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Math Help - number of sample remain

  1. #1
    rcs
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    number of sample remain

    The half-life of an element is 10 years. How much of a 20g sample will remain after 50 years?

    Choices: 0.625g , 1.25g , 2.5g, 5g

    my answer is 2.5g.

    considering: 20g is a half life an element. since it is 50 yrs... then there are five 10 years in a 50 years. so in every 10 years there corresponds half life
    5 time half life = 5 x 1/2 = 2.5 ...

    please help me understand the problem. and hope somebody will correct or check my work. because im not sure of my answer
    thanks
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: number of sample remain

    Sorry, this incorrect. Every 10 years the amount remaining is cut in half. At year 0 you have 20 grams, and ten years later at year 10 you have half of that, or 10 grams. At year 20 you have half of what you had at year 10, or 5 grams. Continue on in this manner, cutting the amount in half for each 10 year period, and what do you get at year 50?

    To make an equation for this you can raise 1/2 to the number of half life periods to determine the fraction of material remaining. Since the half life is 10 years, and you want to know how much is remaining after 50 years, that's 5 half-life periods. So (1/2)^5 = 1/32, and hence 1/32nd of the original amount is remaining after 50 years. What's 1/32nd of 20 grams?
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  3. #3
    rcs
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    Re: number of sample remain

    Quote Originally Posted by ebaines View Post
    Sorry, this incorrect. Every 10 years the amount remaining is cut in half. At year 0 you have 20 grams, and ten years later at year 10 you have half of that, or 10 grams. At year 20 you have half of what you had at year 10, or 5 grams. Continue on in this manner, cutting the amount in half for each 10 year period, and what do you get at year 50?

    To make an equation for this you can raise 1/2 to the number of half life periods to determine the fraction of material remaining. Since the half life is 10 years, and you want to know how much is remaining after 50 years, that's 5 half-life periods. So (1/2)^5 = 1/32, and hence 1/32nd of the original amount is remaining after 50 years. What's 1/32nd of 20 grams?

    Therefore ... I got it is 0.625 in 50 years... Is this correct?
    Last edited by rcs; January 21st 2013 at 01:10 PM.
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  4. #4
    MHF Contributor ebaines's Avatar
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    Re: number of sample remain

    No, try again. 20/32 = ??
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