Questions & explanations
1. Which of the following statements correctly compares nuclear fission and fusion based on the binding energy per nucleon curve?
- Fission of a heavy nucleus releases energy because the products have lower binding energy per nucleon.
- Fusion of light nuclei releases energy because the product has higher binding energy per nucleon.
- Both fission and fusion release energy because the products have lower binding energy per nucleon.
- Fusion releases more energy per event than fission, but less energy per nucleon.
Answer: Fusion of light nuclei releases energy because the product has higher binding energy per nucleon.
The binding energy per nucleon curve peaks at iron. For light nuclei, fusion moves them toward the peak, increasing binding energy per nucleon and releasing energy. For heavy nuclei, fission does the same. Option b correctly states that fusion products have higher binding energy per nucleon.
2. Why does the fusion of two deuterium nuclei into a helium-4 nucleus release energy?
- Because the binding energy per nucleon of helium-4 is higher than that of deuterium
- Because the mass of helium-4 is greater than the sum of masses of two deuterium nuclei
- Because the Coulomb repulsion between deuterium nuclei is converted into energy
- Because the strong nuclear force is weaker in deuterium than in helium-4
Answer: Because the binding energy per nucleon of helium-4 is higher than that of deuterium
Fusion of light nuclei releases energy because the product nucleus has a higher binding energy per nucleon. For deuterium (A=2), E_b/A ≈ 1.1 MeV; for helium-4 (A=4), E_b/A ≈ 7.1 MeV. The increase in binding energy per nucleon results in a net energy release of about 24 MeV per fusion event.
3. The binding energy per nucleon for U-235 is 7.6 MeV and for medium-mass nuclei is 8.5 MeV. What is the approximate energy released per fission of one U-235 nucleus?
- 200 MeV
- 0.9 MeV
- 211.5 MeV
- 1786 MeV
Answer: 200 MeV
Gain in binding energy per nucleon = 8.5 - 7.6 = 0.9 MeV. For 235 nucleons, total energy released = 0.9 × 235 ≈ 211.5 MeV. However, typical value is about 200 MeV due to neutron losses and fragment distribution. Option a (200 MeV) is the commonly accepted approximate value.
4. A sphere of U-235 has a critical mass of 52 kg. If the same material is shaped into a thin rod, what happens to the critical mass?
- It becomes larger than 52 kg.
- It becomes smaller than 52 kg.
- It remains 52 kg.
- It becomes exactly 26 kg.
Answer: It becomes larger than 52 kg.
Critical mass depends on geometry. A sphere has the smallest surface-to-volume ratio, minimizing neutron leakage. A thin rod has a larger surface-to-volume ratio, so more neutrons escape, requiring more material to achieve criticality. Hence critical mass increases.
5. The mass defect Δm of a nucleus is given by which of the following expressions? (Z = atomic number, A = mass number, m_p = proton mass, m_n = neutron mass, M = nuclear mass)
- Δm = Z m_p + (A - Z) m_n + M
- Δm = Z m_p + A m_n - M
- Δm = (A - Z) m_p + Z m_n - M
- Δm = Z m_p + (A - Z) m_n - M
Answer: Δm = Z m_p + (A - Z) m_n - M
Mass defect is the difference between the sum of masses of individual nucleons and the actual nuclear mass. A nucleus has Z protons and (A - Z) neutrons, so total nucleon mass = Z m_p + (A - Z) m_n. Subtracting nuclear mass M gives Δm = Z m_p + (A - Z) m_n - M.
6. For the fission reaction n + U-235 → Ba-141 + Kr-92 + 3n, the atomic masses are: U-235 = 235.0439 u, Ba-141 = 140.9144 u, Kr-92 = 91.9262 u, n = 1.0087 u. What is the Q-value in MeV?
- 173.3 MeV
- 186.5 MeV
- 200.2 MeV
- 193.8 MeV
Answer: 200.2 MeV
Q = (mass of reactants - mass of products) × 931.5 MeV/u. Reactants: U-235 + n = 235.0439 + 1.0087 = 236.0526 u. Products: Ba-141 + Kr-92 + 3n = 140.9144 + 91.9262 + 3×1.0087 = 235.8667 u. Δm = 0.1859 u. Q = 0.1859 × 931.5 = 173.2 MeV ≈ 173.3 MeV.
7. Why do fusion reactions require extremely high temperatures?
- To overcome the strong nuclear force between nuclei
- To overcome the Coulomb repulsion between positively charged nuclei
- To increase the binding energy per nucleon of the reactants
- To provide enough neutrons to initiate the reaction
Answer: To overcome the Coulomb repulsion between positively charged nuclei
Fusion requires nuclei to come within the range of the strong nuclear force (~1 fm). However, both nuclei are positively charged and experience Coulomb repulsion. High temperature gives them enough kinetic energy to overcome this barrier.
8. In the fission reaction n + U-235 → Ba-141 + X + 3n, what is the missing nucleus X?
- Sr-92
- Kr-94
- Kr-92
- Xe-140
Answer: Kr-92
Conservation of nucleon number A: left side 1+235=236, right side 141 + A_X + 3 = 236 → A_X = 92. Conservation of charge Z: left side 0+92=92, right side 56 + Z_X + 0 = 92 → Z_X = 36. The element with Z=36 is krypton (Kr), so X is Kr-92.
9. Identify the type of nuclear reaction: ²³⁵U + n → ¹⁴¹Ba + ⁹²Kr + 3n
- Fission
- Fusion
- α-decay
- β-decay
Answer: Fission
A heavy nucleus (U-235, A=235) splits into two medium-mass nuclei (Ba-141 and Kr-92) along with neutrons. This is the definition of nuclear fission. Fusion involves light nuclei combining, while α and β decay emit single particles.
10. In a nuclear reactor, fast neutrons of energy 2 MeV are slowed down to thermal energy 0.025 eV. The fission cross-section for thermal neutrons is 600 barns and for fast neutrons is 1 barn. How many times more effective is a thermal neutron compared to a fast neutron in causing fission?
- 6000
- 60
- 600
- 6
Answer: 600
The effectiveness is directly proportional to the fission cross-section. Thermal neutron cross-section is 600 barns, fast neutron cross-section is 1 barn. Ratio = 600/1 = 600. Thus thermal neutrons are 600 times more effective.
11. What is the energy equivalent of 1 atomic mass unit (u) according to Einstein's mass-energy equivalence?
- 1863 MeV
- 465.75 MeV
- 931.5 MeV
- 931.5 J
Answer: 931.5 MeV
According to Einstein's equation E = mc², 1 u = 1.660539 × 10⁻²⁷ kg. Using c = 3 × 10⁸ m/s, the energy equivalent is 1.660539 × 10⁻²⁷ × (3 × 10⁸)² = 1.494 × 10⁻¹⁰ J, which equals 931.5 MeV. Thus, 1 u corresponds to 931.5 MeV.
12. Which of the following statements about binding energy is correct?
- Binding energy is the energy released when a nucleus is formed from its nucleons.
- Binding energy is the energy required to remove one nucleon from the nucleus.
- Binding energy is the energy equivalent of the total mass of the nucleus.
- Binding energy is the energy released when a nucleus undergoes fission.
Answer: Binding energy is the energy released when a nucleus is formed from its nucleons.
Binding energy is defined as the energy required to disassemble a nucleus into its individual nucleons, which is equal to the energy released when the nucleus is formed from free nucleons. This energy is given by E_b = Δm c².