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Thread: Just needed help on this one

  1. #1
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    Just needed help on this one

    I kinda got stuck on this one here.

    It says:
    Einsteinium (254Es) has a half-life of 270 days. How much of a 5-gram sample would remain after 2160 days?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by dc52789 View Post
    I kinda got stuck on this one here.

    It says:
    Einsteinium (254Es) has a half-life of 270 days. How much of a 5-gram sample would remain after 2160 days?
    recall that $\displaystyle r = \frac {\ln 2}{\text{half life}}$

    use that $\displaystyle r$ in the exponential decay formula: $\displaystyle N(t) = N_0e^{-rt}$

    where $\displaystyle N(t)$ is the amount remaining after time $\displaystyle t$, $\displaystyle N_0$ is the initial amount, $\displaystyle r$ is the rate of decay

    you want to find $\displaystyle N(2160)$
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  3. #3
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    Quote Originally Posted by Jhevon View Post
    recall that $\displaystyle r = \frac {\ln 2}{\text{half life}}$

    use that $\displaystyle r$ in the exponential decay formula: $\displaystyle N(t) = N_0e^{-rt}$

    where $\displaystyle N(t)$ is the amount remaining after time $\displaystyle t$, $\displaystyle N_0$ is the initial amount, $\displaystyle r$ is the rate of decay

    you want to find $\displaystyle N(2160)$
    For r, would it be best if it's nearest to the hundredth or the thousandth?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by dc52789 View Post
    For r, would it be best if it's nearest to the hundredth or the thousandth?
    well, that depends on a lot of things. what would your professor want? how many decimal places does your text usually use? etc. follow those guidelines. personally, i use as many decimal places as possible, and then round off my final answer if required
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    Quote Originally Posted by Jhevon View Post
    well, that depends on a lot of things. what would your professor want? how many decimal places does your text usually use? etc. follow those guidelines. personally, i use as many decimal places as possible, and then round off my final answer if required
    He asked to give the answer to the nearest thousandths of a gram.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by dc52789 View Post
    He asked to give the answer to the nearest thousandths of a gram.
    ok, so work with the nearest ten-thousandths and then round it off to the nearest thousandths when finished
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  7. #7
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    Quote Originally Posted by Jhevon View Post
    ok, so work with the nearest ten-thousandths and then round it off to the nearest thousandths when finished
    o k...I have 0.414 as my answer. Is it correct?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by dc52789 View Post
    o k...I have 0.414 as my answer. Is it correct?
    that's not what i got
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  9. #9
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    Quote Originally Posted by dc52789 View Post
    I kinda got stuck on this one here.

    It says:
    Einsteinium (254Es) has a half-life of 270 days. How much of a 5-gram sample would remain after 2160 days?
    You don't need logarithms for this. Saying its half-life is 270 days means you multiply by 1/2 every 270 days. 2160/270= 8 so 2160 days is 8 270 day perionds: 5 gms will be multiplied by 1/2 8 times: 5(1/2)^8= 5/256 grams.
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  10. #10
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    Quote Originally Posted by HallsofIvy View Post
    You don't need logarithms for this. Saying its half-life is 270 days means you multiply by 1/2 every 270 days. 2160/270= 8 so 2160 days is 8 270 day perionds: 5 gms will be multiplied by 1/2 8 times: 5(1/2)^8= 5/256 grams.
    wow...that helps a lot. Thanks.
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