Stellar nuclear fusion begins with 1 H and ends with 56 Fe. Younger stars fuse h

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?

Explanation / Answer

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 %

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.