SMA ON IFR FLT PLAN EXECUTING MISSED APCH HAS NMAC.

Narrative

WE WERE ON AN IFR FLT PLAN DOING INST APCHS AT TOPEKA BILLARD ARPT; KS (TOP). ON THE FIRST APCH ILS 13 AT TOP MY STUDENT WAS OVERWHELMED WITH THE COMS SO AT THE MISSED APCH POINT WE WENT BACK FOR ANOTHER ILS 13 AT TOP. THIS APCH WORKED OUT FAIRLY WELL AND AT THE MISSED APCH POINT WE WERE TO FLY RWY HDG AND CLB TO 3000 FT MSL. OUR PLAN WAS TO FLY THE VOR 22 AT TOP. WHEN WE TOLD BILLARD TWR THAT WE WENT MISSED APCH THEY TOLD US TO CONTACT KANSAS CITY CTR 120.5. WHEN WE SWITCHED OVER TO KANSAS CITY CTR IT TOOK A LITTLE WHILE TO CHK ON BECAUSE OF ALL THE TFC THAT CTR WAS HANDLING. AND WHEN WE CHKED ON WE WERE LEVELING AT 3000 FT MSL RWY HDG (APPROX 130 DEGS). I WAS GETTING THE NEXT APCH PLATE OUT FOR MY STUDENT WHEN I LOOKED UP AND SAW AN SMA APPROX 200 FT ABOVE AND 500 FT VERT TO THE R OF US. AT THAT SAME TIME KANSAS CITY CTR TOLD US OF THE TFC. NO EVASIVE ACTION WAS DONE BY EITHER PLANE. THE PROBLEM AREAS AS I SEE IT ARE TWOFOLD: 1) EVEN THOUGH I WAS ON AN IFR FLT PLAN INSIDE AN ATA I MUST KEEP CONSTANT LOOKOUT FOR TFC AT ALL TIMES. DON'T JUST LET ATC WATCH OUT FOR US; AND ON NICE SUNNY DAYS BE EXTRA CAREFUL. 2) ATC SHOULD HAVE POINTED OUT THE TFC A LOT EARLIER.