The Hydrogen Spectrum

A hot solid glows with every colour. Hot hydrogen glows with just a few sharp ones, the same everywhere in the universe. Those lines were a fingerprint no classical theory could explain.

Line spectra#

A lamp filament, sent through a prism, gives a continuous spectrum. Hydrogen heated in a sealed tube gives a line spectrum: only certain sharp wavelengths, such as 656.3 nm and 486.1 nm, with nothing in between. Hydrogen also emits lines in the ultraviolet and infrared.

The lines fall into series. Within each series the gaps shrink toward shorter wavelengths, approaching a series limit: the Lyman series (ultraviolet), the Balmer series (visible), the Paschen series (infrared), and so on. All the wavelengths fit one formula:

Why Rutherford’s atom can’t be right#

Hydrogen is one electron and one proton. In Rutherford’s picture the electron circles the proton, the Coulomb force supplying the centripetal force. Mechanically fine, but Maxwell’s equations say an accelerating charge must radiate continuously. So the electron should lose energy, spiral inward, and crash into the proton, emitting a smoothly changing range of wavelengths on the way.

Reality: hydrogen at room temperature is perfectly stable and emits nothing. When excited by heat or a discharge it emits only those sharp wavelengths, always the same, from a lab in Delhi to the Sun. Classical physics had no explanation: something new was needed.