I’m kind of skepitical of the “dirty bomb” idea. Frankly, it sounds like a load of bullshit, because of the πr2 thing. Namely, if you want to irradiate and area to a sufficient extent to cause immediate radiation sickness, then keeping it concentrated is your best bet. A very small bomb, at most.
The other extreme would be a huge bomb to spread radioactive material over, say, a city. At which point it barely raises the radioactivity above background levels. Or at least doesn’t cause immediately apparent effects. Imagine terrorists issuing a statement like, “Sure, it doesn’t seem so bad TODAY, but wait 'til you see the slight bump in cancer rates in 20 years.”
Indeed, on looking it up, I see that the experts are skeptical, too, and tests conducted by Israel didn’t find much effectiveness. That could be why we haven’t seen one used.
For that matter, then you don’t need to put any radioactive material in it at all, but just claim it.