If Rydberg’s constant is R, the longest wavelength of radiation in Paschen series will be $\frac{\alpha }{7R}$ where $\alpha =$_________.

Longest wavelength corresponds to transition between n = 3 and n = 4

$\begin{array}{rl} & \frac{1}{\lambda }={\mathrm{RZ}}^2(\frac{1}{3^2}-\frac{1}{4^2})={\mathrm{RZ}}^2(\frac{1}{9}-\frac{1}{16})\\ & =\frac{7{\mathrm{RZ}}^2}{9\times 16}\\ & \Rightarrow \lambda =\frac{144}{7\mathrm{R}}\text{for}\mathrm{Z}=1\therefore \alpha =144\end{array}$