Nuclear bombs are expensive to make and require highly sophisticated industrial facilities. However, many terrorist groups would be content with causing a mass panic, and maybe scaring the whole population of a city to flee. They may prefer to use a 'dirty nuclear bomb', than a proper atom bomb. Many people will only hear the words 'nuclear bomb' and run. A dirty bomb uses an amount of radioactive material, maybe powdered or granulated, packed with an explosive.
When the bomb explodes, the radioactive material is dispersed. How far the radioactive material is dispersed depends on the strength of the explosion and weather conditions - wind and rain, and will not be more than a few miles typically.