Ask Me Help Desk - Beryllium-11 decomposes into boron-11 with a half-life of 13.8 secs. How long will it

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Beryllium-11 decomposes into boron-11 with a half-life of 13.8 secs. How long will it

Beryllium-11 decomposes into boron-11 with a half-life of 13.8 secs. How long will it take 240g of beryllium-11 to decompose into 7.5g of beryllium-11?

Quote:

Originally Posted by aries27

Beryllium-11 decomposes into boron-11 with a half-life of 13.8 secs. How long will it take 240g of beryllium-11 to decompose into 7.5g of beryllium-11?

Half-life is given by $T=\frac{-1}{k}ln(2)$ .

Since we are told that the time is 13.8 seconds, then

$k=-.050228$

So, we have the formula $A=A_{0}e^{-.050228t}$

$A_{0}=240, \;\ A=7.5$

Sub in $A_{0} \;\ and \;\ A$ and solve for t.

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