Yes that's only one of the reasons the bomb was droped!
The U.S knew what the P.O.W'S where going through, plus if they
invaded japan the loss of U.S ground force's would be in the hundred's
of thousand if not a million or more. So the first a-bomb fell and the
Japanese goverment still wouldn't surrender! They where trying to
find a way to save face, as the japanese put it. So the second a-bomb
was droped, and after two a-bomb's killed ten's of thousand's, the japanese military still wanted to fight! But the goverment of japan said that's it,we surrender, the war with the U.S. is over.