Hydrogen Spectrum & Spectral Series question from MHT CET 2026 (12 May, Shift 2)

Answer: (a)

1. $\frac{1}{\lambda} = R\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$: the first line ($n_2 = n_1 + 1$) has the smallest energy gap, so the longest $\lambda$.
2. The series limit ($n_2 \to \infty$) has the largest gap, so the shortest $\lambda$.
3. So the answer is (a) longest and shortest.