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Homework Help: De Broglie problem

  1. Mar 11, 2008 #1
    1. The problem statement, all variables and given/known data
    What is the length of a one-dimensional box in which an electron in the n=1 state has the same energy as a photon with a wavelength of 500 nm

    2. Relevant equations

    E=h^2/8mL^2 and E=hc/lambda

    making it
    L=sqrt( (h*lambda)/(8cm) )

    3. The attempt at a solution

    I plugged in for those numbers and did not come out with the correct number. any suggestions?
  2. jcsd
  3. Mar 14, 2008 #2
    Are you sure that 8 should not be a 4?
  4. Mar 14, 2008 #3


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    The eightfold way is right here. 1/8=(L/2)^/2.
    I think your first h should be hbar.
  5. Mar 21, 2008 #4
    The energy if the first state of an indefinite one-dimensional box is:
    Where m is the mass of the particle and L is the length of the box.
    The photon has the energy given by
    Where [tex]\lambda[/tex] is the wave length.
    And therefore the length L is [tex]L=\sqrt{\frac{\pi\hbar\lambda{c}}{4m}}[/tex]
    Last edited: Mar 21, 2008
  6. Mar 26, 2008 #5

    Shooting Star

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    Homework Helper

    Which is wrong. It should be [tex]\sqrt{\frac{\pi\hbar\lambda}{4mc}[/tex], which is identical to what the OP psingh had written correctly. Replacing [itex]h[/itex] by [itex]2\pi\hbar[/itex] won't do any good.

    Perhaps the OP made some arithmetical mistake...
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