SOLUTION: The half-life of Radium 266 is 1590 years how many years does it take for 100mg of Radium 266 to decay to a mass of 70mg?

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Question 1199238: The half-life of Radium 266 is 1590 years how many years does it take for 100mg of Radium 266 to decay to a mass of 70mg?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The half-life of Radium 266 is 1590 years
how many years does it take for 100mg of Radium 266 to decay to a mass of 70mg?
:
The radioactive decay formula:
A = Ao*2^(-t/h), where:
A = resulting amt after t years
Ao = initial amt
t = time of decay
h = half-life of substance
:
In this problem we can write it
100*2^(-t/1590) = 70
2^(-t/1590) = 70%2F100
2^(-t/1590) = .7
using nat logs%28-t%2F1590%29%2Aln%282%29+=+ln%28.7%29
ln(2^(-7/1590)) = ln(.7)
log equiv of exponents
%28-t%2F1590%29%2Aln%282%29+=+ln%28.7%29
%28-t%2F1590%29 = ln%28.7%29%2Fln%282%29
calc
-t%2F1590 = -.51457
t = -1590 * -.51457
t = 818 years