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<x<L (inside the well) is: 
1/√(5U₀) : 1/√(6U₀) 
= √6 : √5

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