The Energy of the Trapped Electron in a One-Dimensional Space

[quantumech]

Homework Statement

Calculate the length of the space L in nm if an electron is trapped in one dimensional space of length L, and shows an absorption at 523nm due to transition from ψ2 to ψ3.

Homework Equations

Energy expression for particle in box:

Ev= (n²h²)/(8mL²) n=1, 2, 3...

The Attempt at a Solution

I don't understand what I am suppose to do with 523 nm. Once I know that I can continue. Please help with this. Thanks.

 

[buffordboy23]

First, the general formula for the energy of your eigenstates is incorrect. There should be a pi-squared term in the numerator.

Electrons can only be located in specific orbits, right? So the given 523 nm value is the wavelength of the absorbed photon. What is the energy of the photon?

$$E_{photon}=\frac{hc}{\lambda}$$

EDIT: I changed h-bar to h.