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
