Our guide had a Geiger-meter (and if you want, you can rent your own for the trip) and in some places he showed us the radiation levels. Generally, a transatlantic flight will expose you to more radiation than a trip to Chernobyl. But it depends on where you go – and what you do. At this point, the level in the grass is quite high, so don't roll around in it! The soil is contaminated by radiation, and the radioactivity is going deeper, about 20 cm by now. Ultimately, they will have to do something, as the fresh-water for Kiev ultimately comes from this area (but at much deeper levels).