How Are Proton Energies Quantized in a Nano-Scale Box?

[Kavorka]

Homework Statement

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.

Homework Equations

K = p²/2m
λ = h/p

The Attempt at a Solution

The first part seems simple, I could graphically derive that L must equal nλ/L if there are nodes at each end. What I want to make sure about is part b. Would I have to use K = p²/2m, use the mass of a proton, and plug in p = h/λ getting K = h²/2λ²m?

 

[TSny]

... L must equal nλ/L...

Just a little typo here.

Your work looks good.