Atomic Mass Units: Discrepancy Explained?

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The discussion centers on the confusion regarding the mass of the carbon-12 atom being defined as exactly 12 atomic mass units (amu), despite the combined mass of its protons and neutrons exceeding this value. The key point is that the mass of a carbon-12 atom accounts for the binding energy that holds the nucleus together, which effectively reduces its overall mass. This binding energy results from the strong nuclear force, and when protons and neutrons are bound within an atom, they exhibit a different mass than when they are isolated. The apparent discrepancy arises from the difference between the mass of individual nucleons and the mass of the nucleus as a whole, highlighting the importance of binding energy in nuclear physics.
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Been many years since I took general and org chem and am currently reading general chem textbook as refresher. Came across defintion of amu (atomic mass unit). Text says that the mass of the carbon-12 atom is defined to be exactly 12 amu. However, a couple of pages over, I read that the mass of the proton is about 1.007 amu, and the mass of the neutron is about 1.009 amu. Add up the masses of 6 protons and 6 neutrons for the carbon-12 atom, and you come up with more than 12 amu. I can't resolve this apparent discrepancy. I've consulted other texts, etc. Does some type of relativistic effect bear on this situation? In other words, does, for example, an isolated proton have a mass of 1.007 amu, but then when part of an atom have a slightly different mass because of some relativistic effect? HELP!
 
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The mass difference is the "binding energy" for 12C.
 
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