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Question: What is the exact relationship between half-life and relaxation time?

I just wanted to nail down the difference/similarity between these two concepts. I did a web search, and even found a direct reference, but it was an exercise in an on-line textbook asking exactly what I am asking, and I copied and pasted that exercise question as my question above.

Now, we all know that half-life is the time it takes for the substance to decay to half its size, and relaxation time is the time it takes for the substance to decay to 1/e of its size, so why have both concepts? My guess is that it is similar to the difference between degree measure and radian measure: Half-life is useful when dealing with specific practicalities, whereas relaxation time is more convenient when discussing theory.

Regards,

Mike Jones

22.May.2011 (Beijing time)

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Excellent analogy! –  André Nicolas May 22 '11 at 5:03
3  
More, I think, like the difference between natural and common logarithms. –  Gerry Myerson May 22 '11 at 6:06
    
@Gerry Myerson: What you're offering is an obsolete analogy. With modern technology, common logarithms are no longer needed for computational purposes. They still have a purpose though, which, ironically, is theoretical, namely, to serve as a gentle introduction for students to logarithms. For example, log10(100) = 2, and log10(1000) = 3, and log10(100000) = 5, so we have an easy illustration of the fact that log(xy) = log(x) + log(y). Degree measure and radian measure, on the other hand, will presumably be with us forever:-) –  Mike Jones May 22 '11 at 14:52

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