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if a sample of radioactive material of 355g and a half-life of 3.75years. The remaining sample is 22.1875g how many half-lives have the material gone through and how old is the material?

DarkCalculis  Feb 16, 2018
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 #1
avatar+86649 
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Don't know about the big brain part....but.....we have this exponential decay form :

 

22.1875   =  355 (1/2)^(t / 3.75)       we want to find "t"

 

Divide both sides by 355

 

22.1875 / 355  =  (1/2)^(t/3.75)       take the log of both sides

 

log  ( 22.1875 / 355)  =  log (1/2)^(t / 3.75)      and we can write

 

log  ( 22.1875 / 355)  =   (t / 3.75) * log (1/2)   divide both sides by log (1/2)

 

log  ( 22.1875 / 355) / log (1/2)  =  t / 3.75      multiply both sides by 3.75

 

3.75 log  ( 22.1875 / 355) / log (1/2)  =  t  =   15  years old

 

Note that since a half-life lasts 3.75 years....it has gone through

 

15  / 3.75  =   4 half-lives

 

That worked out kinda' nice and neat  .....!!!

 

 

cool cool cool

CPhill  Feb 16, 2018
 #2
avatar+179 
+1

nice job you did good

DarkCalculis  Feb 16, 2018

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