d
For longest wavelength in Paschen's series:

\(\frac{1}{\lambda}=\mathrm{R}\left[\frac{1}{\mathrm{n}_1{ }^2}-\frac{1}{\mathrm{n}_2{ }^2}\right]\)

\(\text { For longest } \mathrm{n}_1=3\)

\(\frac{1}{\lambda}=\mathrm{n}\left[\frac{1}{(3)^2}-\frac{1}{(4)^2}\right]\)

\(\frac{1}{\lambda}=\mathrm{R}\left[\frac{1}{9}-\frac{1}{16}\right]\)

\(\frac{1}{\lambda}=\mathrm{R}\left[\frac{16-9}{16 \times 9}\right]\)

\(\Rightarrow \lambda=\frac{16 \times 9}{7 \mathrm{R}}=\frac{16 \times 9}{7 \times 1.097 \times 10^7}\)

\(\lambda=1.876 \times 10^{-6} \mathrm{~m}\)