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

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