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Math Help - half-life word question

  1. #1
    Junior Member
    Joined
    Feb 2009
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    half-life word question

    When platinum-197 undergoes a nuclear decay it becomes gold-197. The half life of platinum-197 is 20 h

    a) how long would it take to turn 90% of a 1kg of platinum-197 into gold.

    My answer:

    0.90=1(0.5)^(t/20)
    0.90/1=0.5^(t/20) log of both sides
    log 0.90=t/20 log0.5
    (log 0.90/log0.5)*20=t
    3.04 hours=t

    answer in my book is 66.4 hours! what am i doing wrong! Thanks in advance!
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  2. #2
    MHF Contributor
    Grandad's Avatar
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    South Coast of England
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    Hello jepal
    Quote Originally Posted by jepal View Post
    When platinum-197 undergoes a nuclear decay it becomes gold-197. The half life of platinum-197 is 20 h

    a) how long would it take to turn 90% of a 1kg of platinum-197 into gold.

    My answer:

    0.90=1(0.5)^(t/20)
    0.90/1=0.5^(t/20) log of both sides
    log 0.90=t/20 log0.5
    (log 0.90/log0.5)*20=t
    3.04 hours=t

    answer in my book is 66.4 hours! what am i doing wrong! Thanks in advance!
    You've just turned 10% into gold!

    Try 0.10 = 1\times 0.5^{t/20} instead!

    Grandad
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