# Do some half-lives change over time?

I was recently doing some physics tuition on radioactivity and the student claimed her chemistry teacher had said that radioactive substances can be grouped into two divisions: those whose half-life is constant and those whose half-life changes over time.

I had never heard of this before and can't think of any reason why a half-life should change, so does anyone else know anything about this?

(I know some half-lives can be altered under certain conditions, but I'm talking about a natural change over time).

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The short answer is no: halflives are constant.

However, let's discuss a situation in which that comment might have some kind of truth behind it. If you have a parent nucleus that decays to a radioactive daughter so that there will be two (or more) decays before stability. In general there are two possibilities for this:

• The daughter has a shorter halflife than the parent. In this case the concentration of the daughter is always $\displaystyle\frac{\tau_\text{daughter}}{\tau_\text{parent}}$ of the parent concentration. This means that the concentration of the daughter actually decays on the parent's halflife (because the daughter is constantly refreshed from the parent).
• The daughter has a longer half life than the parent. In this case the daughter will accumulate steadily as the parent decays away.

The latter case is interesting to us here because at the start the sample will register an activity that decays with the parent's (short) halflife, but after a number of those halflifes have passed the activity of the sample will be dominated by the daughter and exhibit a longer halflife.

That is something that your instructor could have meant which would not be wrong. However, the halflife of each isotope remains the same: it is only the halflife of the sample (which contains more than one isotope) that varies.

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Thanks, OP here (sorry, couldn't remember password, had to sign in under a different name). I did consider what you mention, but it doesn't seem to fit particularly well with having two distinct categories of radionuclide. I suspect the answer is one or both of a) the student's misremembering what the teacher said and/or b) the teacher talking nonsense. Wouldn't be the first time... – James Jan 9 '13 at 14:48

There have been reports of annual modulation of radioactive decay rates in certain elements. That is, a change in decay rates that depends (apparently) on the position of the Earth around the sun. Here is a fairly recent example (disclaimer: I can't get behind the paywall at the moment). The effect is very small and at the moment there is no consensus on the cause. It is probably a systematic error in the measurements themselves. A more exotic (and unlikely) possibility is new physics.

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Well if it varies with the square of the distance to the sun it's probably something new. – Joshua Nov 7 '15 at 5:06

The following may have little practical use (at least so far), but it seems very interesting to me that, strictly speaking, the exponential law (and, therefore, constant half-life) is incompatible with quantum mechanics (this is an old result by Khalfin). It is very difficult to observe the deviations from the exponential law though. Some details and a reference to Khalfin's work can be found in Nature vol. 335, p. 298 (22 September 1988).

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Is this the same work refernced in Long time deviations from exponential decay in radioactivity? – dmckee Jan 9 '13 at 11:04
Yes. There is also a somewhat earlier work - L. A. Khalfin (1957, Doklady Akad. Nauk USSR, 115, 277) - the original paper in Russian (L.A.Khalfin, Sov.phys.Doklady 2, 340 (1957) - the English translation). – akhmeteli Jan 9 '13 at 11:59