The Concept of Half-Life

When an atom of a radioactive isotope decays, two things happen. First, energy is given off from the conversion of mass to energy according to Einstein's famous formula, E = mc2. (The newly formed atom and any emitted particles are always lighter than the original atom - and it is this difference in mass that is converted to energy.) Simultaneously the original element is transmuted to an element with a lower atomic number. The secondary element is called the daughter (or progeny) of the first; it can be either a stable isotope or can itself be radioactive and go through a radioactive decay. Eventually, however, the original element decays to a stable form, and no more energy is given off.

One can deduce from this that a radioactive element has a finite amount of energy to emit. Either it emits this energy very rapidly - in which case the radiation is intense and short-lived - or slowly, which would logically result in a relatively low radiation output. You can't have it both ways - a serious problem in nuclear medicine, as some of the intensely emitting therapeutic isotopes cannot be stored for more than a day.

Half-life is the time in which half the initial number of radioactive atoms decay.

If you stop to think about this phenomena, it's difficult not to have some kind of religious experience. Just think: In a tiny piece of (for example) uranium, one atom may have an internal "clock" that commands it to disintegrate in a second, while an adjacent atom in the same small sample will not decay for 13,500,000,000 years. How do they know then to "do their thing?" It's a problem that science may never solve.

Iodine 131 (used in thyroid diagnosis and ablation) has a half-life of about eight days. Thus if we started with a gram of 131I, after eight days and fifty-seven minutes we would have only a half-gram with the other half having been transmuted to stable tellurium. In another eight days we would have only one-fourth. After eighty days - ten half-lives - there is less than 1/1000 of the original specimen; beyond thirty half-lives, the isotope is considered to have disappeared. With its relatively short half-life, 131I is an intensely radioactive isotope.

Let's look for a moment at one of the most ubiquitous radioactive isotopes around: 238U, the primary uranium isotope making up 99.3% of the element's existence on Earth. [There are approximately 5,000 pounds of uranium in a volume of average soil one square mile by one foot deep.] It has a half-life of 4.5 billion years - approximately the same time estimated for Earth's age. Uranium takes 207,000,000,000 times as long to decay as 131I - with an inverse (longer time, less radiation) emission rate in approximately that proportion. Obviously it is a weak sister when it comes to being radioactive - which is fortunate for us or it would all be gone.

So, just in case I haven't made this clear, let me emphasize the following:

Short half-life = intense emitter, but gone after a short time

Long half-life = low activity and inherently not dangerous

Those who oppose nuclear technology want us to believe "Long half-life = dangerous," but it's just not true.

Understanding the concept of half-life and its relationship to intensity makes one realize that Barry Commoner - when he invokes references to a "nuclear priesthood watching over wastes for thousands of years" - is either terribly ignorant himself or is hoping that we are.