Question

An electron in a one-dimensional box of width L = .75 nm decays from the n = 3 state to the ground state by emitting two photons. What are their wavelengths?

Answer 1

Answer: 232 nm

Explanation: As it is well known the energy for the one dimentional box is given by:

$E=\frac{h^2}{8mx L^2} *n^2$

where h is the Planck constant, m the electron mass and L the width of the box. n is the energy level

For n=3 we a energy equal :9.62 * 10^-19 J= 6.01 eV

For n=1 the energy is: 1.069 *10^-19 J=0.66 eV

The energy difference Is 5.35 eV so by using this relationship

λ=1240/Energy = 232 nm