Q2(a). Emission and eigenvalues in a box
(i) Find the wavelength of the light emitted when 5 × 10⁻²⁸ g particles in a 3 Å one-dimensional box goes from n = 2 to n = 1 level. (ii) Verify Ĥψ = Eψ for the particle in a one-dimensional box. (8+7 marks)
Answer in brief
The emitted wavelength is 5.43 × 10⁻⁸ m, or 54.3 nm. The sine functions satisfy the Hamiltonian eigenvalue equation with Eₙ = n²h²/(8mL²).
Part of VKC Basic
Read the key points and the full model answer with VKC Basic
VKC Basic (₹999 for 6 months) opens every solved answer, the notes, the handbook and the daily answer archive. Every Mains test series includes it.
The full model answer
As written for the answer booklet: the diagram carries the working, the lines stay short. Read here only; it is not offered as a download.
Coversparticle in a one-dimensional boxeigenvalue equationHamiltonian operatoremission wavelengthenergy levels
All parts of Question 2
- 2(a) Emission and eigenvalues in a box15 marks
- 2(b) NO and the nitrosonium ion15 marks
- 2(c) Bond orders of oxygen and carbon monoxide10 marks