Discussion
The shortest wavelength observed in Paschen back series of hydrogen spectra is (RH = 10967757·6 m−1)
Answer: D
The shortest wavelength is 8205 Å (the paper's 'Paschen back series' means the Paschen series).
Paschen lines end on \( n = 3 \). The shortest wavelength is the series limit, an electron falling from \( n = \infty \):
\[ \begin{aligned} \frac{1}{\lambda} &= R_{H}\left(\frac{1}{3^{2}} - 0\right) \\ \lambda &= \frac{9}{10967757.6}\ \text{m} \approx 8206\ \text{\AA} \end{aligned} \]
The option gives this limit as 8205 Å. 7800 Å and 7349 Å are shorter than the limit, so they cannot be Paschen lines at all, and 9546 Å, longer than the limit, belongs to a transition from a finite upper level, not the shortest line.
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