Well… first things first: Welcome to Fluther.
As you start to study radioactivity you’ll find that no one even knows for certain if there are measurable human effects to radioactivity below a certain level of around 25 Rem. There are some scientists who think that there are small effects, and they may actually be beneficial, and others who think that there are ‘slight changes’ in blood only, and those effects are minimal and neither bad nor good. Above 25 Rem there are more and more changes detected.
So 25 Rem is set as a threshold lifetime dose that “we don’t have to worry about”, which is why the NRC sets an allowable annual dose at (I think I recall) around 2.5 Rem, and in practice limits the exposure of radiation workers to much less than that, in order to ensure that they never exceed the annual dose.
This means that in order to be commercially available for sale in the USA, your granite counter top (or any other consumer product sold without restrictions) has to emit less than 2 mR (milli-Rem, or 1/1000 th of a Rem) per hour at a minimal distance. In other words, you can detect and measure some amount of radiation from the product, but nothing that you could then measure for its effect in people, at least not with whatever tools and methodology you’re likely to use in a school science project.
Some of the suggested studies aren’t bad, but one thing that you’re going to need as you study ‘radioactivity in granite counter tops’ is the background radiation in people’s homes even without granite. Concrete has some radioactivity, as well as the radon that some people still have in their homes. And since many parts of the country (New England, for example) are close to granite ledges, then they’ll already have some background radiation from that. Parts of the Rocky Mountains and the High Plains will also have more cosmic radiation, because of the thinner atmosphere overhead (and the rocks near the surface), and areas near coal deposits also may have ‘significant’ (though not ‘unsafe’) levels of radiation.
There’s a lot to know about radiation, and it’s a good project to get into, but… there’s a limit to how much you can learn about it in one night in order to submit any kind of testable hypothesis for your science project tomorrow.