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Difference between half life and time constant

Posted: 09 Nov 2015 ?? ?Print Version ?Bookmark and Share

Keywords:half life? decay? exponential? scaling?

We usually come across the expression "half life". That term is typically voiced regarding the duration of something nasty like radiation emanating from nuclear waste. It may be instructive to look at the applicable equation for half life in terms of a decaying exponential.

Suppose we have a decay process that has a half-life which we will call "T half". There will be some value of time constant for that decay process which we will call "Tau". With some admittedly arbitrary but convenient scaling, we may draw the following:

We now see the universally applicable value of the ratio of time constant divided by half life.

Since half life is the time required for a decay process to go from 100% to 50% while the time constant is the time required for a decay process to go further, from 100% to ( 1 / e ) or 36.7879...%, the fact that the time constant is greater than the half life comes as no surprise.

In short: Tau = T half / ln(2)

Just to mention, this was not an academic exercise. I once had to know this ratio in a medical imaging project using the radioactive element Technetium which is Periodic Table element number 43 and which is radioactive with a half-life of only thirty minutes.

I think I should have been wearing a lead apron.

About the author
John Dunn contributed this article.

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