Ratio of wavelength of series limit of Paschen and Brackett series for a single electronic species is :

$\frac{1}{\lambda }=R\cdot \left(\frac{1}{n_f^2}-\frac{1}{n_i^2}\right)$

Here

• $\mathrm{R}$ is the Rydberg constant, equal to $1.097\cdot {10}^7{\mathrm{m}}^{-1}$
• $n_i$ is the initial energy level of the electron
• $n_f$ is the final energy level of the electron 

$\frac{1}{\lambda }=R{Z}^2\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right]$

$\begin{array}{r}\frac{1}{{\mathrm{\lambda }}_p}=R{Z}^2\left[\frac{1}{9}-\frac{1}{\mathrm{\infty }}\right]\\ \frac{1}{{\lambda }_B}=R{Z}^2\left[\frac{1}{16}-\frac{1}{\mathrm{\infty }}\right]\end{array}$

$\frac{\lambda P}{\lambda B}=\frac{9}{16}$