Infinite Square Well Electron Jumps from n=4 to ground state

[Mrbilly]

Homework Statement

An electron is trapped in an infinite square-well potential of width 0.5 nm. If the electron is initially in the n=4 state, what are the various photon energies that can be emitted as the electron jumps to the ground state?

Homework Equations

ΔE=13.6(1/n_f²-1/n_i²)
E_n=hbar²n²∏²/(2mL²)

The Attempt at a Solution

Im not quite sure if this is a trick or not, but I thought that I did not need the energy equation for the 1-D infinite well, E_n, but just needed to use the ΔE equation and do n=4->n=1. Or do I also need to find the energy at n=4 and n=1 and show those as well?

 

[nasu]

This (4->1) is one possible transition but not the only one. The electron does not have to go "straight" from 4 to 1.