# Electron in a one-dimensional box emitting a photon

1. Dec 3, 2012

### Ezequiel

1. The problem statement, all variables and given/known data

An electron in a one-dimensional box emits a photon when it moves from energy level E4 to E2. Find the wavelength of the emitted photon.

Length of the box L = 0.300 nm

2. Relevant equations

En = n2E1
E1 = $\frac{h^2}{8mL^2}$

λ = $\frac{hc}{E_i - E_f}$

3. The attempt at a solution

E1 = 4.18 eV
E2 = 22 E1 = 16.7 eV
E4 = 42 E1 = 66.9 eV

So, λ = $\frac{hc}{66.9 - 16.7}$ = 24.7 nm

Is this right?

2. Dec 3, 2012

### TSny

Looks good to me. Nice work.

3. Dec 4, 2012

Thanks!!