mass of 2 g. Each H2 molecule has two protons, so we can put
Proton Mass = 1g / 6.022E23 = 1.672 621777(74).10-27 kg.
we divide by 1000 to get the answer in kg,
Proton Mass=1.672 621777(74)×E-27 kg.
In this notation E-1 means 0.1, E-2 means 0.01, E-3 means 0.001, and so on.
The reason it was stated that the mass was very close to two grams comes from the fact that 12 g of C12 has N protons and neutrons which are bound into the carbon nuclei. There is a slight difference between the mass of a proton and a neutron, and there is also the mass deficit from the nuclear binding energy. This makes the above calculation an approximate one.
There are many ways of determining the proton mass experimentally. In recent years computing the proton mass from Quantum Chromo-Dynamics (QCD) which deals with the interactions of quarks and gluons has been a theoretical goal. Any discrepancy between the observed mass and the calculated mass would mean that QCD would have to be re-examined.
Calculating the mass of a proton from scratch requires intensive calculation and super computers. the calculation methods involved in QCD require the usage of theoretical lattice quantum chromodynamics theory which in turn requires some heavy computational processing. A proton is made of 3 quarks (2 up quarks and 1 down quark) and "virtual" gluons zipping between them causing strong forces that holds quarks together to form the proton. Nonsense, I know, but I need to put in a link to particle physics and QCD.
In 2008, the proton mass calculation was completed, and the calculated mass was within the experimetal range of the very latest experimental techniques. So it seems QCD has passed this test.
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