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Finding Mass of Isotope After Radioactive Decay by Half-Life

  1. Feb 6, 2013 #1
    1. The problem statement, all variables and given/known data

    A radioactive sample contains 2.25g of an isotope with a half-life of 3.8 days.
    How much of the isotope in grams will remain after 11.0 days?

    2. Relevant equations



    3. The attempt at a solution

    Hi! I've just started college this semester. I'm taking Introductory Chemistry. Right now we are doing nuclear chemistry. This problem is confusing, though, because I'm not sure if I can just divide the half-life like a normal number.. My professor doesn't teach. Literally.

    I tried doing this problem this way:

    It starts off with 2.25g.
    After 3.8 days (one half-life) it's 1.125g.
    After 7.6 days (two half lives) it's 0.5625g.
    But in another half-life, 11.4 days would have passed. More than 11. In 11.4 days it would be 0.28125g.

    Is this correct? How would I calculate this? My book doesn't tell me.. Is there a specific way? It only tells me that it's "beyond the scope of this book". Please help!
     
    Last edited: Feb 6, 2013
  2. jcsd
  3. Feb 6, 2013 #2

    tiny-tim

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    welcome to pf!

    hi rakeru! welcome to pf! :smile:
    in other words, after 3.8n days it's 2.25 times 1/2n

    so after n days it's 2.25 times 1/2n/3.8

    so you need to find 211/3.8 :wink:
     
  4. Feb 7, 2013 #3
    Hi!!

    So I was looking up similar questions previously and it turns out that one person said the same thing as you.

    I tried it first with others just in case and it worked. :D

    I did: 2.25g × 1/211/3.8

    And I got 0.302537977g.

    The question had also told me to give the answer in three significant figures so: 0.303g, right?

    Uhm, I hope it works! I'm going to submit my answer now.. :) Thank you so much!
     
  5. Feb 7, 2013 #4

    tiny-tim

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    hi rakeru! :smile:
    yup, looks fine! :smile:
     
  6. Feb 7, 2013 #5
    Yup! I got it right :) Thank you.
     
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