Question 253889
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Beryllium-11 decomposes into boron-11 with a half life of 13.8 seconds. 
How long will it take 240 g of beryllium-11 to decompose into 7.5 g of berlyium-11?
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This problem is very special and very specific.



For the complete solution,  there is  NO  NEED  to write many-store complicated exponential functions.


There is a special method and a special approach/reasoning,  and this problem 
is  SPECIALLY  CREATED  for you to learn this special solution method from me.


Notice that  the ratio    {{{240/7.5}}}    is    32.



        It means that  5  (five) half-lives happened in this decay process

        from 240 gram of Beryllium-11 to 7.5 grams of Beryllium-11,  because    {{{2^5}}} = 32.



5  half-lives is  5  times  13.8  seconds,   or   5 * 13.8 = 69 seconds.



<U>ANSWER</U>.  &nbsp;&nbsp;It will take &nbsp;69 seconds for 240 grams of &nbsp;&nbsp;Beryllium-11 &nbsp;to decompose into &nbsp;7.5 grams of Beryllium-11.
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Solved and explained in a way how it &nbsp;SHOULD &nbsp;be done 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;and how it is &nbsp;EXPECTED &nbsp;to be done.


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