Calculating the width of the box for a particle in a box

[tarletontexan]

Homework Statement

A ruby laser emits light of wavelength 694.3 nm. If this light is due to the transition from n=2 to n=1 state of the electron in a box, what is the width of the box?

Homework Equations

K=2pi/Lambda
kL=npi

The Attempt at a Solution

Thinkin about the problem, i have calculated K as shown in my formula to be 9049669 but when i use this k to find L then i end up with 694.3 again. I don't know if this is the answer or if this is a really big mistake?

 

[fzero]

The K and k in those equations are not the same. $$K = 2\pi/\lambda$$ is the wavenumber of the emitted photon. $$k = n\pi/L$$ are the wavenumbers of the electron wavefunctions. You need to compute the difference in electron energy levels and equate that to the energy of the photon.