Question 88634: If 40 mg of a radioactive substance decays to 5mg in 12 minutes, find the half-life, in minutes, of the substance.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! If 40 mg of a radioactive substance decays to 5mg in 12 minutes, find the half-life, in minutes, of the substance.
:
The half life formula: A = Ao* 2^(-t/h)
Where:
A = Amt at time t
Ao - initial amt
h = half-life
:
Substitute for A, Ao, and t to find h:
40*2^(-12/h) = 5
:
2^(-12/h) = 5/40; divide both sides by 40
:
ln(2^(-12/h)) = ln(5/40)
:
(-12/h)* ln(2) = ln(5/40); log equivalent of exponents
:
(-12/h)*.693147 = -2.07944
-12/h = -2.07944/.693147
-12/h = -3
-3h = -12
h = -12/-3
h = 4 minutes is the half life
:
:
Check on a calc: 40*2^-12/4) = 5
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