For the Balmer series, in the spectrum of H atom, v = RH\1n12 - 1n22\, the correct statements among (I) to (IV) are:…

🧠 Decoding the Balmer Truths The Balmer series is our window into the atom. It describes any electron falling to the second shell ($n=2$). As the electron falls from higher and higher shells, it releases more energy, which means shorter wavelengths. But there's a limit—shells aren't infinite!

🗺️ The Statement Audit

• (I) True: Spectral lines cluster (converge) as $n \to \infty$. This is because the energy levels $E_n = -13.6/n^2$ get closer and closer near the ionization limit.
• (II) True: By definition, the Balmer series corresponds to transitions ending at $n_1 = 2$.
• (III) True: Longest wavelength = Smallest energy. The smallest jump possible to level 2 is from level 3.
• (IV) False: These lines tell us about level $n=2$. To calculate Ionization Energy, we need the energy required to go from $n=1 \to \infty$ (Lyman series).

⚡ The "Energy Gap" Visual Think of the energy levels as steps on a ladder. The bottom steps are far apart ($1 \to 2$ is huge). The top steps are tiny ($100 \to 101$ is almost nothing). That's why statement (I) is always true for any series!

⚠️ Common Traps Statement (IV) is the subtle one. You could theoretically use Balmer lines to find the Rydberg constant, and then calculate IE. But the statement implies you can read IE directly from the series wavenumber, which is incorrect.

$\boxed{\text{Answer: (B)}}$