A bit confused about binding energy and fusion?

Question

So I've heard either nickel-62 or iron-56 is the heaviest nucleus you can produce exothermically by fusion, because these have the highest binding energy per nucleon or lowest mass per nucleon respectively. But if I look up the masses of these isotopes, and then consider trying to fuse them with helium, it looks like it should be exothermic. E.g.

56Fe + 4He -> 60Ni

55.9349375 u + 4.002602 u = 59.9375395 u > 59.9307864 u

62Ni + 4He -> 66Zn

61.9283451 u + 4.002602 u = 65.9309471 u > 64.9292410 u

I considered that I should be using masses of ionized nuclei, but even if I use the mass of the alpha particle instead of neutral helium, I still get more mass on the left hand side. If anything that underestimates the extra left-hand-side mass. For the bigger atoms, subtracting out the electrons should remove more from the right hand side, which has all the same electrons as the left hand side plus two more.

It occurs to me that there should be no rule about fusion getting past the binding energy per nucleon peak. The only rule should be that you can't fuse two elements that are *both* above the binding energy per nucleon peak. Say you try to fuse two elements with BEPN a and b, and m and n nucleons respectively. Then to be exothermic the resulting nucleus has to have BEPN c

c > (am + bn) / (m + n)

If both a > c and b > c then (am + bn) / (m + n) > (cm + cn) / (m + n) = c, so it's impossible. But if either a < c or b < c then it's possible. This is the case where am is for 62Ni, bn is for 4He, and c is for 66Zn. b < c < a.

But I'm explicitly told here - http://en.wikipedia.org/wiki/Alpha_process - that a similar reaction 56Ni + 4He -> 60Zn is endothermic. I checked that one out too and yeah the reactant masses add up to more than the product mass.

What's the deal?

Update:

Hmm, maybe I get it. 56Ni + 4He is exothermic, but there is no original helium left in those stars that are doing that reaction. The He comes from photodisintegration, e.g. 56Ni + gamma -> 52Fe + 4He, which is endothermic. So the complete reaction is

2x56Ni -> 56Ni + 52Fe + 4He -> 52Fe + 60Zn

2x55.942132 u = 111.884264 u < 51.948114 u + 59.941827 u = 111.889941

Is that right?

Dozo · Accepted Answer

I do not see your point. The mass per nucleon of iron is 55.9349375/56 = 0.99884 which is less than that of nickel (59.9375395/60 = 0.99896). Clearly, remvoing nucleons from iron therefore costs more energy than removing nucleons from nickel and thus iron is the more stable one.

? · Answer

"yet do no longer you decide on capability to bind the nucleons jointly (binding capability)?" No. The opposite is actual. 'Binding capability' ability the quantity of capability mandatory to cut up issues (because of the fact they entice); it rather is a very deceptive call. for instance, if the binding capability of two debris is 100MeV, which ability to fully separate the sure debris you ought to grant 100MeV. If the mass of the sure debris is M1 and the finished mass of the two separate debris is M2, then M2>M1. The mass has been greater advantageous slightly via placing apart the debris. M2-M1 is spoke of as the mass disease, or mass distinction. in this occasion, using E=mc², you may discover 100MeV is reminiscent of the mass distinction. you have presented 100MeV of capability and because capability is reminiscent of mass, the finished mass of the gadget has greater advantageous. If the separated debris connect jointly the opposite is actual. They lose mass - the quantity of mass lost is the mass disease. The lost mass is converted into capability and released. capability released = (M2-M1)c². in the reaction ²H + ³H --> ?He + n the mass of ²H + ³H is a little greater advantageous than the mass of ?He + n. The lost mass (the mass disease) is became into capability and released, oftentimes in the style of the kinetic capability of the debris, yet in addition as some gamma photons. desire that enables.

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A bit confused about binding energy and fusion?

2 Answers