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As I was studying chemistry, I encountered atomic mass units (amu) and based on some calculations, I realized that some numbers don't work out.

Apparently, 12 amu is the mass of a single carbon-12 atom. However, the mass of the atom is (mainly) composed of six protons and six neutrons. Since both protons and neutrons weigh a tad more than 1 amu, how is this possible?

Furthermore, if it were true, that would convey that 1 amu is more than $1.661 \times 10^{-24}$ grams. It doesn't work out even without considering electrons. Did we get the numbers wrong, or the mass of an atom of C-12 more than 12 amu?

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marked as duplicate by Curt F., Jan, Todd Minehardt, ringo, M.A.R. Jun 25 '16 at 7:53

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  • $\begingroup$ When protons and neutrons are bound together by the strong nuclear force, some energy is released -- and, since $E=mc^2$, a little mass goes with it. en.wikipedia.org/wiki/Nuclear_binding_energy $\endgroup$ – Oscar Lanzi Jun 24 '16 at 22:43
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    $\begingroup$ Also note that the unified atomic mass unit $\mathrm u$ should not be confused with the obsolete atomic mass unit $\mathrm{amu}$ (which is deprecated since 1961). The atomic mass of C-12 is about $12.0005\ \mathrm{amu}$ (as used in chemistry until 1961) or $12.0000\ \mathrm u$ (by definition, since 1961). However, this small difference is not related to your actual question. $\endgroup$ – Loong Jun 24 '16 at 22:57

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