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The 1/e Factor

  1. Aug 6, 2010 #1
    The quantity 1/e is one that I've seen quite a bit in physics. Especially when describing 'lifetimes' of various things (ie radiative lifetimes). I'm curious about why this value is used. I've heard explanations about how it's a probabilistic thing or that it's just a sort of 'standard candle' for measuring these quantities.

    To put my question in another form: The value of 1/e is close to that of 1/3. So why don't we just use 1/3 instead. What is it that makes 1/e more useful or preferred.

    Thanks!
     
  2. jcsd
  3. Aug 6, 2010 #2
    Nothing special about e, as using another basis simply corresponds to a change of scale of the exponent:

    [tex]e^x=b^y\qquad\Leftrightarrow\qquad y=x\log_be[/tex]

    I think the practical reason we use e is that

    [tex]\frac{de^x}{dx}=e^x[/tex]

    instead of

    [tex]\frac{db^x}{dx}=e^x\log b[/tex]
     
  4. Aug 7, 2010 #3

    Vanadium 50

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    Petr is right - sometimes we use different exponents (decibals, half-lives) but usually the math just works out so much easier with e that people use that one.
     
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