Plasmon mode of a sphere the frequency of the uniform Plasmon mode of a sphere is determined by the depolarization field E = – 4πP/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 is w²₀ = 4πne²/3m. Because all electrons participate in the oscillation, such an excitation is called a collective excitation or collective mode of the electron gas.