SOLUTION: If 525 mg of a radioactive element decays to 400 mg in 48 hours, what is its half-life?

Question 332189: If 525 mg of a radioactive element decays to 400 mg in 48 hours, what is its half-life?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
If 525 mg of a radioactive element decays to 400 mg in 48 hours,
what is its half-life?
:
The half-life formula: Ao*2^(-t/h) = A
Where
A = amt after t (400)
Ao = initial amt (525)
t = time (48 hrs)
h = half-life of substance
:
525*2^(-48/h) = 400
Divide both sides by 525
2^(-48/h) =
2^(-48/h) = .762
Use nat logs
ln(2^(-48/h)) = ln(.762)
log equiv of exponents
*ln(2) = ln(.762)
=
using a calc
= -.392
-48 = -.392h
h =
h = +122.45 hr is the half-life of the substance
:
:
Check this in the half-life formula, using a calc
Ao*2^(-t/h)
enter 525*2^(-48/122.45) results: 400.1 ~ 400; confirms our solution
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