What is the length of an infinite potential well for an electron?

[Lotto]

Homework Statement

If we produce microscopic spheres (nanoparticles) of cadmium selenidewith a size of 2,34nm, they will glow bright green when irradiated by UV light with a wavelength of 536nm. When enlarged to a size of 2,52nm, the wavelength of the emitted light shifts to the yellow region with a wavelength of 570nm. What would the size of spheres need to be to make them emit orange with a wavelength of 590nm?

Relevant Equations

hc/lambda=(m^2-n^2)h^2/(8mcL^2)+E(g)

I have a nanoparticle of cadmium selenide with a diameter d. When it emits a photon with a wavelenght lambda, it happens because an electron jumps from the conduction band to the occupied band across a forbidden band. I can suppose that jump as a jump from a higher energy level (the conduction band ) to a lower energy level ( the occupied band) in the infinite potential well of a length L that is unknown. I can write three equation that are different only in lambdas and the lenghts of the well L. When I know the lenght, then I can easily calculate the size of the third nanoparticle.

But how to determine the lenghts? Couldn't it be the diameters of the nanoparticles?

 

[jbsteele]

No, the length of the potential well is not related to the size of the particle. The length of the potential well is determined by the energy difference between the conduction band and the occupied band. This energy difference is related to the wavelength of the photon emitted when an electron jumps from the conduction band to the occupied band. To determine the length of the potential well, you will need to calculate the energy difference between the bands, and then use that information to determine the length of the well.