The saturation current form 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 × 10^4 A/m^2-K^2 for pure tungsten and 3.0 × 10^4 A/m^2-K^2 for thoriated tungsten. The work function of pure tungsten is 4.5 eV and that of thoriated tungsten is 2.6 eV.

Sol. i = AST2 e^-∅/KT i base 1 = i i base 2 = 100 mA A base 1 = 60 * 10^4 A base 2 = 3 * 10^4 S base 1 = S S base 2 = S T base 1 = 2000 T base 2 = 2000 ∅ base 1 = 4.5 eV ∅ base 2 = 2.6 eV K = 1.38 * 10^–23 J/k i = (60 * 10^4) (S) * (2000)^2 e^-4.5*1.6*10^-19 /1.38*10^-23 *2000 100 = (3 * 10^4) (S) * (2000)^2 e^-2.6*1.6*10^-19 /1.38*10^-23 *2000 Dividing the equation i/100 = e^[-4.5*1.6*10/1.38*2 (-2.6*1.6*10/1.38*20)] ⇒ i/100 = 20 * e^-11.014 ⇒ i/100 = 20 * 0.000016 ⇒ i = 20 * 0.0016 = 0.0329 mA = 33 μA