The particle in a box model is often used to make rough estimates of energy level spacings. For a metal wire 10 cm long, treat a conduction electron as a particle confined to a one-dimensional box of length 10 cm. 

(a) Sketch the wave function ψ as a function of position for the electron in this box for the ground state and each of the first three excited states. 

(b) Estimate the spacing between energy levels of the conduction electrons by finding the energy spacing between the ground state and the first excited state.