According to Isaac Asimov's Essays, (a site that lists them and what books they are collected in, and reviews them, but doesn't go in-depth as ths blog does), "The Explosions Within Us" first appeared in Only A Trillion , in other words it was written specifically for the book, and published for the first and only time in 1957.
The Quotable Asimov
All mathematical treatment of radioactive breakdown is statistical in nature and statistics work more poorly as the numbers grow smaller.
It is all very well to speak of radioactive atoms that occur in the soil, as I have been doing in the previous chapter. There is something objective and detached about atoms exploding within rocks and soil. But plants grow in the soil and animals live on plants. Is it possible that radioactive atoms may find their way into living tissue and even into our own bodies?
It is not only possible, it is certain.
Asimov discusses the trace elements in our body, broken down by atom. (We need only a trace of cobalt to survive, but that trace actually consists of several million atoms.)
He also talks about the existence of the radioactive potassium-40 in our bodies. There is three times as much potassium-40 in our bodies as iodine.
"There is always a chance" Asimov comments "...that the unfortunate molecule that finds itself in the path of a free radical (a water molecule with a piece knocked off by a beta particle) may be one of the nucleo-protein molecules called "genes". There are several thousand genes in each cell, each gene controlling some particular facet of the cell's chemistry. If one of those genes is damaged or altered as a result of a collision with a free radical, the cell's chemical is also altered to some extent...this change is called a mutation."
He then moves on to discuss carbon-14, and how much of that is in our bodies, and why that enables us to date dead bodies (as in mummies).
This is the same as saying that if you live to be 70, the chances that a particular cell in your body will ever have experienced even a single carbon-14 breakdown in its genes is only one in 260.
So sleep in comfort!
Asimov has a note at the end of this article, pointing out he''d wriiten it in November 1956. He'd wriiten an article on the same topic that had appeared in the February 1955 issue of Journal of Chemical Education. "That, I believe, was the first mention in print of the relationship of carbon-14 to genetics." He goes on to say, "In 1958, when atmospheric testing of nuclear bombs still went on wholesale, Linus Pauling published a paper in Science (Nov 14, 1958) which commented that the increase in carbon-14 content in the atmosphere would increase the incidence of undesirable mutations. Asimov states he received a letter from Pauling "which refers in most kindly fashion to my article." But he doesn't say exactly what Linus said (and if you read Yours, Isaac Asimov, a collection of Asimov's correspondence, typically Linus only wrote when he was pointing out an error in on of Asimov's articles.)