How Thick Should Ligands Be for Electron Tunneling in Quantum Wires?

[rey242]

Hello,

I'm having trouble imagining a specific portion of a homework problem.
Heres the problem:

"Consider a ligand stabilized gold nanoparticle. The gold nanoparticle itself can be
considered as “box” and the ligands as the “walls”. If the de Broglie wavelength
of the gold nanoparticle corresponds to the diameter of the nanoparticle and is 1.4
nm. If such ligand functionalized gold nanoparticles are lined up to form a
quantum wire, for what values of the ligand thickness do you anticipate that
electrons will be able to tunnel through the ligand barrier and conduct?"

I'm having trouble imagining the gold nanoparticle's placement. Is it a box within a box of ligands? Also, I'm having trouble with the electrons, would they be the same wavelength of the gold nano particle?

Any help would be great, thank you!

 

[NateD]

In this problem, the gold nanoparticle can be considered as a box with walls made of ligands. The diameter of the gold nanoparticle is 1.4 nm which corresponds to the de Broglie wavelength of the electron. When these ligand stabilized gold nanoparticles are lined up to form a quantum wire, electrons can tunnel through the ligand barrier and conduct when the thickness of the ligand barrier is less than or equal to the de Broglie wavelength of the electron. This means that the thickness of the ligand must be less than or equal to 1.4 nm in order for electrons to be able to tunnel through it and conduct.