How does a glow stick use hydrogen peroxide, an oxalate ester, and a fluorescent dye to make light?

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A glow stick functions through a process known as indirect or sensitized chemiluminescence.

When you break the inner tube of a glow stick, you release hydrogen peroxide, which acts as an oxidizing agent. This substance reacts with an oxalic acid ester contained within the stick. This chemical reaction produces a high-energy intermediate molecule.1

Because this intermediate is unstable, it transfers its excitation energy to a fluorescent dye (a fluorophore) present in the mixture. This transfer excites the dye molecules to a higher energy state. As these dye molecules return to their ground state, they release the absorbed energy in the form of visible light, causing the glow stick to illuminate.1