A free proton moves back and forth between rigid walls separated by a distance L = 0.01 nm. 

(a) If the proton is represented by a one-dimensional standing de Broglie wave with a node at each wall, show that the allowed values of the de Broglie wavelength are given by λ = 2L/n, where n is a positive integer. 

(b) Derive a general expression for the allowed kinetic energy of the proton and compute the values for n = 1 and 2.