To be presice: the tritium itself doesn't glow. It emits weak radioactive radiation which excits a fluorescent dye which then emits the visible light you see. Although it has the same chemical properties as ordinary hydrogen and its level of radiation is - as said before - very low, the use of tritium in e.g. watches, smoke detectors, et cetera is strictly regulated in most European countries. Latest surveys (2008) have shown that tritium can be very toxic when assimilated by human body and should therefore be handled very carefully.
The guest is right, it's a fluorophore that is glowing when excited by the radiation. Not to fear though, tritium only emits beta particles which are unable to penetrate the glass it is encased in. In fact, beta particles cannot even penetrate human skin. Tritium is, therefore, completely safe unless it is inhaled or ingested. Furthermore, the amount of tritium present in that tiny tube would diffuse so fast if it were to break that it would be indistinguishable from the background radiation that is present everywhere on earth.
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