Take 63Cu and as per the definition of binding energy per nucleon it will cost you 8.752 MeV to rip off one nucleon. This is an energy expenditure, it is endothermic.
Now consider the binding energy per nucleon for 62Ni. It is 8.794 MeV per nucleon. This is the end product of ripping a nucleon off of 63Cu all of the other nucleons in the corresponding nuclei are irreverent beyond this specific reaction. The ripped off nucleon is in this case, irrelevant as it has no binding energy associated with it. The weight of the corresponding nuclei is irrelevant, the weight of the nuclei contained in a mole of the isotope is irrelevant (perhaps). If you do consider them complications enter in- see my edit below.The only thing that is relevant is the energy expended to rip off this single nucleon. or conversely to add this nucleon to the selected nuclei or moles worth of the isotope.
63Cu at 8.752 MeV/ nucleon (which is directly proportional to the energy in a mole of 63Cu) Multiplying the binding energy per nucleon by the number of nucleons is not the same as considering a mole of the material(more on this later). This vs 62Ni at 8.794 MeV per nucleon..
So, one mole of 63Cu would require 8.752 MeV * (6.02 *10^23 nuclei / mole ) = x amount of energy to remove this Avagodros number of nucleons from one mole of 63Cu.
One mole of 62Ni would require 8.794 MeV * (6.03 *10^23 nuclei/ mole)= Y
The moles cancel out and the proportions do not change so using the binding energy per nucleon is the same proportionatly of using energy per mole. By using the total energy per nucleon * the number of nucleons in the nucleus, you are getting a measurement involving weight, not moles.
[edit-I think it is legitimate to say that 63 grams of 63Cu has more binding energy than 62 grams of 62Ni, but this does not mean that an equivalent wt of 62 Ni does not have more energy. Still not sure this is what I'm trying to get at. Another way of stating things may be that one mole of 63Cu (~63 grams) has 551.3849 MeV * Avagadro's Number of binding energy. but ~ 63 grams (1.0161 moles) of 62Ni has a total binding energy of 554.0401 MeV * Avagadros Number of binding energy. The 62 Cu is short 2.6539 MeV on a weight to weight comparison. This raises more questions but it does illustrate that you need to consider everything if you are using the total binding energy per nucleus data. The binding energy per nucleon avoids this complication (?). Remember the binding energy per nucleon = the binding energy per mole. Things are still unsettled though. The larger difference compared to the difference due to using the single nucleon reaction above may reflect the appropriate total binding energy difference, but not the competing energy difference. The delta strong force vs delta electromagnetic force change may be reflected in the difference in the two numbers . The Electromagnetic mediated force may have increased by ~ 0.042 MeV more than the strong force contribution, thus this amount of binding energy per nucleon change. The total binding energy per nucleus went up by6.1227 MeV This would fit with the strong force going up by ~ 3.0403 MeV, while the opposing electromagnetic force increased by 3.0823 MeV. This assumes that the delta energy change of the two forces were balanced at 62Ni, and ignores other contributing interactions, but it does (perhaps conviently) shows that the destabilizing electromagnetic mediated effects have become relatively bigger. Remember though, that the strong force has built up a big lead and it will take another ~ 150 nucleon additions before it catches up fully.. ]
The product of ripping off one nucleon from Cu63 is 62Ni. The difference is one free proton which has zero binding energy . The net is that the binding energy of the product nucleus +proton went up compared to the reactant nucleus by the difference of product - reactant.= (8.794 +0) - 8.752. =0.042 MeV . That the binding energy of 62Ni per nucleon (or per mole) went up, means it released energy (attractive binding energy is considered positive in this evaluation- the more common graphical presentation where the 62Ni forms a positive peak on the binding energy per nucleon graph. Reverse the reaction and you will see that the fusion (adding one nucleon) is endothermic- requires energy input) The proton can be ignored, but I included it to keep the book keeping intact. This also illustrates that considering that the proton is somehow contributing energy is faulty. It is essentially along for the ride. What is important is the binding energy of the BOUND nucleons within a specific nucleus. You can not start with the binding energy / nucleon for a certain nucleus, then tear off all of the nucleons and say - see here is the energy released/ or consumed. It ignores the energy balance of all of the steps it took o get there. You have to sequentially proceed one nucleus at a time in the chain and recalculate (or look up ) the relevant binding energy per nucleon for that nucleus, etc. etc. Using the total binding energy would only be a valid predictor of the energy balance if the binding energy per nucleon in different nuclei stayed constant or changed in a linear manner, or intermediates were totally ignored. It does not work because of the competing forces. The relationships are non linear and even reverses- as is obvious when looking at the binding energy per nucleon (or binding energy per mole) of a nucleus/ isotope graph or data tables.
The total binding energy does describe the energy difference between a bound nucleus and the energy of the nucleons that make it up, but only in this absolute sense. It cannot be applied to intermediate steps as the results vary for each step. If nature was all or nothing, either you have completely free nucleons, of you have them bound into selected final nucleus without any intermediate steps, then it is meaningful. But except for H-H fusion or H+Neutron fusion, it occurs only vary rarely or not at all.
Oh no, another analogy
Consider a trip from San Francisco, Ca. to Reno, Nev. You can say you started at Sea Level and ended up at ~ 4,000 ft (?). So the energy expenditure (or gain on the return trip ) was 4,000 ft * a constant.
But, there are mountains in the way. You climb to perhaps ~ 10,000 feet then cost down to ~ 4,000 feet. If you look at the end points alone you have a very distorted view of what is actually occurring.
Considering power output per weight vs molar output can be miss leading. One mole of Uranium 235 fission releases much more energy than one mole of hydrogen (D-T) fusion, but one gram of hydrogen fusion yields much more energy than one gram of uranium. I once saw a formula for energy balance expressed as binding energy per nucleon *A /A. The first A would give you the total binding energy, but they divide by A again! It seemed silly. But, it does keep the bookkeeping in order (I think) while reflecting the true molar relationship of the binding energy per nucleon graph.
And another example on the other side. Rip off a nucleon from 62Ni to leave 61Fe. Binding energy difference between product and reactant is
8.703 MeV - 8.794 MeV = -0.091 MeV. This is negative, implying a endothermic fission, or the reverse - an exothermic fusion. This is reasonable and consistent with the above example and multiple references that unequivocally state that 62Ni is the turning point, the most tightly bound and stable nucleus. Also note that the energy yields or expenditures are closer to what I would expect for reactions close to Ni. This is also widely supported by the literature. You just do not get much energy out of these reactions. That is why a star that reaches this stage is on it's last leg. Using the total binding energy per nucleus to get results of multiple MeV differences bothered me and should have been a red flag to everyone that something was wrong. My two previous attempts to do this comparison was faulty due to the use of the inappropriate data (the total binding energy per nucleus data obtained by BE/nucleon *A) which I was arguing against. Dumb, I know. It didn't help that I screwed the math up also,
http://www.nndc.bnl.gov/amdc/masstables ... mass.mas03
To error is human... and I'm very human.