SOLUTION: The half-life of radium is approximately 1690 years. If a laboratory has 50 mg of radium, how long will it take for the substance to decay to 40 mg, to the nearest 10 years?

Question 808944: The half-life of radium is approximately 1690 years. If a laboratory has 50 mg of radium, how long will it take for the substance to decay to 40 mg, to the nearest 10 years?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The half-life of radium is approximately 1690 years.
If a laboratory has 50 mg of radium, how long will it take for the substance to decay to 40 mg, to the nearest 10 years?
:
The radioactive decay formula: A = Ao*2^(-t/h), where
A = Amt remaining after t time
Ao = initial amt (t=0)
t = time of decay
h = half-life of substance
:
50*2^(-t/1690) = 40
Divide both sides by 50
2^(-t/1690) =
2^(-t/1690) = .8
using natural logs
ln[2^(-t/1690)] = ln(.8)
ln(2) = ln(.8)
=
using the calc
= -.3219
t = -1690 * -.3219
t = 544 ~ 540 yrs

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