Binding Energy

• What is the definition of binding energy per nucleon?

  Binding energy of a nucleus divided by nucleons

  
• What does a higher binding energy per nucleon indicate?

  Higher stability of the nucleus

  
• What can be inferred from a graph of binding energy per nucleon against nucleon number?

  The stability of elements can be inferred

  
• What are the key features of the binding energy per nucleon graph at high values of A?

  • Higher binding energies per nucleon
  • Gradual decrease with increasing A
  • Heaviest elements are unstable and undergo fission
  • Fission reactions release less binding energy

  
• Which element has the highest binding energy per nucleon?

  Iron (A = 56)

  
• What are the key features of the binding energy per nucleon graph at low values of A?

  • Lower binding energies per nucleon
  • Stable when N = Z
  • Weaker electrostatic forces in light nuclei
  • Fusion reactions release greater binding energy

  
• Why do helium, carbon, and oxygen not fit the trend in binding energy per nucleon?

  They have unique stability characteristics
• What is the significance of Helium-4 in terms of binding energy per nucleon?

  It is a particularly stable nucleus

  
• How can carbon-12 and oxygen-16 be described in relation to helium nuclei?

  They are bound together helium nuclei
• What are the similarities between fusion and fission?

  • Total mass of products is less than reactants
  • Mass defect equals released binding energy
  • Both release energy
• What are the differences between fusion and fission?

  • Fusion combines smaller nuclei; fission splits larger nuclei
  • Fusion occurs in light nuclei (A < 56); fission in heavy nuclei (A > 56)
  • Fusion releases more energy per kg than fission
• What contributes to nuclear stability in light nuclei?

  Attractive nuclear forces dominate over repulsive forces
• What contributes to nuclear instability in heavy nuclei?

  Repulsive electrostatic forces dominate over attractive forces
• What is the equation representing the decay of uranium-235 in fission?

  $^{235}_{92}U +$$^{1}_{0}n \rightarrow ^{91}_{38}Sr +$$^{142}_{54}Xe +$$3^{1}_{0}n$
• How do you calculate the energy released in the fission process?

  1. Identify binding energy per nucleon for isotopes
  2. Calculate binding energy for each isotope
  3. Use the formula: Energy released = Binding energy after - Binding energy before

  
• What is the binding energy of U-235 nucleus?

  $1763 \text{ MeV}$
• What is the binding energy of Sr-91?

  $746 \text{ MeV}$
• What is the binding energy of Xe-142?

  $1235 \text{ MeV}$
• How is the energy released calculated from the fission process?

  Energy released = $(1235 + 746) - 1763$
• What is the energy released from the fission process?

  $218 \text{ MeV}$
• How do you calculate the energy released by 1 kg of uranium-235?

  1. Calculate energy released by 1 mol of U-235
  2. Convert energy from MeV to J
  3. Determine proportion of U-235 in the sample
  4. Calculate total energy released
• What is the energy released by 1 mol of uranium-235?

  $(6 \times 10^{23}) \times 218 \text{ MeV}$
• How do you convert energy released from MeV to J?

  Multiply by $1.6 \times 10^{-13} \text{ J}$
• What is the energy released from 1 kg of uranium containing 3% U-235?

  $2.67 \times 10^{12} \text{ J}$
• What should be included when drawing a graph of binding energy per nucleon against nucleon number?

  • Best fit curve
  • Cross to show helium anomaly
  • Correctly labeled axes and units
  • Numbers on axes, especially at iron's position