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Logarithmic Half-Life prob.

  • Thread starter SETHOSCOTT
  • Start date
  • #1
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Homework Statement


The half-life of a radioactive substance is 194 days. How many days will it take for 80% of the substance to decay?


Homework Equations





The Attempt at a Solution


I had to make 1/2n=1/5. I did this by finding log25=n. After this, I needed to only multiply by the number of days it took the half-life to occur, which was 194, and got 451 (approx.) as a reasonable answer.
 
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Answers and Replies

  • #2
diazona
Homework Helper
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There is absolutely enough information there. I could tell you the answer right now (but I won't, that's what you get to do ;-)

I'd advise you to go back and double-check that equation, though.
 
  • #3
HallsofIvy
Science Advisor
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In one "half life", T, (1/2)C= CekT. The Cs cancel, and you solve that for k. After you know that you can solve 0.8C= Cekt for t.

But you don't need to use "e". If T is the half life then [itex]C(t)= C(0)(1/2)^{t/T}[/itex] because every time "T" days, you multiply by1/2. Solve [itex].8C= C(1/2)^{t/194}[/itex].
 
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  • #4
diazona
Homework Helper
2,175
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The Attempt at a Solution


I had to make 1/2n=1/5. I did this by finding log25=n. After this, I needed to only multiply by the number of days it took the half-life to occur, which was 194, and got 451 (approx.) as a reasonable answer.
Looks good...
 
  • #5
52
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=) omg! Thanks!
 

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