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?

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.