The smallest wavelength of Lyman series is 91 nm. The difference between the largest wavelengths of Paschen and Balmer series is nearly __________ nm.

N = 4 __________
N = 3 __________ paschen
n = 2 __________ Balmer
n = 1 __________ Lyman
Smallest wavelength of lyman
\( \frac{1}{\lambda}=R(\frac{1}{12}-\frac{1}{\infty^{2}}) \)
\( R=\frac{1}{\lambda}=\frac{1}{91}nm^{-1} \)
\( \lambda_{max} \)
for balmer series
\( n_{1}=2\rightarrow n_{2}=3 \)
\( \frac{1}{\lambda_{B}}=R(\frac{1}{4}-\frac{1}{9}) \)
\( \frac{1}{\lambda_{B}}=\frac{1}{91}(\frac{5}{36}) \)
\( \lambda_{B}=(\frac{91\times36}{5})=655.2nm \)
\( \lambda_{max} \) paschen
\( n_{1}=3\rightarrow n_{2}=4 \)
\( \frac{1}{\lambda_{p}}=\frac{1}{91}(\frac{1}{3^{2}}-\frac{1}{4^{2}})=\frac{1}{91}\times\frac{7}{144} \)
\( \lambda_{p}=(\frac{91\times144}{7})=1872nm \)
\( \Delta\lambda=\lambda_{p}-\lambda_{B}=1872-655.2 \)
\( \Delta\lambda=1216.8 \)
\( \Delta\lambda\approx1217 \)