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16 October, 11:51

The potential-energy function u (x) is zero in the interval 0≤x≤l and has the constant value u0 everywhere outside this interval. an electron is moving past this square well. the electron has energy e=6u0. part a what is the ratio of the de broglie wavelength of the electron in the region x>l to the wavelength for 0

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  1. 16 October, 11:58
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    Look first for the relation between deBroglie wavelength (λ) and kinetic energy (K):

    K = ½mv²

    v = √ (2K/m)

    λ = h / (mv)

    = h / (m√ (2K/m))

    = h/√ (2Km)

    So λ is proportional to 1/√K.

    in the potential well the potential energy is zero, so completely the electron's energy is in the shape of kinetic energy:

    K = 6U₀

    Outer the potential well the potential energy is U₀, so

    K = 5U₀

    (because kinetic and potential energies add up to 6U₀)

    Therefore, the ratio of the de Broglie wavelength of the electron in the region x>L (outside the well) to the wavelength for 0
    1/√ (5U₀) : 1/√ (6U₀)

    = √6 : √5
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