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Deriving half thickness equation from exponential decay law?? (Medical Physics) watch

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    How do I derive the half thickness equation from the exponential decay law??
    i.e.
    Derive x1/2 = ln2/µ
    From I=I0e^-µx

    (the '1/2' and '0' are subscript)

    Thank you!!
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    It's the thickness at which I = 0.5 I0

    So, 0.5I0 = I0 e^-µx

    Rearrange gives 0.5 = e^-µx

    Then take ln of both sides, you'll need to rearrange again and remember that ln 0.5 = -ln2
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    I=I0e-µx

    divide through by I0

    I/I0=e-µx


    and we're interested in the point x=x1/2 at which I=I0/2
    1/0.5 = e-µx
    2=e-µx

    take logs of both sides
    ln (2) = -µx
    divide through by -µ

    ln (2) /-µ=x
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    (Original post by phys981)
    It's the thickness at which I = 0.5 I0

    So, 0.5I0 = I0 e^-µx

    Rearrange gives 0.5 = e^-µx

    Then take ln of both sides, you'll need to rearrange again and remember that ln 0.5 = -ln2
    (Original post by Joinedup)
    I=I0e-µx

    divide through by I0

    I/I0=e-µx


    and we're interested in the point x=x1/2 at which I=I0/2
    1/0.5 = e-µx
    2=e-µx

    take logs of both sides
    ln (2) = -µx
    divide through by -µ

    ln (2) /-µ=x
    Thank you so much!!!
 
 
 
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