Retrieval Practice — Nuclear Energy & Binding Energy — Nuclear Energy & Binding Energy

Q1. State the equation for mass-energy equivalence and define each term.

E = mc².
E = energy (J), m = mass (kg), c = speed of light (3.0 × 10⁸ m s⁻¹).

Q2. Define the atomic mass unit (u) and state its value in kg and MeV.

One-twelfth of the mass of a carbon-12 atom. 1 u = 1.661 × 10⁻²⁷ kg = 931.5 MeV.

Q3. Define mass defect and state the equation to calculate it.

The difference between the total mass of separated nucleons and the measured mass of the nucleus. Δm = Zmₚ + (A−Z)mₙ − m_total.

Q4. Define binding energy.

The energy required to completely separate a nucleus into its individual protons and neutrons.
Equivalently, the energy released when the nucleus is formed from isolated nucleons.

Q5. Why does iron-56 sit at the peak of the binding energy per nucleon graph?

Iron-56 has the highest binding energy per nucleon (~8.8 MeV), making it the most stable nucleus.
Nuclei lighter than iron can gain stability by fusion; nuclei heavier than iron gain stability by fission.

Q6. Why does fusion require extremely high temperatures?

Both nuclei are positively charged, so electrostatic repulsion must be overcome.
The nuclei need very high kinetic energy to get close enough for the strong nuclear force to bind them.

Q7. Define induced fission.

Fission that occurs when a nucleus absorbs a slow-moving (thermal) neutron and splits into two smaller daughter nuclei, releasing neutrons and energy.

Q8. What is a thermal neutron? State its typical energy and speed.

A neutron in thermal equilibrium with its surroundings.
At ~300 K: kinetic energy ≈ 0.04 eV, speed ≈ 2700 m s⁻¹.

Q9. Define critical mass.

The minimum mass of fissile material needed to sustain a steady chain reaction, where exactly one neutron from each fission event causes another fission.

Q10. State the purpose of the moderator in a nuclear reactor.

To slow down fast fission neutrons to thermal speeds through elastic collisions, so they can be absorbed by U-235 and induce further fission.

Q11. State the purpose of control rods and name two suitable materials.

To absorb excess neutrons and control the rate of fission.
Materials: boron and cadmium.

Q12. How is high-level nuclear waste stored?

Cooled in water ponds for several years, then vitrified (mixed with molten glass), encased in steel/lead/concrete containers, and stored deep underground.

Q13. State one benefit and one risk of nuclear power.

Benefit: produces no greenhouse gases and provides high energy density.
Risk: produces radioactive waste that remains dangerous for thousands of years.

Q14. How do you calculate the energy released in a nuclear reaction from binding energies?

Energy released = total binding energy of products − total binding energy of reactants.
Binding energy of an isotope = binding energy per nucleon × mass number.