A80 Controller experienced operational error involving two general aviation aircraft when one aircraft responded to missed approach instructions; turned and descended toward another aircraft; position workload and distractions listed as causal factors.

Narrative

I was working SAT-P sector at A80 approach. I had Aircraft X (C177) on a southbound vector to join the Runway 20L LOC at PDK Airport. I had Aircraft Y (C172) on a westbound vector for the ILS 20L at PDK. Aircraft X was at 4;000 FT; Aircraft Y was at 3;000 FT. I was busy at the time releasing aircraft off of PDK; LZU. I was also accomplishing coordination with ZTL. I issued Aircraft X missed approach instructions of heading 090 degrees and altitude 3;000 FT as the aircraft was doing practice approaches. Aircraft X did not respond. I prompted the aircraft for a response by saying; 'Aircraft X.' Aircraft X responded; '090 and 3;000.' I heard what I thought was an appropriate readback of missed instructions. Aircraft X; however; turned and descended directly toward Aircraft Y. When I recognized the situation; I turned Aircraft X immediately to a 240 degree heading and Aircraft Y to a 360 degree heading. Aircraft Y did not respond to my first transmission and had to be called again. Separation got down to 2.57 miles and 200 FT. I believe that my workload as well as both pilots' lack of attention contributed to my operational error. Aircraft X was not listening when I gave him missed approach procedures and Aircraft Y was not paying attention when I gave a very critical vector. ATL and A80 airspace is some of the busiest in the world. Unless someone can get pilots to pay attention and remain actively engaged in their flight; then there is no remedy. I had an operational error that could easily have been prevented if: 1) Aircraft X actively listened to instructions; or 2) Aircraft Y heard my first transmission and turned in a timely manner. Lack of attention happens here by pilots daily -- not just GA; but air carrier pilots as well. People need to get their heads in the game as lives truly are at stake!