Question

Determine the series limit of Balmer, Paschen and Bracket series, given the limit for Lyman series is 912 Å.

Answer 1

Data : \(\lambda _{L\infty}\) = 912 Å

For hydrogen spectrum, \(\cfrac{1}{\lambda}\) = R_H\((\cfrac{1}{n^2}-\cfrac{1}{m^2})\)

as n = 5 and m = ∞ 

From Eqs. (1) and (2), we get,

\(\cfrac{\lambda_{ pa\infty}}{\lambda_{L\infty}}\) = \(\cfrac{R_H} {R_H/9}\) = 9

∴ λ_pa\(_\infty\) = 9 λ_lL\(_\infty\) = (9) (912) = 8202 Å

\(\cfrac{\lambda_{ pf\infty}}{\lambda_{L\infty}}\) = \(\cfrac{R_H} {R_H/9}\) = 25

∴ λ_pf\(_\infty\) = 25λ_L\(_\infty\) = (25) (912) = 22800 Å 

This is the series limit of the pfund series.