1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    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]
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook