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Error propagation for value not directly measurable

  1. Jun 29, 2012 #1
    1. The problem statement, all variables and given/known data
    This should be very simple:
    Given the following (boundary frequency for photoelectric effect):

    [itex]\nu = \frac{\phi}{h}[/itex]

    what would be the error on [itex]\nu[/itex]?

    2. Relevant equations
    3. The attempt at a solution

    [itex]\varphi[/itex] and h are both determined through linear regression (y = mx + c). Where

    h =em and [itex]\varphi = -ec[/itex]. The errors on m and c are supplied courtesy of computer software.

    My understanding is that the product/division rule for error propagation can be used:

    [itex]\delta \nu = \nu\sqrt{(\frac{\delta \varphi}{\varphi})^{2}+(\frac{\delta h}{h})^{2}}[/itex]

    my instructor disagrees
     
    Last edited: Jun 29, 2012
  2. jcsd
  3. Jul 1, 2012 #2

    vela

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    Sounds right to me. What's your instructor's idea for how to propagate the error?
     
  4. Jul 2, 2012 #3
    well, i spoke to her now and she says that the systematic error on the voltage (digital multimeter) should be included.

    [itex]eU = h\nu + \varphi[/itex] (1)

    where [itex]\varphi[/itex]is the work function.
    The boundary frequency is given as [itex]\nu_{b} = \frac{\varphi}{h}[/itex] (2)

    Of course we can write the [itex]\nu_{b}[/itex] in terms of voltage using (1), but we determined [itex]\varphi[/itex] and [itex]h[/itex] using linear regression which also supplied the standard error on those values. I'm not really sure how to determine the errors on [itex]\nu_{b}[/itex] now. Should I ignore the error on [itex]\varphi[/itex], combine (1) and (2) and just use the error for the voltage provided by the multimeter manufacturer?

    [itex]\delta \nu_{b} = \nu_{b} \sqrt{(\frac{\delta h}{h})^2 + (\frac{\delta U}{U})^2}[/itex]
     
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