{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

EE372_Solutions4

EE372_Solutions4 - EE372 Assignment 4 Solutions 1...

This preview shows pages 1–2. Sign up to view the full content.

EE372 Assignment 4 Solutions 1. Nanoparticles A hot research topic at the moment are nanoparticles, very small grains of various semi- conductors. An electron that is inside a nanoparticle is equivalent to an electron inside a three dimensional square well. The potential outside the well is not infinite but instead is roughly the work function of the material. However, the first few infinite 3-D square well energies are a good first approximation for the quantized energies of the electron inside a nanoparticle. a) Use the formula for the electron’s energy in the infinite 3-D square well to derive a formula for the energy difference between the first excited state and the ground state. b) The nanoparticles can be induced to give off light by exciting the electron. The formula derived in part (a) gives the energy of the photon emitted when the electron goes from the first excited state to the ground state. Calculate the dimension a required so that the photons emitted are red (1.8 eV), green (2.4 eV), or blue (3.5 eV). Such nanoparticles might someday be used in colour displays. Answer: a) The energy of an electron in an infinite 3D square well is E n 1 n 2 n 3 = ¯ h 2 π 2 2 ma 2 n 2 1 + n 2 2 + n 2 3 The ground state energy is E 111 and the first excited state energy is E 211 . So the energy difference is Δ E = h 2 π 2 2 ma 2

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 3

EE372_Solutions4 - EE372 Assignment 4 Solutions 1...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online