The following is a comment received by the Volokh Conspiracy:
In my law school moot court final…Justice Kennedy asked me a hypothetical question that basically posed the question here: can the government conduct warrantless searches by electronic means for nuclear material inside a home. I do not remember my answer, but I remember that he was unimpressed by it. At the reception following the competition, he told me that I had missed the obvious answer. Sadly, he never told me what that answer was, and I still do not know.
I agree with Hugh Hewitt that the most obvious answer is it would never be unreasonable to conduct such searches by aiming radiation devices at homes. But, like Hugh, I have no confidence that this answer is obvious, or persuasive to Justice Kennedy.