Final answer:
Out of the given compounds, 4-tertbutylcyclohexanone would likely not show up under UV light because it lacks a conjugated system or an aromatic ring, which are typically required for UV absorption.
Step-by-step explanation:
To determine which of these compounds would not show up under UV, we need to consider their structures and the presence of conjugated systems or functional groups that can absorb UV light. Typically, compounds with conjugated pi systems or aromatic rings can absorb UV light due to п - * transitions. Among the given compounds, eugenol, anisole, phenol, and 1-(3-methoxyphenyl)ethanol all have aromatic rings, which would likely show up under UV light. On the other hand, 4-tertbutylcyclohexanone does not have a conjugated system or an aromatic ring, making it the compound that would likely not appear under UV light.