# Why does nuclear fusion not occur with nuclei with a nucleon number higher than 56? Please tell me if I am correct

Please tell me if my assumption is correct. So nuclear fusion does not occur with nuclei (with a nucleon number higher than 56) because the binding energy of the product nucleus is lower than the binding energy of the nuclei fusing together. Due to the product nucleus having a lower binding energy (and thus lower mass defect), this must mean that mass has been gained through the reaction which is impossible because energy is released...????

Please let me know if I am wrong, I am really struggling to understand the concept of binding energy :(

Your understanding is incorrect. For instance the binding energies of an alpha particle (28.30 MeV) and a 56Ni (483.99 MeV) nucleus sum to 512.29 MeV. They fuse to give 60Zn, which has a binding energy of 514.99 MeV. i.e. the reaction is still exothermic.

There are two factors that stop this happening to a great degree in stars.

First, the alpha particle has to come from somewhere. If it has to be ripped out of another 56Ni nucleus then that does require additional energy.

Second, to overcome the increasing Coulomb barrier for fusion onto nuclei with higher proton numbers requires increasingly high temperatures. At these temperatures, the photons in the gas are capable of photodisintegrating the heavier nuclei. Thus they are not present in any great concentration.

Heavier elements are predominantly made by neutron captures and decay.

• I know it was just a typo, but I am today beginning a crusade to establish "aloha particle" as an alternative name for the stable $A=4$ nucleus. – rob Sep 9 '20 at 19:35
• Thanks, my teacher had confused me by saying it was impossible to fuse to heavier nuclei without applying external energy. I didn't know a fusion reaction could still be exothermic after having more than 56 nucleons. Cheers for the help. – Phoooebe Sep 10 '20 at 7:27

I am really struggling to understand the concept of binding energy :(

Binding energy is the difference between the invariant mass of all the nucleons (protons and neutrons)added up, and the invariant mass of the nucleus divided by the number of nucleons. The nucleons (protons and neutrons) are bound because it needs energy to set them free.

Looking at the curve, below the Fe family it is possible to have a new nucleus by the additionof two different nuclei, and end up with smaller binding energy per nucleon, and thus gain energy. The dynamics of binding nuclei to make a nucleus are such that after Fe there is no possibility to have fusion, i.e. gain energy per nucleon by making a nucleus with smaller binding energy per nucleon.