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Why do europium and terbium produce red and green colors in optical displays?

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A line graph showing electron probability distributions for gadolinium, with separate curves for 4f, 5s, 5p, 5d, and 6s orbitals. The x-axis shows distance from the nucleus in atomic units and the y-axis shows probability P2(r). — rare-earth element Electron probabilities, P²*(r)*, for the 4f, 5s, 5p, 5d, and 6s electrons of gadolinium.

Europium and terbium produce specific colors in optical displays because they are rare-earth elements with unpaired 4f electrons that undergo electronic transitions when activated by electrons or photons. These transitions result in the emission of intense, sharp colors.1

In the context of phosphors used in televisions and other displays, these ions act as activators when added to host materials (such as yttrium oxide or yttrium vanadate) in small quantities:1

Europium (Eu³⁺): Produces an intense red color. The introduction of europium-based phosphors in 1961 significantly improved the brightness and intensity of color television images.1
Terbium (Tb³⁺): Produces a green color.1

The specific color emitted depends on the excited-state energy levels of the activator ions within the host crystal. While these ions are responsible for the primary colors, other ions like Eu²⁺ and Tm³⁺ are also utilized in various applications for their specific blue emissions.21