Gotta correct you on that one:
The ‘big bang’ as known from the typical nuclear explosion would not happen if a dirty bomb detonated, simply because of the nature of the dirty bomb itself. While in nuclear bombs, the explosion is a result of an uncontrolled nuclear reaction in the bomb itself, whereas the dirty bomb is a regular type of explosive which is used to distribute added (but not mixed into the explosive itself!) radioactive material. A nice (though somewhat extreme) example would be the disaster of Chernobyl nuclear power plant reactor 4. The explosion itself was caused by the pressure buildup of superheated steam, and when the reactor lid blew off, the nuclear fuel has been shot into the atmosphere. (and, as you might recall if you were born anytime in the first half of the 1970′s, caused a Europe-wide fallout of caesium-137)