Mass Defect and Binding Energy - UNSOLVED PRACTICE SET
Chapter: Nuclei | Topic: Mass Defect and Binding Energy
MASS DEFECT AND BINDING ENERGY - UNSOLVED PRACTICE SET
Topic: Mass Defect and Binding Energy
Multiple Choice Questions
Q1. The mass defect of a nucleus is defined as:
- The difference between the mass of the nucleus and the mass of its protons
- The difference between the sum of masses of individual nucleons and the actual mass of the nucleus
- The mass of the nucleus divided by the mass number
- The mass of the electrons in the atom
Q2. The binding energy of a nucleus is:
- The energy required to remove one nucleon from the nucleus
- The energy required to completely separate all nucleons from the nucleus
- The energy released when one nucleon is added to the nucleus
- The kinetic energy of nucleons inside the nucleus
Q3. The binding energy is related to the mass defect by:
- E_b = ฮm ร c
- E_b = ฮm ร cยฒ
- E_b = ฮm / cยฒ
- E_b = ฮm ร cยณ
Q4. 1 atomic mass unit (u) is equivalent to an energy of approximately:
- 1 MeV
- 931.5 MeV
- 13.6 eV
- 511 keV
Q5. The mass defect is always:
- Positive
- Negative
- Zero
- Either positive or negative
Q6. The packing fraction is defined as:
- The binding energy per nucleon
- The mass defect divided by the mass number
- The difference between the actual mass and the mass number, divided by the mass number
- The total mass of the nucleus
Short Answer Questions
Q7. Define mass defect and binding energy. How are they related?
Q8. Calculate the mass defect and binding energy for a helium-4 nucleus (mass = 4.0026 u). Given: mass of proton = 1.0073 u, mass of neutron = 1.0087 u.
Q9. Why is the mass of a nucleus always less than the sum of the masses of its constituent nucleons?
Q10. What is the significance of binding energy in understanding nuclear stability?
Q11. Calculate the binding energy per nucleon for carbon-12 (mass = 12.0000 u).
Q12. Explain how Einstein's mass-energy equivalence (E = mcยฒ) is demonstrated in the concept of binding energy.
Long Answer Questions
Q13. Define mass defect and binding energy. Derive the relationship between them using Einstein's mass-energy equivalence. Explain why the mass defect arises.
Q14. Explain the process of calculating binding energy from mass defect. Describe the steps involved and discuss the significance of binding energy in determining nuclear stability.
Q15. Compare the concepts of mass defect, binding energy, and binding energy per nucleon. Explain how each of these quantities provides different information about the nucleus.
Numerical & Application-based Problems
Q16. For an oxygen-16 nucleus (mass = 15.9949 u):
(a) Calculate the mass defect.
(b) Calculate the total binding energy in MeV.
(c) Calculate the binding energy per nucleon.
(d) Compare this with the binding energy per nucleon of helium-4 (mass = 4.0026 u).
Q17. A deuteron (ยฒH nucleus) has a mass of 2.0141 u. The mass of a proton is 1.0073 u and the mass of a neutron is 1.0087 u.
(a) Calculate the mass defect of the deuteron.
(b) Calculate the binding energy of the deuteron in MeV.
(c) Calculate the binding energy per nucleon.
(d) Explain why the deuteron's binding energy per nucleon is much less than that of helium-4.
Q18. In your school's physics exhibition, a student presents a project on nuclear binding energy.
(a) She calculates the binding energy of iron-56 (mass = 55.9349 u). Calculate the mass defect and total binding energy. Given: m_p = 1.0073 u, m_n = 1.0087 u.
(b) She then explains that iron-56 has one of the highest binding energies per nucleon. Calculate this value and explain why this makes iron-56 particularly stable.
(c) The student compares the binding energy of uranium-235 (mass = 235.0439 u) with that of iron-56. Calculate the binding energy per nucleon for uranium-235 and explain why energy is released when uranium undergoes fission.
(d) A classmate asks why we don't get energy by combining iron nuclei into heavier elements. Explain using the concept of binding energy per nucleon and the shape of the binding energy curve.
(e) In India's nuclear power program at NPCIL (Nuclear Power Corporation of India Limited), understanding binding energy is crucial. Explain how the mass defect in fission of uranium-235 translates into usable electrical energy, and calculate the energy released when 1 kg of uranium-235 undergoes complete fission (assume 200 MeV per fission event).