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Math Help - Decay Word Problem

  1. #1
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    Decay Word Problem

    Alcheny is the ancient study of turning substances into gold using chemical or sometimes magical means. When platinum 197 undergoes a nuclear process known as beta decay, it becomes gold 197, which is a stable isotope. The half life of platinum 197 is 20 h.

    a) how long would it take to turn 90 percent of a 1 kg sample of platinum 197 into gold?

    b) do you think this is a viable "get rich quick" scheme? why or why not?

    my work:

    for part a) I used the equation
    0.90=(1/2)^t/20
    and then solved for t
    but I cant get the right answer in the back of the book

    for part b) if i used the answer in the back, which is 66.4 h, then would b) be yes it is a viable trick because it only takes 2.5 days to get the gold? correct me if i am wrong and state why please
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  2. #2
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    Quote Originally Posted by skeske1234 View Post
    Alcheny is the ancient study of turning substances into gold using chemical or sometimes magical means. When platinum 197 undergoes a nuclear process known as beta decay, it becomes gold 197, which is a stable isotope. The half life of platinum 197 is 20 h.

    a) how long would it take to turn 90 percent of a 1 kg sample of platinum 197 into gold?

    b) do you think this is a viable "get rich quick" scheme? why or why not?

    my work:

    for part a) I used the equation
    0.10=(1/2)^t/20
    and then solved for t
    but I cant get the right answer in the back of the book

    for part b) if i used the answer in the back, which is 66.4 h, then would b) be yes it is a viable trick because it only takes 2.5 days to get the gold? correct me if i am wrong and state why please
    Your equation describes the amount of platinum. So if you have 0.9 kg Au there are only 0.1 kg Pt left.

    to b) Of course you get gold, but platinum is much more expensive then gold and this special isotope of Pt is rather seldom.
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