Or BE/ nucleon *A / A/mole, ie: Binding energy per nucleon = binding energy per mole.
Now the multiplication by A (atomic wt) then immediately divided by A makes sense.
Remember that a proton does not have binding energy. And, actually a nucleus does not have binding energy per say, but potential energy. The binding energy is expressed as the energy you have to expend to remove all of the nucleons from a selected nucleus. . This makes the convention of using negative values for the binding energy convenient. The binding energy of free protons and neutrons is zero. The bound nucleus has some negative binding energy that has to be overcome to reach the zero binding energy of the unbound nucleons is zero. This added (positive) energy is the kinetic energy that needs to be added to demolish the nucleus into it's individual nucleons. . The negative convention does not need to be used, it is just convenient.
http://www.chem.purdue.edu/gchelp/howto ... gy.htm#Top
We have been arguing apples and oranges. When I say 62Ni has the highest binding energy per nucleon, I am also saying that 62Ni has the highest binding energy per mole.Using the above negative convention this is easily translated as 62Ni has the lowest potential energy of any nucleus which is directly proportional to saying has the most binding energy per nucleon or per mole. When comparing energy levels via the binding energy per nucleus. It is a per unit of weight comparison, not a per mole basis. we have been comparing the energy associated with 63 grams of 63Cu compared to 62 grams of 62Ni. As I said, the free nucleons have zero binding energy, so they can be ignored. We are talking about the binding energy in specific bound nuclei, It makes no difference what other ingredients may have been involved, it is the end bound nuclei that are being compared.Expressing Nuclear Binding Energy as Energy per Mole of Atoms, or as Energy per Nucleon
The energy calculated in the previous example is the nuclear binding energy. However, nuclear binding energy is often expressed as kJ/mol of nuclei or as MeV/nucleon.
If you are comparing the explosive power of a hydrogen- oxygen mixture, with a methane- oxygen mixture, the costs of electrolyzing the hydrogen from water or the mining of methane or the photosynthesis of the oxygen are external to this consideration. You have two items, and the comparison is between them. It becomes more complicated with three or more items, but the comparison holds.
If you calculate the atomic weight difference, you need to correct for the different masses per mole. The missing mass is a portion of this, but only a small portion. To compare the two you need to incorporate this mass difference. The binding energy per nucleon or per mole tells you how much the missing mass contributes. to this correction.
Basically the comparison would be the binding energy per nucleon. If you prefer the binding energy per nucleus. for this comparison you would need to consider 63 g of nickel to 63 g of Copper. A measure of 63 g of nickel = 63g/ 62 g/ mole = 1.016 moles of Ni. Or conversely 62 g of Cu/ 63g/mole Cu = 0.984 moles of Cu. This correction needs to be multiplied to the total binding energy / nucleus. This will give you the binding energy difference of any number of comparable nuclei, when starting with nearly equal masses of the test nuclei. It is unfair to say that 63 grams of Cu has more binding energy than 62 grams of Ni. This is a round about way of getting back to the binding energy per nucleon data.
Eg:
62Ni BE/nucleon (or mole)= 8.794 MeV per mole * 1.016 moles = 8.934 MeV/ g * 63 g of 62Ni. = Total binding energy of 562.84 MeV
63Cu BE/ mole = 8.752MeV / mole = 8.752 MeV *1.000 moles = 8.752 MeV/ g * 63 g of 63Cu = Total binding energy of 551.37 MeV.
Now it is apparent that near equal masses of 62Ni has more binding energy than the corresponding mass of 63Cu. This is a direct comparison of the missing mass + real mass mass of the coresponding isotopes. The values are skewed somewhat in terms of the actual binding energy effect because both the strong force contribution and the electromagnetic contribution to this one nucleon different comparison at the Iron plateau is close. It is the excess of one over the other for this particular step that determines the actual balance . But, this does demonstrate that equal masses of these two isotopes have different binding energies and that the Ni isotope actually has more on a weight basis as well as a molar basis . This is the opposite of what would be suggested on a molar basis by ignoring the different molar masses as is the case with the total binding energy per nucleus data.
This is a roundabout way to derive the energy balance but it illustrates the fallacy of considering the binding energy per nucleus relationship only. Instead of all this convoluted calculation it is more direct to just use the binding energy per nucleon (mole). With this approach. The binding energy / nucleon * atomic wt/ atomic wt/ mole gives the binding energy per mole, which is the initial number. This implies the appropriate use of this data for determining energy change per units of moles. The binding energy per nucleus is a weight dependent measure. and care has to be taken to correct for different weights.
As I mentioned, the actual balance ( energy in or out) is more complicated due to the competing forces that make up the total, and in this region the competing effect is more profound. Further away from this turning point, the binding energy per nucleon (or mole) gives more accurate results as the dominating effect of the faster growing force comes closer to the total.
Dan Tibbets
