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E raised to a power with units

  1. Oct 16, 2008 #1
    When e is raised to a power with units of mass what is the units of the resulting solution?
     
  2. jcsd
  3. Oct 16, 2008 #2

    Hurkyl

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    e^{mass}. But more likely, there's a constant missing from your formula.
     
  4. Oct 16, 2008 #3
    It can never be done that way. e, or any other constant, can only be raised to a dimensionless quantity. So, if you find a mass term in the exponent, there must also be one or more terms together having a dimension of M-1, and vice versa.
     
  5. Oct 16, 2008 #4

    Hootenanny

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    In dimensional analysis, the argument of an exponential must be dimensionless. In other words the argument of an exponential cannot have any units associated with it.

    Edit: I see that I have been beaten to it.
     
  6. Oct 16, 2008 #5
    I have simplified the example because the actual formula has e raised to multiple units. I thought if I could understand how a single unit is handled then I could figure out all of the units would be handled in the actual formula.

    The unit mass is associated with a numerical value so e^mass can be computed. I just don’t understand what the units would be after the calculation.
     
  7. Oct 16, 2008 #6

    Hurkyl

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    What, praty tell, is the unit on the exponent (in its entirety)?
     
  8. Oct 16, 2008 #7
    I have been working in kg, Js, and meter, seconds. I think I can change kg into eV and then into Js and perhaps I can arrive at a unitless exponent.

    Thanks for the guidance.
    RON
     
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