Then why did Japan surrender? Anyway, the Hiroshima bomb was especially dirty because most of most of the fissile material did reach critical mass, and was instead scattered around the city after being irradiated by the blast.
Japan surrendered because Russia sliced through their army in Manchuria. They were terrified of them since Khalkin Gol in 1939. Sometimes the best way to end a war is picking who you surrender to. They wanted to surrender to the U.S. only. Smart move. It worked out very well for them.
Is that what you meant to write? (Your remark about "being irradiated" is totally superfluous, since the fissile material - enriched U-235 - was already radioactive, and so didn't "need" additional irradiation to be deadly.)
Regards,