JEE Main 2023 · 6 April · morning · Single correct · +4 / −1
The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest wavelength is :
- (a) A
- (b) C
- (c) B
- (d) D
Answer and solution
Answer (d) D
Solution
Physics sir · 3 steps
Shortest wavelength means the biggest energy drop, and the largest gaps are the ones down to n = 1.
- Wavelength and energy. The emitted photon carries the energy difference, Δ E = hc/λ. So the shortest wavelength comes from the largest Δ E.
Δ E = 13.6(1/n_f²-1/nᵢ²) eV
- Read the diagram. From the figure, A is 4 → 3, B is 4 → 2, C is 3 → 2 and D is 3 → 1. Put each into the formula.
Transition Jump Δ E Wavelength A 4 → 3 13.6 × 7/144 = 0.66 eV longest B 4 → 2 13.6 × 3/16 = 2.55 eV short, but not shortest C 3 → 2 13.6 × 5/36 = 1.89 eV long D 3 → 1 13.6 × 8/9 = 12.09 eV shortest - So. D releases about 12.1 eV, far more than any other transition, so it emits the shortest wavelength. The answer is (d).
The idea to keep. Since λ = hc/Δ E, the shortest wavelength comes from the biggest energy gap. Hydrogen levels crowd together as n grows, so a jump down to n = 1 beats any jump between the upper levels.
Answer from the NTA final answer key. Solution by PrepWiser.