@RocketGuy “short half life means a lot of particles come out every second (high rate) the first few days.” Partially true. Not every release from a radioactive decay has the same damage capacity. And it also depends on how much you have in the beginning. If you have very little gold, the amount of radiation coming off it quickly falls to near zero.
But there is another piece of the puzzle that needs to be looked at. I have neither the appropriate tool handy nor the patience to explain decay chains. You’d need a Chart of the Nuclides to properly trace the chains. When radioactive isotopes decay, they give up energy in the form or wave (x-ray, gamma) or particle (Alpha, Beta, Neutron) to get to a stable state. When this happens, the isotope actually changes into something completely different. This is called a daughter product. But the daughters might also be radioactive, resulting in more release of energy. This goes on until a stable element is found.
Also, with gold having many isotopes in the nanosecond range for half-life, those isotopes would be gone before the order was processed. Half-life is the amount of time it takes a given isotope to cut the amount of radioactivity in half. First half life is half the original, second half life is a quarter of the original, third is an eighths, etc. Convention says that after 7 half-lives the radiation is effectively gone (stops being able to be measured accurately). Of course this is a thumb rule and really depends on how much you start with.