Question

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

Answer 1

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

\(\frac{1}{\lambda} = RZ^2(\frac{1}{3^2} - \frac{1}{4^2}) = RZ^2(\frac{1}{9}- \frac{1}{16})\)

\(=\frac{7RZ^2}{9\times 16}\)

\(\Rightarrow \lambda = \frac{144}{7R}\) for Z = 1

\(\therefore \alpha = 144\)