# Quantum-Dot Fluorescence - Hypothetical Semiconductor

## Homework Statement

Consider a hypothetical semiconductor with band gap 1eV, Relative electron mass is 0.05 and relative hole mass is 0.5.
In a cube-shaped quantum dot of this material with side length L = 3nm, what is the energy associated with a transition from (2 1 1) electron state to the (1 1 1) hole state?

## Homework Equations

confinement energy of a particle trapped in a 3D box:

$E_n = \left(\frac{h^2}{8mL^2}\right)\left(n_x^2 + n_y^2 + n_z^2\right)$

## The Attempt at a Solution

so, an electron has been excited into the a higher energy state (2 1 1) from (1 1 1) producing an exciton, the hole remains in state (1 1 1).

the band gap energy $E_g = 1eV$

the recombination energy is $E_r$

i have a formula which says that:

$E_r = E_g + E_e + E_h$

where Ee and Eh are confinement energies of the electron and hole respectively.

do i just sum up Eg Eh and Ee to get the recombination energy?
I would have thought i'd need to work out the difference between the (2 1 1) and (1 1 1) state of the electron.