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DeBroglie wavelength in infinite potential well

  1. Aug 8, 2012 #1
    nvm i figured it out. it was not in reference to n=4. equation used would be wavelength = 2L/n

    1. The problem statement, all variables and given/known data
    An electron is in an infinite potential well of width L. Which is not an allowed deBroglie wavelength for the electron to have when n=4?
    wavelength(k) = 3L, 2L, L/2, or L/3


    2. Relevant equations
    k=h/p
    would states in an infinite square well be useful too?


    3. The attempt at a solution
    The answer I was given is 3L which is throwing me off because I thought it would be L/3. there at 2 wavelengths at n=4. 3L= 6 wavelengths which is still integer. I was thinking L/3 because 2/3 is not a valid wavelength. Was the answer i was given wrong or am I doing something wrong?
     
    Last edited: Aug 8, 2012
  2. jcsd
  3. Aug 9, 2012 #2
    Question is asking that "Which is not an allowed deBroglie wavelength for the electron to have when n=4?"

    As you know that de-broglie wavelength is an integral multiple of h/mv.

    Here you use formula ,
    λ = 2L/n

    If electron is excited , then there are infinite number of wavelengths.

    If it is de-excited , then there will be only 6 combination of wavelengths ,
    4-3,4-2, 4-1, 3-2, 3-1, 2-1.

    Now the answer you were given was correct.

    Hint : Let h/mv = R

    Then ,

    λ = R2L/n

    2L/n must always be an Integer. In which option it will not be an integer ?
     
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