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1-D standing de Broglie wave

  1. Apr 6, 2015 #1
    1. The problem statement, all variables and given/known data
    A free proton moves back and forth between rigid walls separated by a distance L = 0.01 nm.
    a) If the proton is represented by a one-dimensional standing de Broglie wave with a node at each wall, show that the allowed values of the de Broglie wavelength are given by λ = 2L/n, where n is a positive integer.
    b) Derive a general expression for the allowed kinetic energy of the proton and compute the values for n = 1 and 2.

    2. Relevant equations
    K = p2/2m
    λ = h/p
    3. The attempt at a solution

    The first part seems simple, I could graphically derive that L must equal nλ/L if there are nodes at each end. What I want to make sure about is part b. Would I have to use K = p2/2m, use the mass of a proton, and plug in p = h/λ getting K = h2/2λ2m?
     
  2. jcsd
  3. Apr 6, 2015 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Just a little typo here.

    Your work looks good.
     
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