Determine the ratio n(T)/n(1000 K ) for a tungsten emitter at temperatures T = 300 K , 2000 K , and 3000 K . Here, n(T) denotes the number of thermions emitted per second by the surface at temperature T . The work function of tungsten is 4.52 eV .

Step-by-step solution

According to the Richardson-Dushman equation, the number of thermions emitted per second by a surface at temperature T is given by: n(T) T^2 e^ - W k_B T The ratio of the number of thermions emitted at temperature T to that at 1000 K is: n(T) n(1000) = ( T 1000 )^2 e^ - W k_B ( 1 T - 1 1000 ) Given the work function W = 4.52 eV and the Boltzmann constant k_B 8.62 10⁻⁵ eV/K , we have: W k_B = 4.52 8.62 10⁻⁵ 52436 K For T = 300 K : n(300) n(1000) = ( 300 1000 )^2 e^ -52436 ( 1 300 - 1 1000 ) n(300) n(1000) = 0.09 e^