Protactinium-234 has a half life of 1.17 minutes. How long does it take for a 10 mg sample to decay to 2 mg?

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Answer 1 · 2015-12-06T22:09:16

Solve $(1/2)^(t/1.17)=2/10$ by taking logs to find time $2$ minutes $43$ seconds.

We need to solve $(1/2)^(t/1.17)=2/10=1/5$

Taking logs of both sides:

$(t/1.17) log(1/2) = log(1/5)$

So:

$t/1.17 = (log(1/5))/(log(1/2)) = (-log(5))/(-log(2))$

So $t = 1.17 * (log(5))/(log(2)) ~~ 1.17 * 0.69897/0.30103 ~~ 2.71666$ minutes

or about $2$ minutes $43$ seconds.