Thermionic Work Function
The work function is also important in the theory of thermionic emission. Here the electron gains its energy from heat rather than photons. According to the Richardson-Dushman equation the emitted electron current density, J (A/m2), is related to the absolute temperature T by the equation:
where W is the work function of the metal, k is the Boltzmann constant and the proportionality constant A, known as Richardson's constant, is given by
where m and -e are the mass and charge of an electron, and h is the Planck constant.
Thermionic emission—electrons escaping from the heated negatively-charged filament (hot cathode)—is important in the operation of vacuum tubes. Tungsten, the common choice for vacuum tube filaments, has a work function of approximately 4.5 eV. Various oxide coatings can substantially reduce this.
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