SOLUTION: Radium-226 is a radioactive element with a half-life of 1600 years. How much of a 1000 g sample of the element will be present after 6400 years? How long will it take for the 1

Question 191308: Radium-226 is a radioactive element with a half-life of 1600 years.
How much of a 1000 g sample of the element will be present after 6400 years?
How long will it take for the 1000 gram sample to decay to 1 gram?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Radium-226 is a radioactive element with a half-life of 1600 years.
How much of a 1000 g sample of the element will be present after 6400 years?
:
The half-life decay formula: A = Ao(2^(-t/h))
where:
Ao = initial amt
A = resulting amt after t years
h = half-life of substance
t = time in years
:
A = 1000(2^(-6400/1600))
A = 1000(2^-4)
A = 1000 * .0625
A = 62.5 grams after 6400 yrs
:
:
How long will it take for the 1000 gram sample to decay to 1 gram?
1 = 1000(2^(-t/1600))
Divide both sides by 1000 and we can write this:
2^(-t/1600) =
2^(-t/1600) = .001
log(2^(-t/1600)) = log(.001)
*log(2) = log(.001)
*.30103 = -3
Multiply both sides by 1600, results
-.30103t = -4800
t =
t = 15,945.25 yrs for 1000 g to decay to 1 g
;
:
Check by using this in the following equation with a calc
A = 1000(2^(-15945.25/1600))
A = 1.000; confirms our solution
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