Adigrat University
Department of Chemistry
Assignment Guidelines:
All students are required to attempt every question to ensure a comprehensive understanding of
quantum chemistry concepts. However, your group submission should focus exclusively on your assigned
questions as specified in the group distribution below.
Group 1 Question numbers: 1, 5, 9, 13, and 17
Group 2 Question numbers: 2, 6, 10, 14, and 18
Group 3 Question numbers: 3, 7, 11, 15, and 19
Group 4 Question numbers: 4, 8, 12, 16, and 20
Submission Deadline: Friday, August 22, 2025
1. How does the classical wave theory fail to explain blackbody radiation, and how did Planck resolve
this issue?
2. What experimental observations in the photoelectric effect could not be explained by classical physics?
3. How does Einstein’s explanation of the photoelectric effect support the particle nature of light?
4. How does the Compton effect provide evidence for the particle nature of light?
5. Why do atoms emit line spectra rather than continuous spectra?
6. What experimental observations led to the failure of Rutherford’s atomic model?
7. What limitations does the Bohr model face when applied to multi-electron atoms?
8. How does de Broglie’s hypothesis explain the quantization of electron orbits in Bohr’s model?
9. Describe the experimental evidence supporting the wave nature of particles.
10. How does Heisenberg’s uncertainty principle challenge classical notions of measurement?
11. Compare the predictions of classical and quantum mechanics for a particle in a box.
12. Calculate the probability of finding the particle between x = L/4 and x = L/2 for n = 1. Contrast
the probability density |ψn (x)|2 for n = 1 and n = 10.
13. Derive the allowed energy levels for a particle confined to a ring. How does quantization arise in this
system?
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14. What are the eigenfunctions and eigenvalues for a particle moving freely on the surface of a sphere?
Relate them to angular momentum quantization.
15. How is the harmonic oscillator model applied to describe the vibrational spectra of diatomic molecules?
What is the limitation of this model?
16. Using the hydrogenic wavefunctions, prove that r for the 3d orbitals is greater than for 4s, despite
the latter having higher principal quantum number. What physical principle does this demonstrate?
17. In the presence of a weak magnetic field, the 2p level splits into 5 states. Draw the energy level
diagram and calculate the splitting using first-order perturbation theory.
18. Contrast Raman and IR selection rules. Why is N2 Raman-active but IR-inactive? How does
resonance Raman spectroscopy enhance sensitivity?
19. Why are approximation methods necessary in quantum chemistry, particularly for many-electron
systems like the helium atom? Contrast this with exactly solvable systems (e.g., the hydrogen atom).
20. Explain the challenges in solving the Schrödinger equation for the helium atom analytically. How
does the electron-electron repulsion term complicate the problem, and what approximation methods
are typically employed?
Important Notes:
• Submissions received after the deadline will not be considered.
• All group members must contribute equally
• Plagiarism will result in zero marks.
