Quantum Particle in a box problem HELP

[krugertown]

Quantum! Particle in a box problem! HELP!

An electron in a rigid box absorbs light. The longest wavelength in the absorbstion spectrum is 600nm. How long is the box?


\lambda = c/f
E=hf
E= n²*((h²)/(8mL²))

so i figured out E from the wavelength to frequency formula and the E=hf. then i just Solved for L. i used n=1 and i keep getting the wrong answer. Should n be a different value?

 

[cepheid]

The longest wavelength of light consists of the lowest energy photons. The lowest energy photon corresponds to the *smallest* change in the electron's energy as a result of it making a transition from a lower level to a higher level. CHANGE is the operative word here. When the electron absorbs a photon, it gains energy and goes from one of the lower energy states of the particle in a box to one of the higher energy such states. Therefore, rather than looking at only one of the particle in a box energies (i.e. only one value of n), you really need to be comparing two different energies, taking the difference between them. What is the smallest such difference? What transition corresponds to the smallest energy change, and therefore would have to have been caused by the lowest energy photon?