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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?

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    $\begingroup$ Your math is telling you exactly what you expect: that the carbon nucleus is a bound system. $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Apr 28, 2015 at 4:16
  • $\begingroup$ 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! $\endgroup$
    – CuriousOne
    Commented Apr 28, 2015 at 4:22
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    $\begingroup$ 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. $\endgroup$
    – userLTK
    Commented Apr 28, 2015 at 4:24
  • $\begingroup$ Could any of you address why it isn't the other way around? I though binding energy added to the mass. $\endgroup$
    – Arturo don Juan
    Commented Apr 28, 2015 at 4:29
  • $\begingroup$ @dmckee maybe you could help answer my comment right above? $\endgroup$
    – Arturo don Juan
    Commented Apr 28, 2015 at 4:45

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You are getting the right thing. This is the binding energy formula.

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

When the constituents come together to form a bound state the total mass is lowered not raised. Binding energy is the energy corresponding to the mass lost by the constituents as a result of them entering the bound state.

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