At 2000 K , the saturation current from a thoriated-tungsten cathode is 100 mA . Determine the saturation current for a pure-tungsten cathode that has the same surface area and operates at the same temperature. In the Richardson–Dushman equation, the constant A 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 is 4.5 eV for pure tungsten, while it is 2.6 eV fo

Step-by-step solution

According to the Richardson-Dushman equation, the saturation current is given by: I = S A T^2 e^ - / (kT) For pure tungsten, the saturation current is: I_p = S A_p T^2 e^ - _p / (kT) For thoriated tungsten, the saturation current is: I_t = S A_t T^2 e^ - _t / (kT) Taking the ratio of the two currents: I_p I_t = A_p A_t e^ -( _p - _t) / (kT) Substituting the given values: A_p A_t = 60 10^4 3.0 10^4 = 20 _p - _t = 4.5 eV - 2.6 eV = 1.9 eV kT = 1.38 10⁻²³ 2000 1.6 10⁻¹⁹ eV = 0.1725 eV Calculating the exponent term: _p