LOL! That’s ok, when I first saw it it looked exactly like what a “Fat Man” patch might have looked like (if they’d had them). If you has said “Army Air Corps, Pacific Theater” that’s what I would have suggested.
Here is the patch of the 509th Composite Group. No idea if this patch was before or after their missions, as the mushroom cloud motif had been in use by similar groups.
http://historywarsweapons.com/509th-composite-group/
“The 509th CG was created based on the 393rd Bomb Squadron, a unit of B-29 Superfortresses from the 504th Bomb Group, which had been sent to Wendover, Utah, to be converted into the Composite Group.”
Thus, until they had a unit patch, which might have been after their missions, they might have been wearing their former unit patches.
The current logo shown at Sandia, NM, for the 509th is an anniversary patch.
http://en.wikipedia.org/wiki/Sandia_Base
http://i.ebayimg.com/24/!B5rGUU!B2k~$%28KGrHqN,!g0EyrwpLPRQBMuls6ToGw~~_3.JPG