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Half life Question

Discussion in 'MCAT Study Question Q&A' started by TheRealAngeleno, Aug 11, 2011.

  1. TheRealAngeleno

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    Hey guys can someone go through the thought process in solving this question? I have it down to C & D but I don't know where to go from here. Thanks!

    What is the half-life of a material that obeys first-order decay kinetics if 40% of its original quantity remains after one hour?

    A. 30 min
    B. 46 min
    C. 50 min
    D. 64 min
     
  2. docntrainin

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    You need to know that because it follows first order kinetics, the half-life is constant. If only forty percent remains after one hour, then you know that the half life is less than one hour (100 --> 50 should take less time than going from 100 -->40, which takes one hour). This narrows down your answers to A,B, or C. A is too much of a difference, so the answer choice should be either B or C. Someone else want to try?
     
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    #2 docntrainin, Aug 11, 2011
    Last edited: Aug 11, 2011
  3. docntrainin

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    Alright, wow! This question was bugging me because I wanted to leave you with an answer. So I did some digging and found this equation:

    Time of half life = time (ln 2) / log (initial concentration / final concentration)

    Time of half life = 60 min (ln 2) / log (100 / 40 ) = approx. 45 min

    Your answer is B. I would have guessed B just because 50 min, C seemed "too perfect":smuggrin:
     
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  4. indianjatt

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    Exactly, but if this was on the mcat.... how would u approximate the lns....
     
  5. geeyouknit

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    First order mean's it's constant. That means in X min, amount decreases by half.
    It can't be A, because if it was 30 min, 1 hour would be two half lives so it would be at 25%.
    If it's C, then at the 50 min mark, there's 50 % left. In another 10 min, 1/5 of amount would have decreased ( if its constant ), so you'd be left with 80% (4/5) of the amount that's left at the 50 min mark (50% left).
    80% of 50% is 48%.

    That means you'd have 48% of original amount left. So it has to be B.
    EDIT: 80% of 50% is 40%. My bad. It's C
    Hope that helps. I know the second paragraph can get confusing.
     
    #5 geeyouknit, Aug 11, 2011
    Last edited: Aug 16, 2011
  6. Kent Money

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    Umm, isn't 80% of 50% equal 40%? Not 48%

    I think that would make C the correct answer...
     
  7. geeyouknit

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    Yea, sorry, I don't know what I was multiplying. I seem to be making a lot of those silly mistakes.
     
  8. Swagster

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    I did it backwards.

    If 30 min, then there would be 25% after one hour.
    If 46 min, then there would be 50% after 46 min, 25% after 1 hour 32 min, so about 40% after one hour.
    If 50 min, then there would be 50% after 50 min, 25% after 1 hour 40 min, so about 45% after one hour.
    If 64 min, then there would be over 50% after one hour.

    This is a TBR question, right? I remember not liking their solution as much as mine.
     
  9. neurodoc

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    Here's the general equation for exponential decay half-life (from the definition):

    N(t)=N(0)(1/2)^t/t1/2, where N(0)=initial quantity at t=0, N(t)=quantity remaining at time t, and t1/2=the "half life."

    So, N(0)=1, t=1 hour, and N(t)=0.4 and 0.4=1x(1/2)^1/t1/2. Taking ln of both sides and simplifying yields: t1/2=ln0.5/ln0.4=0.7565hours, or 45.3882 minutes, which means 46 minutes is the closest answer.

    Of course you could guesstimate this answer without using a calculator, as previously described.:sleep:
     
  10. Class1P

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    if there is 40% left after 60 minutes wouldn't the half life be just under an hour since 60% is gone in an hour.? I'd say 50min
     
  11. MedPR

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    It's 46 minutes.

    In a half life of 46 minutes you would have 40 left at 57.5 minutes.

    In a half life of 50 minutes you would have 40 left at 62.5 minutes.

    Since only 60 minutes has passed, your half life must be less than 50 minutes long.
     
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    #11 MedPR, Mar 20, 2012
    Last edited: Mar 20, 2012
  12. MrNeuro

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    how'd you do that?
     
  13. MedPR

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    At the first half-life you have 50% of the original. In this case you only have 40%.

    So if you setup a ratio: 50/40 = 1.25, you can use that ratio to find out how much time would pass for X amount to be remaining for any half-life you want.

    This method really only works since there are only 4 possible answers (actually 2 since you can easily rule out 30min and 60min). It's a guess and check type of thing.

    So anyway, if the half-life is 46 minutes, 46*1.25 = 57.5 Same for if the half-life is 50minutes. 50*1.25 = 62.5 or whatever I said earlier.
     
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  14. MrNeuro

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    huhhh?? isn't the margin of error for both the same

    and maybe im just tired but can you explain the ration again?
     
  15. MedPR

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    Maybe I made up something that doesn't work. I'm not really sure.

    Anyway, I did the math the long way (with the logs and all that crap) and with a calculator and it came out to be something like 45.7.
     
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  16. MrNeuro

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    yeah same i just don't have ln memorized.....:scared:
     

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