Physics Question #128

Leo Capistrano, a 20 year old male from the Internet asks on February 2, 2000,

How long would a single molecule of a radioactive element last? If the half-life of U-235 reduces its mass by half, and the resulting mass is also reduced into half by another half-life term, then a given mass would last indefinitely, because a half would always remain. In other words, some molecule of that radioactive mass would last longer than the rest of the molecules. Isn't the lifetime of a single molecule of that radioactive a constant? Is the concept of "half-life" valid?

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The answer

Ian Keith Affleck answered on February 2, 2000

The time it takes for a radioactive atom to decay is not a constant. This is because the conditions within each radioactive atom are not identical -- unlike, say, the conditions in a pot of water that you start at room temperature and heat at a known rate on the stove. In the latter case you can predict with some accuracy the time it takes to bring the water to boil.

In an atom, on the other hand, nobody knows the exact amount of energy distributed amongst the constituent particles at any one time.

We do know, however, the probability of certain energy distributions, and therefore we can make predictions such as the elapsed time during which an individual atom has a 50/50 chance of decaying. Based on this knowledge, you can group billions of such atoms together and state with great accuracy the time it takes for half of the atoms in that group to decay.

As an analogy, think of a large population of people. We can't say when an individual person in that population will die, but we can feel fairly confident predicting how long it would take for half of the population to die. The larger the population; the more accurate our prediction.

In both cases, we rely on statistical analysis to help us make useful guesses about the world around us.

Yes, this means that some lucky radioactive atoms hang around much longer than others. Uranium is one of the most abundant minerals in the earth's crust, and all of it was formed billions of years ago in the heart of a dying star. The star eventually exploded, spewing its constituent atoms into the universe, some accreting together long afterwards to form planets like Earth. Some uranium atoms decayed immediately after the star exploded; some have been around ever since and today form the fuel of nuclear power reactors.

The fact that some uranium atoms last longer than others is no more remarkable than some people living longer than others.

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