I'm not sure in what magazine or periodical "The Atoms That Vanish" first appeared. Wikipedia, a useful resource but one that must be verified by outside sources, says it was "first published in Change!, 1957".
But the Asimov Online site says that it was "First Published In: 1957, The Tyrannasaurus Prescription (collection #37)"
All I know for sure is that it appeared in Asimov's first collection of essays, Only A Trillion, which was published in 1957, and has not been included in any other collection since then.
Asimov discusses radioactive half-life, and gives data on the half-life of various isotopes. (All this information is still valid today.)
I think I can assume that the readers of this book all know that there are atoms which are unstable and which break down by ejecting particles from within their nuclei. Sometimes the ejection of one particle is sufficient to allow what remains of the nucleus to be stable. Sometimes a dozen or more particles must be ejected one after the other in order for stability to be attained.
First, Asimov makes a point of talking about percentages and statistics.
Dealing with a large group of objects, however, is not the same as dealing with only one object. Once you have a large group, you can use statistics to predict the future, The larger the group, the more accurate (percentage -wise) the prediction. (My bolding.)
I mention this paragraph because today, in September 2008 we are undergoing are Presidential Election Cycle, and not a day passes that some article, based on the results of a poll, is published. And within the body of the article, sweeping statements are made about an entire group of people, for example: 67% of all White Democrates won't vote for Obama because he's black. 90% of all White Democrats think blacks are lazy. (Those aren't the actual numbers from the article, I'm just making them up, but the gist is the same.)
And yet, if you do down to the very bottom paragraph of the article, you're told how many people participated. In the case I'm referring to above, it was 2,227 people, but typically generalizations are categorically stated to be true, based on a poll sampling of 1,000 people.
And to me, a poll sampling of 1,000 people, when it's a question of what 300 Million people will do, is way too small a sample size to be saying so postively, ALL people think this. ALL people think that. Sure, opinion polls have their place, but the way the poll data is stated is done so in such a way as to sway people to believe something. Otherwise, the sample size would be revealed in the first paragraph, and instead of saying, "All Democrats think that.." they would stay "All Democrats who participated in this poll think that..."
(And, as an aside, Asimov was a Democrat. I'm a Republican.)
But enough of that digression. Back to the essay.
Half-life of Isotopes
Asimov mentions throughout the article some of the isotopes and their half-lifes. There are also several tables which illustrate his comments, (and explains how scientists have come to date the existence of the Universe, and the Big Bang Theory - though he doesn't mention it by that name.)
Uranium-238 - 4 and a half billion years
Uranium-235 - 700 Million years
Thorium-232 - 14 billion years
Potassium 40 - 1 and a 5th billion years
Rubidium-87 - 62 billion years
Riddle me this, gentle reader. (And use the Comment section to explain it to me and other readers.) How do we know that Rubidium-87 has a half-life of 62 billion years?
If the Universe has been in existence for only 5 billion years, how can we deduce how long Rubidium-87 takes to break down?
The chances, however, would be 30 to 1 against there being even a single atom of astatine-215 present.
And then there's Wikipedia...
I just checked Rubidium at Wikipedia, and the author of the very detailed article there says that it has a half-life of 49 billion years (not the 62 billion Asimov says.)