Step 1: Understanding the Concept:
Spectral series in hydrogen: Lyman (n=1), Balmer (n=2), Paschen (n=3), Bracket (n=4), Pfund (n=5). Transition from higher \(n_2\) to fixed \(n_1\).
Step 2: Detailed Explanation:
Here, \(n_1 = 3\), so the series is Paschen. Transition from \(n_2 = \infty\) to \(n_1 = 3\) gives the maximum energy and hence the shortest wavelength within the Paschen series.
Step 3: Final Answer:
The transition corresponds to the shortest wavelength of the Paschen series.