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It is possible, but will likely have some problem crossing through the Equator due to the circulation in and near tropical zone. But it is possible. The flow the steering wind vectors in the north south direction would be weak once it gets below 10 degrees latitude.

Updated, to clarify my answer. First of all, the question the I asker posted did not limit the transport of radioactive material to just atmospheric means (i.e. wind). However, in light of what is currently going on, I would think it would be safe to make that assumption for this question. In any case, my answer would have been the same. My answer WAS and still is that it is not likely to happen, but it is also not impossible either. By that, I meant, there is no way that we can say it is impossible based on the definition of the word "impossible". If it was impossible, then the chance is zero with no if, ands, or buts. If there is any way that radioactive material can be transported from Japan to Australia by natural or means aided by humans, then it is not impossible. As I have stated in my answer, I find it unlikely any radiation will make it past the equator by atmospheric means through the natural circulation found at latitudes below 20 degrees north and 10 degrees south. But if you where to place in the water current or place it on a vehicle, is is pickup and carried through to the other hemisphere, then the the answer would be yes, it is possible.

Now what are the chances of radioactive air crossing the equator by atmospherically means. It would likely be very very low chance. But having such a minute chance would still not mean impossible base on the definition of the word. It would be like saying what are the chances that somebody would guess or predict correctly that Japan would suffer through a 9.0 earthquake that would cause a very deadly Tsunami and would cause trouble with two of its nuclear nuclear powered power plants. My answer would be the same, It would be highly unlikely that someone would make that prediction that it would happen that day, but you really can't say that it can't happen. Just about every day, somebody in this world be telling us that the world is coming to an end as we know it. If this trend continues, one of these days, it will come true.

It would be acceptable and maybe I should of given that term as my answer to this question. However, I don't think my old answer was incorrect either.This reasoning is based on the fact that air can cross from one side of he equator to the other. If anybody can prove that air one one side of the hemisphere absolutely can not cross over to the other side, then I will say that my answer is wrong.. Otherwise, in science, no matter how low the chance may be, if the chance is not zero or is nearly zero, it would be wrong to say that it is zero. You can not say it is zero when you really mean near zero or nearly impossible.. Those two terns may sound the same, but in reality, they are not the same.

Now, taking a look at the given question and the answer. My answer of "not likely' would still be correct because we are expecting it to occur. So what is wrong with adding to it that it is possible. It is like a doctor telling you that you had very low chance of getting cancer. Why can't he just say it is impossible for you to get it.

And by how the question is worded, there , it would be wrong to say it can never happen. It is possible to transport, if not by moving air, you cam still do it by other means, Unless you can say that any air molecule that reaches the equator can not cross over to the other side for any reason or that it just can't cross the to the other even by man made reasons, likely by ship, plane, or car, etc because the laws of physics proves that air in the northern hemisphere will never mix or get in contact with air in the southern hemisphere, won't ever allow air from one side of the hemisphere to cross over to to make contact with air from the southern hemisphere, then I would agree that it would that it would be impossible. Because in that case, it would fit the definition of the word "impossible". Otherwise, if it is possible even if the chances are extreme low. Based on some of the answers given, I think sometimes, even those who I think are very bright amd appears to have a good over-all understanding in science will sometimes get into a bad habit of "rounding of" answers to the nearest absolute,. I have to watch myself at times too. That is when usually we get ourselves into trouble.