The saturation current from a thoriated-tungsten cathode at 2000 K is 100 mA. What will be the saturation current for a pure-tungsten cathode of the same surface area operating at the same temperature? The constant A in the Richardson-Dushman equation is 60 × 104 A m-2K-2 pure tungsten and 3.0 × 104 A m-2K-2 for thoriated tungsten. The work function of pure tungsten is 4.5 eV and that of thoriated tungsten is 2.6 eV.
According to Richardson-Dushman Equation thermionic current i is
where, n is the thermions emitted, S is the surface area, T is the absolute temperature, k is the Boltzmann constant, A is the constant depend on nature of metal and ϕ is the work function.
Given,
Ittungsten=100 mA
T=2000 K
Attungsten=3 × 104 A m-2 K-2
Aptungsten=60× 104 A m-2 K-2
Φttungsten =2.6 eV
Φptungsten =4.5 eV
Now,
