Unlike a free particle, a bound or confined particle can have difinite engergy and momentum (e.g. an lectron cofined to the hydrogen atom). Suppose a particle of mass m moves in a one-dimensional box of length L. The potential engergy of the particle in the box is zero, so all its (non-relativisitc) engergy is kinetic, E = p^2/2m. The de Broglie wavelength lambda of the partcle is quantized by the standing wave condition: n(lamda/2) = L, where n is any positive interger.
a) Show the allowed (i.e quantized) energies are given by E subscript n = n^2 E subscript 1, where E sub 1 = h^2/ (8mL^2)
b) Evaluate E sub n for electrons in a box of size L = .1nm and draw energy level diagram for n = 1 to n = 5.
c) What is the wavelength of the photon emitted when the electron makes a transisiton from n = 2 to n = 1?