Question

Plasmon mode of a sphere:

1. The frequency of the uniform plasmon mode of a sphere is determined by the depolarized field E=-4pP/3 of a sphere, where the polarization P=-ner, with r as the average displacement of the electrons of concentration n. Show from F=ma that the resonance frequency of the electron gas in sqrt(4pne²/3m).
2. What is the cutoff energy (eV) of EM wave on Na metal, below this energy the light is reflective.
3. What the energy (eV) of a volume plasmon and surface plasmon of Na metal when electrons or photons excite electron Fermi gas of Na metal. The energy of volume plasmon = sqrt(2) of the surface plasmon (see the exercise of Kittel’s textbook by applied the boundary conditions of EM wave at surface )

Answer 1