How is it a substance can emit photons of visible light after absorbing ultra violet photons but not with infrared

Question

radiation

The re-emitted photons must be of lessor energy (longer wavelength) than the incident photons.

In a one-photon absorption process, the absorbed photon must have more energy that the re-emitted visible photon. Infrared phtns have less energy thn visible ones because of their lower frequency.

When you irradiate a material with high-intensity infrared laser light, it IS possible to obtain visible emission, with negligible heating, because of multiple-photon absorption and scattering processes that can occur. You do not see this occur in everyday processes, but I have observed it in the laboratry. So, the premise of your question is not quite correct. Tell your teacher and score some extra brownie points.