UPSC Combined Geo-Scientist, Mains · 2026 · Mains Paper II
Q1(p). Non-radiative decay competing with fluorescence
Question
An excited molecule can lose energy without emitting light. Name two non-radiative decay processes and explain one reason why these processes compete with fluorescence.
Answer in brief
Internal conversion (S₁→ S₀, same spin) and intersystem crossing (S₁→ T₁). They compete because they are first-order processes of similar rate, so Φ_f=k_f/(k_f+k_(IC)+k_(ISC)+k_q[Q])<1.
Key points
- an isoenergetic radiationless step to a high vibrational level of a lower electronic state of the same multiplicity; fast when the vibrational overlap is large (small energy gap, flexible molecule).
- a spin-forbidden change to the triplet state, helped by spin–orbit coupling (heavy atoms).
- fluorescence rate k_f≈10⁷–10⁹ s⁻¹ is only slightly faster than k_(IC) and k_(ISC); all channels deplete S₁ in parallel, so the fluorescence quantum yield and lifetime τ=1/(k_f+k_(IC)+k_(ISC)) are reduced.
The full model answer
Worked out step by step, as it should go in the answer booklet. The solution sheet follows it.
- Internal conversion: an isoenergetic radiationless step to a high vibrational level of a lower electronic state of the same multiplicity; fast when the vibrational overlap is large (small energy gap, flexible molecule).
- Intersystem crossing: a spin-forbidden change to the triplet state, helped by spin–orbit coupling (heavy atoms).
- Why they compete: fluorescence rate k_f≈10⁷–10⁹ s⁻¹ is only slightly faster than k_(IC) and k_(ISC); all channels deplete S₁ in parallel, so the fluorescence quantum yield and lifetime τ=1/(k_f+k_(IC)+k_(ISC)) are reduced.
Coversdecay of excited statesNon-radiative decay competing with fluorescence
All parts of Question 1
- 1(a) Compressibility factor and its significance5 marks
- 1(b) Andrew's isotherms and the critical-point conditions5 marks
- 1(c) First-order Bragg angle for the (110) planes5 marks
- 1(d) Intrinsic semiconductor and its conversion to extrinsic5 marks
- 1(e) Fugacity against pressure of a non-ideal gas5 marks
- 1(f) Kₚ and K_c for A+B⇌ C5 marks
- 1(g) Half-life of a nuclide with two parallel first-order decays5 marks
- 1(h) Soap and detergent5 marks
- 1(i) Galvanic cell for 2 Cu⁺leftharpoonsCu²⁺+Cu5 marks
- 1(j) pH when a weak base is 65% neutralised5 marks
- 1(k) Uncertainty in an energy eigenstate5 marks
- 1(l) Expectation value and eigenvalue5 marks
- 1(m) Normal modes of vibration5 marks
- 1(n) Raman activity and polarisability ellipsoids of CO₂5 marks
- 1(o) The incorrect statement on electronic spectra5 marks
- 1(p) Non-radiative decay competing with fluorescence5 marks