Step 1: Personal protective equipment refers to barriers worn to protect the user from a hazard, for example goggles, gloves, masks, gowns and lab coats.
Step 2: A radiation detection badge (film badge or TLD badge) is a monitoring or dosimetry device. It measures the cumulative radiation dose received but does not block or shield the wearer from radiation.
Step 3: Because it monitors rather than protects, the badge is not a PPE. Goggles, gloves and the lab coat all provide a physical protective barrier, so they are genuine PPE. The odd one out is the radiation detecting badge.