Posted by bobjahng2 on Friday, November 19, 2010 at 4:42pm.
You have k at one T (684) and you can calculate k at another T (427) with the Arrhenius equation. Then knowing it is first order, you can use
ln(No/N) = kt.
You can use any convenient number (such as 100) for No, use half that for N (50 if you use 100), plug in k at 427 (that's the T for which you want the 1/2 life), and solve for t. That will be the half-life because you have just 1/2 the number of atoms you started with.
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