We each take turns testing the radioactivity of trees, pieces of concrete, grass and, of course, each other.
The area around the plant is so green and lush and the weather so beautiful that it is simply hard to believe that we are standing on one of the most polluted spots on earth.
How different the site must have looked in the wee hours of April 26, 1986, bustling with activity and brightly lit in the middle of the spring night.
Ironically, the background for the world's worst nuclear explosion lay in the installation of a safety mechanism.
Station managers had noticed that the back-up diesel generators took 45 seconds to power up the plant, meaning that in a power cut the reactor could be in darkness for more than a minute. A system was designed whereby power could be generated from the still-spinning turbines and redirected to power the plant itself.
On the night of the accident the plant was slowed to half its normal speed so the new system could be tested; which is where it all went so horribly wrong.
I wonder what it must have felt like when the crew realised there was something wrong. At first they must have been simply worried about doing something wrong, the ultimate sin in the crumbling Soviet system.
The reactor was running much more slowly than the 700 MW they had been told to run it at. It was already down to 350 MW and dropping.
Had the usual safety settings not been overridden, the plant would already have started to shut down. The only option seemed to be to speed up the plant, and quickly.
With the control rods lifted out of the core, the reactor began to accelerate until it was running at 1000 MW, not only far above the level required for the test, but far above the normal safety settings.
Unsure what to do, the crew hesitated before plunging all the control rods back into the reactor, by which time it was too late. A thin flammable skin on the control rods meant temperatures spiked for four seconds - long enough for the core to pass the point of no return.
Much of what happened next is well known. The reactor exploded, smashing through the inadequate concrete shell above it, and released an enormous radioactive plume into the atmosphere, a cloud that would come to shed radioactive dust on an area stretching from Finland to France and from Russia to Greece.
Authorities waited more than 24 hours before evacuating local families; and more than a week before alerting international authorities, doing so only when Sweden registered unexplained levels of radiation in its airspace.
Local firefighters fought a suicidal battle against the burning reactor, pumping water and shovelling sand into the exposed core even as their own skin began to peel and melt.
Although only 100 or so lives were lost in the weeks following the accident, thousands of people living within an area hundreds of kilometres wide were poisoned.
Tragically, as much loss of life can be attributed to the lack of contingency plans as to the accident itself. Local emergency services responded heroically, but disastrously. No one knew how to deal with a fire burning at 2300C, less so one so toxic that people living hundreds of kilometres away were receiving potentially fatal doses of radiation.
Pouring water into the breached roof of the reactor succeeded only in flooding the basement levels beneath the reactor, creating the perfect conditions for a secondary explosion which, experts suggested, could be 500 times greater than Hiroshima and would basically render Europe uninhabitable.
Divers were sent in to empty the basements in an act of suicidal bravery that may have saved Europe from a nuclear winter. Sand eventually slowed and then stopped the radioactive leak, but fires burned in the core for almost a month before being finally smothered.
If the plant looks much as it did before the accident, the same cannot be said of the town of Pripyat, about five kilometres to the west.
Once a thriving town of 50,000 people, it is now the ultimate ghost town; crumbling, haunted and haunting.
Though the apartments have been burgled and gutted, the walls, street signs and roads remain.
There are still power lines, footpaths and the rusting remnants of banisters, fences and drinking fountains.
The fun park sits eerily silent, trees sprouting through the cement, a child's shoe rotting beneath the abandoned Ferris wheel.
So silent and overgrown is the town that it is difficult to believe that the radiation is real, a view my guide Vita tells me is held by many of the elderly people who have moved back to the abandoned villages that dot the 30km wide exclusion zone.
"Most of them are very old anyway, in their 70s and 80s. So to many of them it is better to live in the place they know rather than survive in some apartment in Kiev."
Much of the exclusion zone now is simply a wasteland of swamps, forest and fields. It looks peaceful, even beautiful.
It is only when Vita places her Geiger counter against the dirt beneath our feet that we see the radiation is still there, 27 years after the accident. Some of it will remain there for at least another 20,000 years.
As we leave the exclusion zone we are asked to pass through a radiation scanner.
The monitors remain silent, and we are free to return to Kiev.
This time, at least, the radiation stays where it belongs.
CHECKLIST
Getting there: Low-cost carrier Flydubai travels to Kiev from Dubai, which can be reached from Auckland with Emirates.
