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Half-Life? @CPhill

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The half-life of radium is 1620 years.  If a laboratory has 12 grams of radium, how long will it take before it has 8 grams of radium left?

Dec 22, 2017

#1
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OK....we can solve this :

8  =  12* (1/2)t/1620        where t is the time (in years) we are looking for

Divide both sides by  12

8/12  = (1/2)t/1620

2/3  =  (1/2)t/1620        take the log of both sides

log (2/3)  =  log(1/2)t/1620          and we can write

log(2/3)  =  (t / 1620) * log (1/2)     divide both sides by log(1/2)

log (2/3) / log (1/2)  =  t  / 1620      multiply both sides by 1620

1620 * log (2/3) / log (1/2)  =  t   ≈  947.6  ≈   948  years   Dec 22, 2017
edited by CPhill  Dec 22, 2017
#2
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Hmm, this seems to make much more sense to me. I thought it should be x/1620, but this other website said x+1620 which wasn't making any sense to me...

Thanks so much for your time!

Julius  Dec 22, 2017
#3
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Thanks, Julius....look at the logic...if  t  =  1620, we have

A(1/2)1620/1620  =

A (1/2)1  =

(1/2)A.........which is exactly what we would expect....1/2 of the amount, A, is what remains after 1620 years   Dec 22, 2017
#4
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Yes, that makes sense!

Julius  Dec 22, 2017