+0  
 
0
80
4
avatar+514 

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?

Julius  Dec 22, 2017
Sort: 

4+0 Answers

 #1
avatar+81022 
+2

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

 

 

 

cool cool cool

CPhill  Dec 22, 2017
edited by CPhill  Dec 22, 2017
 #2
avatar+514 
+2

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
avatar+81022 
+1

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

 

cool cool cool

CPhill  Dec 22, 2017
 #4
avatar+514 
+1

Yes, that makes sense! 

Julius  Dec 22, 2017

13 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details