Question

Stellar nuclear fusion begins with ¹H and ends with ⁵⁶Fe. Younger stars fuse hydrogen to form ⁴He, while older, more massive stars fuse Helium to form heavier elements. Fusion beyond ⁵⁶Fe is impossible because iron-56 has the greatest binding energy per nucleon. Calculate the binding energy per nucleon of ⁵⁶Fe and use it to calculate the maximum total energy per mole of ⁵⁶Fe that could be released through nuclear fusion. What percentage of the maximum total energy is released by the formation of ⁴He?

Answer 1

Number of protons in 56 Fe = 26

Number of neutron in 56 Fe = 30

Energy of protons = 26 x mass of protons x 931.5 MeV ( since 1 amu = 931.5 MeV) = 26 x 1.007825 x 931.5 = 24408.5 MeV

Energy of neutrons= 30 x mass of neutrons x 931.5 MeV ( since 1 amu = 931.5 MeV) = 30 x 1.008665 x 931.5 = 28187.1 MeV

Energy of 56 Fe = 55.934937 x  931.5 MeV ( since 1 amu = 931.5 MeV) = 52103.4 MeV

Therefore Binding Energy = 28187.1 + 24408.5 - 52103.4 MeV = 492.2 MeV

Therefore Binding Energy per nucleon = 492.2 MeV / 56 = 8.789 MeV

Total energy released by one mole of 56 Fe = 6.023 x 10²³ x 56 x 8.789 MeV = 2.964 x 10²⁶ MeV

Binding energy of He can be calculated in a similar fashion and comes out to be 28.3 MeV

% of energy coming from the fusion of H to He = 28.3 x 100/ 492.2 = 5.75 %