D2.2 Atomic Spectra

Heating a gaseous element at low pressure or passing an electric current through the gas imparts additional energy into the atoms. These higher energy atoms can then release the additional energy by emitting photons. For instance, the colors of “neon” signs are produced by passing electric current through low-pressure gases. Interestingly, the photons emitted by the higher-energy atoms have only a few specific energies, thereby producing a line spectrum consisting of very sharp peaks (lines) at a few specific frequencies. Line spectra were intriguing because there was no reason to expect that some frequencies would be preferred over others.

Each element displays its own characteristic set of lines. For example, when electricity passes through a tube containing H₂ gas at low pressure, the H₂ molecules are broken apart into separate H atoms and the H atoms emit a purple color. Passing the purple light through a prism produces the uppermost line spectrum shown in the figure: the purple color consists of four discrete visible wavelengths: 656.4 nm, 486.2 nm, 434.1 nm, and 410.2 nm.

The H-atom emission spectrum also contains lines in the ultraviolet and infrared ranges. In 1888, Johannes Rydberg developed an equation that predicts wavelengths for all hydrogen emission lines:

Here, n₁ and n₂ are positive integers with n₂ < n₁, and the Rydberg constant R_∞ = 1.09737316 × 10⁷ m⁻¹.

Because the wavelengths of hydrogen emission lines were measured to very high accuracy, the Rydberg constant could be determined very precisely. That a simple formula involving integers could account for such precise measurements seemed astounding at the time.