Q.Determine the shortest wavelengths of Balmer and Paschen series. Given the limit for Lyman series is 912 Å.

When hydrogen gas is heated to a high temperature and its emitted light passed through a prism, the result is not a smooth, continuous rainbow (as for a heated solid) but a line spectrum: light emitted only at a small, specific set of discrete wavelengths, with nothing at all in between. In the visible range, for instance, hydrogen emits at exactly 410, 434, 486 and 656 nm and no other visible wavelengths.

Studying hydrogen's full spectrum (including its many lines beyond the visible, in the ultraviolet and infrared) reveals that the lines naturally sort into distinct groups called series, each named for the scientist who identified it and each converging, within itself, toward a limiting shortest wavelength (the series limit) as successive lines get closer and closer together. In increasing order of characteristic wavelength: Lyman (ultraviolet), Balmer (the series containing the four visible lines above), Paschen, Brackett and Pfund (progressively deeper into the infrared). …