Worked examples (Lesson 2)

Example 2.1. A cool hydrogen gas is placed between a white-light source and a spectrometer. Which wavelength is certainly missing from the transmitted light, in the visible region, if the gas atoms are in the ground state? None: the visible Balmer lines start from n = 2, which is empty in the ground state; absorption from n = 1 needs ultraviolet photons (≥ 10.2 eV). Only the UV Lyman lines would be removed. (That is why Fraunhofer's lines appear only for gases whose atoms are already excited, like the hot gases in the Sun's atmosphere.)

Example 2.2. In a spectrum of a gas, the lines are seen at 410 nm, 434 nm, 486 nm and 656 nm. Which gas and series is this? They match the visible Balmer lines of hydrogen (6→2, 5→2, 4→2, 3→2).