Having been to a nuclear reactor facility myself, they hand you these neat one-time-exposure badges that they then take from you after the visit.
I'm guessing they use similar badges for workers that may last longer or allow a stronger dose-over-time before alerting/becoming useless.
I don't remember having such a badge, on various "touristy" visits to reactors (Doonreay, Sellafield a couple of times, a couple of others I can't be sure about, but
maybe Hinkley Point and Sizewell, and I always wanted to visit Trawsfynydd, but there was never time whenever I was just passing). Even the time when it was a school trip to Sellafield (or Calder Hall or Windscale, whatever you know it best as) which included entry to the reactor-hall. Which was actually
less radioactive (during normal operation, while the "Everything is OK, don't worry" huge echoing BIP... BIP.... BIP... was sounding, with the cue to evacuate being
either alarms or lack of a BIP... ) than outside.
But there was a 'gateway' machine to go through (
both ways) to check for scintillations from each person, including putting hands and feet into slots for particular attention. The girl who was a little too hasty and got the "you've removed your hands too quickly" warning sound, on leaving the zone, had to be calmed down quite quickly. I don't know why it was such an alarming alarm. Presumably the "over threshhold" alarm was even more alarmingly alarming, but we never heard that one.