# Protons and Neutrons Overshoot Actual Mass? [duplicate]

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When I add up the mass of 6 protons and 6 neutrons in amu, I get a mass that is greater than the mass of carbon. I thought that it should be the other way around, because I have not including binding energy when I add up the mass of the protons and neutrons.

Proton: 1.007276466812 u

Neutron: 1.00866491600 u

6(1.007276466812)+6(1.00866491600)=12.099

Carbon: 12 u

Why is this so?

## marked as duplicate by John Rennie, Martin, Emilio Pisanty, Kyle Kanos, ACuriousMind♦Apr 28 '15 at 15:21

• Your math is telling you exactly what you expect: that the carbon nucleus is a bound system. – dmckee Apr 28 '15 at 4:16
• So the binding energy of carbon is 0.099u. Since 1u is approx. the mass of a proton, the binding energy would be one tenth of the proton mass, which is 938MeV. That gets us a carbon binding energy of around 93MeV, or so. The exact number seems to be 92.15MeV. Good job! – CuriousOne Apr 28 '15 at 4:22
• The way my chemistry teacher explained it years ago, (He was talking chemical bonds, not atomic), but he said, look at it this way, it takes energy to break bonds, so forming bonds releases energy. A proton weighs X a neutron ways Y, so a Proton bound to a Neutron weighs X + Y minus some binding energy. – userLTK Apr 28 '15 at 4:24
• Could any of you address why it isn't the other way around? I though binding energy added to the mass. – Arturo don Juan Apr 28 '15 at 4:29
• @dmckee maybe you could help answer my comment right above? – Arturo don Juan Apr 28 '15 at 4:45

$$E_{\text{binding}} = (M_{\text{constituents}}-M_{\text{BoundState}})c^2$$