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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?

Qmechanic
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Arturo don Juan
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    Your math is telling you exactly what you expect: that the carbon nucleus is a bound system. – dmckee --- ex-moderator kitten Apr 28 '15 at 04:16
  • 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 04:22
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    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 04:24
  • 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 04:29
  • @dmckee maybe you could help answer my comment right above? – Arturo don Juan Apr 28 '15 at 04:45
  • @userLTK's comment is bang on: binding energy represents the energy needed to get the pieces apart again. – dmckee --- ex-moderator kitten Apr 28 '15 at 04:59
  • Oh ok, I think I get it now. The nuclear potential is very very negative/low (super potential well), so the potential of the ground-state of the bound-state (i.e. the very close nucleon-system called the nucleus) is much lower than when it isn't bound. This lowered energy corresponds to a loss in rest-mass. The energy needed for the system to jump out of the well is the binding energy. Is that right? @dmckee – Arturo don Juan Apr 28 '15 at 05:13
  • Hi Arturo, see the question I've linked. This explains why the binding energy is negative. I made exactly the same mistake when I first started studying physics! – John Rennie Apr 28 '15 at 05:20
  • A bound system has synergy, which releases energy no longer necessary. It's as though the parts are cooperating, so they achieve an efficient bound state at the highest entropy.

    There is a good explanation of why a bound system contains less potential energy than the sum of its parts in the first paragraph of this: http://en.wikipedia.org/wiki/Binding_energy. Also see http://en.wikipedia.org/wiki/Minimum_total_potential_energy_principle

     – Ernie Apr 28 '15 at 06:22
  • Note that the units u and amu are not the same. u is the unified atomic mass unit and it is based on C-12, whereas the amu is based on O (oxigen). – Vera K Jul 25 '17 at 21:41

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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.

Sir Cumference
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gautam1168
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