We measure radiation dose in units called rem. Above 1,000 rem, incapacitation occurs within minutes, followed by extreme fatigue and nausea, then death. For smaller doses, 300 to 500 rem, about half of the victims die within a month.
But reduce the dose a little more, down to 100 rem, and the effects are very mild. At 50 rem, nobody even gets sick.
This 'threshold effect' creates problems for the terrorist. He can put radioactive material into a bomb - but concentrated radioactivity kills fast, so he'll have to protect himself with a ton of lead.