Well, borrowing Occam's razor for a shave this morning, I think I figured it out:
First of all, the assassins didn't need to construct a special room and convince Achashverosh to go into it - they just used the Royal Bathroom. They hid the atom apparatus and the poison in the ..um.. Royal Wiping Sponge. Since they knew Achashverosh had a habit of having a Royal Constitutional for over 45 minutes each morning, they chose to use Carbon-11, with a half-life of just over 20 minutes, so by the time Achashverosh was done, the atom would no doubt decay and release the poison. Just to make sure he would be in there long enough, they fed him plenty of Shmureh Matzah and chicken in pectin for dinner the night before.
Mordechai caught wind of the plot and was able to foil the plan because one of his good friends from shul was the University of Shushan's Chemistry Professor, Dr. Schrodinger. He just had his friend switch the labels on the bottles, so instead of radioactive Carbon-11, they used plain old stable Carbon-12. When the assassins showed up suddenly in the Chemistry Department, the Good Doctor looked up from petting his cat and handed them the "Carbon-11" they requested.
SO--the next morning, one of the assassins handed Achashverosh the rigged sponge as he went in to use the facilities, and they waited patiently. Boy, were they surprised when Achashverosh came out of there after over an hour with a big smile and saying he "felt like a million Darics"! Plot foiled, you know the rest from the Megillah.