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Let's perform two simple calculations and then formulate the relative questions.

  1. By checking Wikipedia, one can know the mass of neutron and proton: $$M_{neutron}=939.5654133(58)MeV/c^2=1.674927471(21)×10^{−27} kg$$ $$M_{proton}=938.2720813(58) MeV/c^2=1.672621898(21)×10^{−27} kg$$ and the neutron (proton) is composed of two down (up) quarks and one up (down) quarks. Also by checking Wikipedia, one can know the mass of up quark and down quark, respectively. $$M_{up-quark} \approx 2.3MeV/c^2 \approx 4.1 \times 10^{-30} kg \qquad M_{down-quark} \approx 4.8Mev/c^2 \approx 8.6 \times 10^{-30} kg $$ One can see immediately that $$M_{neutron} >> 2\times M_{down-quark}+1 \times M_{up-quark}$$ $$M_{proton} >> 2\times M_{up-quark}+1 \times M_{down-quark}$$ One can also see only one percent of the total mass of the neutron/proton is contributed by their building blocks (up- and down- quarks)!So my first question is where is the mass of neutron?

  2. We can perform the similar calculations for Helium-4, which is composed of two protons and two neutrons. By checking Wikipedia, one can also know the mass of helium-4. But we have the following inequality: $$M_{helium-4}=6.645 \times 10^{-27}kg<2\times M_{proton}+2\times M_{neutron}=6.695\times 10^{-27}kg$$ So my second question is: what's the additional mass of helium-4 atom?

My final question is about what's the difference between calculation one (far greater than their constituents )and calculation two (lesser than their constituents)?

Jack
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  • You seem to be trying to re-discover the so-called "constituent quark model", which works reasonable well as a rough estimator of baryon masses once you extend it to more quark types and a binding contribution. But the binding contribution is important. – dmckee --- ex-moderator kitten Feb 27 '18 at 16:07
  • Have a look at this https://profmattstrassler.com/articles-and-posts/largehadroncolliderfaq/whats-a-proton-anyway/ . Most of the mass of the proton and neutron come from the sea of quarks antiquarks and gluons, consequence of QCD strong interactions. – anna v Feb 27 '18 at 17:10

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