UPSC Combined Geo-Scientist
Chemist
- 3 descriptive papers
- 200 marks each
- 3 h per paper
Mains Paper II covers physical chemistry.
Quantum chemistry: every question, 2016 to 2025
40 parts worth 271 marks have been set on this unit in UPSC Geo-Scientist Chemistry Mains Paper II from 2016 to 2025. Each one opens on its own page with the question, the answer in brief and the key points.
Eigenfunctions and eigenvalues. Uncertainty relation, expectation value. Hermitian operators. Schrödinger time-independent equation: nature of the equation, acceptability conditions imposed on the wave functions and probability interpretation of wave function. Schrödinger equation for particle in a one-dimensional box and its solution. Comparison with free particle eigenfunctions and eigenvalues. Particle in a 3-D box and concept of degeneracy.
Notes: Postulates of quantum mechanics: operators, eigenfunctions, Hermitian operators and acceptable wave functions (full notes) · short notes
Notes: Uncertainty principle, de Broglie relation and wave–particle duality (full notes) · short notes
2025
- Q1(k) Conditions for an acceptable wave function5 marks Answered
- Q1(l) No solution with E = 0 for the particle in a box5 marks Answered
- Q8 Degeneracy in a rectangular box with a ≠ b ≠ c10 marks Question only
- Q14 Hermitian character of c and of  + B̂20 marks Question only
2024
- Q1(k) Commutator of position and d/dx5 marks Answered
- Q1(l) Meaning and dimensions of |Ψ(x)|²5 marks Answered
- Q8 i d/dx is Hermitian, d/dx is not10 marks Answered
- Q14(a) Non-degenerate and six-fold levels in a cubic box5 marks Answered
- Q14(b) Energies of the two levels for a 0.5 nm box5 marks Answered
- Q14(c) Wavelength of the (2,2,2)–(1,2,3) transition5 marks Answered
2023
- Q1(k) Degeneracy of the level 6h²/8mL² in a cubic box5 marks Answered
- Q1(l) Is Peⁱᵏˣ + Qe⁻ⁱᵏˣ an eigenfunction?5 marks Answered
- Q7(a) Normalising the particle-on-a-ring function5 marks Question only
- Q7(b) Allowed and forbidden wave functions5 marks Question only
- Q11(a) Box length from the longest-wavelength transition10 marks Answered
2022
- Q1(k) Energy uncertainty of an excited state5 marks Answered
- Q1(l) Eigenvalues of a Hermitian operator are real5 marks Answered
- Q7 Degeneracy in a two-dimensional square box10 marks Answered
- Q11(a) Particle in a box and the absorption bands of polyenes10 marks Question only
2021
- Q1(k) Well-behaved functions: two tests5 marks Answered
- Q1(l) Uncertainty in the velocity of an electron5 marks Answered
- Q7 Particle in a box: probability between L/4 and 3L/410 marks Answered
- Q14(a) Degeneracy in a cubic box; states with E = 101h²/8mL²10 marks Answered
- Q14(b) Particle in a box with sides a, b, c: ψ, E and the Laplacian10 marks Answered
2020
- Q1(k) Hermitian operators5 marks Answered
- Q1(l) Probabilities of quantum states5 marks Answered
- Q8 Momentum expectation in a centred box10 marks Answered
- Q11(b) Mean position in a rectangular box10 marks Answered
2019
- Q1(n) Bohr quantisation from matter waves5 marks Answered
- Q6(b) Second-derivative eigenfunctions5 marks Answered
- Q11(c) Degeneracy in a cubic box5 marks Answered
2018
- Q1(n) Particle-in-a-box eigenvalue5 marks Answered
- Q7 Minimum momentum uncertainty of an electron in a 3 nm molecule10 marks Question only
- Q14(d) Commutator [x, pₓ]5 marks Question only
2017
- Q1(l) Momentum eigenfunction6 marks Answered
- Q10(b) Zero-point energy of a harmonic oscillator5 marks Question only
2016
- Q1(l) Ionization of helium ion5 marks Answered
- Q1(n) Momentum in a box5 marks Answered
- Q8(ii) Ground-state oscillator wavefunction3 marks Answered
- Q13(b) Electronic transition in a box7 marks Answered
UPSC Combined Geo-Scientist (Main) Chemistry Paper II: Model Answers 2021 to 2025
- All fifteen questions of each paper, with the question printed above its answer
- Numericals worked from formula to result with units; graphs with labelled axes
- Topic-wise weightage and a topic-wise index