Calculate n(T)/n(1000 K) for tungsten emitter at =T = 300 K, 2000 K and 3000 K where n(T) represents the number of thermions emitted per second by the surface at temperature T. Work function of tungsten is 4.52 eV.

Sol. i = ne or n = i/e ‘e’ is same in all cases. We know, i = AST2 e^-∅/RT ∅ = 4.52 eV, K = 1.38 * 10^–23 J/k n(1000) = As * (1000)^2 * e^-4.52*1.6*10^-19 /1.38*10^-23 *1000 ⇒ 1.7396 * 10^-17 a)T = 300 K n(T)/n(1000K) = AS*(300)^2 * e^-4.52*1.6*10^-19 /1.38*10^-23 *300/AS * 1.7396 * 10^-17 = 7.05 * 10^-55 b) T = 2000 K n(T)/n(1000K) = AS*(2000)^2 * e^-4.52*1.6*10^-19 /1.38*10^-23 *2000/AS * 1.7396 * 10^-17 = 9.59 * 10^11 c) T = 3000 K n(T)/n(1000K) = AS*(3000)^2 * e^-4.52*1.6*10^-19 /1.38*10^-23 *3000/AS * 1.7396 * 10^-17 = 1.340 * 10^16