This isn't nanotech-related, but it's related to advanced-technology fears.
When the amount of radiation that can be measured is vastly lower than the amount that can make a person sick, and when any amount of present future possible radiation makes a good news story, it's likely that your kids will get scared, and perhaps even traumatized, about things they don't need to worry about. Here's an analogy to help them understand what all the fuss is about.
(If you live in or near Japan, parts of this analogy may still be useful, depending on what happens in the next few days. If you live in Europe or the Americas, you and your kids just plain don't have to worry, and it's a good idea to reduce childhood trauma, isn't it?)
"Radiation is kind of like a noise you don't like. What's a noise you really don't like? (Maybe the neighbor's dog, loud trucks, chalk squeaking on a blackboard.)
OK, so if something made that noise a mile away, you wouldn't care much, right? But if someone made it right next to you, you'd hate it. And if someone made it really, really loud, right next to you, with really big speakers like a rock concert (or Uncle Bob's home theater system), then it might even hurt your ears or make you deaf.
So if there's really a lot of radiation, it can hurt you. Just like a really loud sound can hurt you. But if there's a very quiet sound, then it's not going to hurt you. And even a loud sound, if it's far enough away, it's not going to hurt you.
And just like you can hear sounds that are very very quiet, we can detect radiation that's very very quiet. Far too quiet to hurt you even if you could hear it. Radiation is like a noise that no one likes, so they've built sensors that can detect even very tiny amounts of it. Even in ordinary things like bricks and bananas.
Nuclear reactors make lots of radiation. They use it to make electricity. But they keep the radiation indoors, in very strong buildings, so normally we can't detect any radiation outside them at all.
Over in Japan, there's some reactors that were damaged by the earthquake. They shut down right away, so they're not making much new radiation, but there's still a pretty loud echo inside those buildings, and it's taking a while to fade away. And some of the radiation is getting out. If you were standing next to those buildings right now, it would be like a thunderstorm or a really loud truck or maybe even your sister's music. You wouldn't want to stay there very long, and if you did, you might feel sick. That's why the news shows people wearing masks and baggy clothes - it's like earplugs for radiation.
Now, some people are worried that the buildings could break even more, and a lot of radiation could get out. If that happened, it could be like a hurricane or a rocket going off. It would be very dangerous to be next to it. It would be like a noise that's loud enough to set things on fire. Did you know that a really loud noise can do that?
But even if that happened, it's still thousands of miles away. It's possible that we might, barely, be able to detect some of that radiation over here. But even then, it won't be loud enough to hurt us. It would be like a giant rocket taking off in (a nearby town). You could hear it, and it would certainly make the news, but it would be too far away to hurt you.
Now, some people are scared of any amount of radiation, just like your friend ____ is scared of ____. (Pick something your kid is not scared of.) So they'll be talking like it's really scary if they can detect it at all. But you're a big boy/girl and you don't have to be scared of ____ just because ____ is. So if you hear a news story that sounds scary, come talk to me about it, and I'll tell you whether there's any actual danger, OK?"
To help assess the danger:
Radiation doses are measured in Sieverts, or milliSieverts (mSv, 0.1% of a Sievert), or microSieverts (μSv, 0.1% of a milliSievert, or one-millionth of a Sievert). A banana will deliver about 36 μSv of radiation. That is easily detectable by modern instruments, and bananas often set off radiation detectors.
Exposure to radiation on the order of 800,000 μSv or more at one time can make you sick.
People get around 3,000 μSv per year naturally - more if they live at high altitudes, or areas with radon, or eat a lot of bananas, or get a lot of X-rays.
Nuclear plant workers are limited to 50,000 μSv per year. That's the equivalent of eating several bananas per day. People living in high-altitude places like Colorado get 10,000 μSv per year naturally.
The highest level of radiation reported on-site at the Japanese reactors, so far (Wednesday the 16th afternoon) is (10,000 μSv) (edit: other sources say 400,000) per hour, but that lasted only a few minutes. The workers there are incredibly brave, and we owe them more than we can possibly repay. But any radiation at the plant will be diluted and decayed with distance.